WorldWideScience

Sample records for nonplanar fracture geometries

  1. Effect of electron temperature on small-amplitude electron acoustic solitary waves in non-planar geometry

    Science.gov (United States)

    Bansal, Sona; Aggarwal, Munish; Gill, Tarsem Singh

    2018-04-01

    Effects of electron temperature on the propagation of electron acoustic solitary waves in plasma with stationary ions, cold and superthermal hot electrons is investigated in non-planar geometry employing reductive perturbation method. Modified Korteweg-de Vries equation is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdV equation reveal that the phase velocity of the electron acoustic waves increases as one goes from planar to non planar geometry. It is shown that the electron temperature ratio changes the width and amplitude of the solitary waves and when electron temperature is not taken into account,our results completely agree with the results of Javidan & Pakzad (2012). It is found that at small values of τ , solitary wave structures behave differently in cylindrical ( {m} = 1), spherical ( {m} = 2) and planar geometry ( {m} = 0) but looks similar at large values of τ . These results may be useful to understand the solitary wave characteristics in laboratory and space environments where the plasma have multiple temperature electrons.

  2. Effect of Random Natural Fractures on Hydraulic Fracture Propagation Geometry in Fractured Carbonate Rocks

    Science.gov (United States)

    Liu, Zhiyuan; Wang, Shijie; Zhao, Haiyang; Wang, Lei; Li, Wei; Geng, Yudi; Tao, Shan; Zhang, Guangqing; Chen, Mian

    2018-02-01

    Natural fractures have a significant influence on the propagation geometry of hydraulic fractures in fractured reservoirs. True triaxial volumetric fracturing experiments, in which random natural fractures are created by placing cement blocks of different dimensions in a cuboid mold and filling the mold with additional cement to create the final test specimen, were used to study the factors that influence the hydraulic fracture propagation geometry. These factors include the presence of natural fractures around the wellbore, the dimension and volumetric density of random natural fractures and the horizontal differential stress. The results show that volumetric fractures preferentially formed when natural fractures occurred around the wellbore, the natural fractures are medium to long and have a volumetric density of 6-9%, and the stress difference is less than 11 MPa. The volumetric fracture geometries are mainly major multi-branch fractures with fracture networks or major multi-branch fractures (2-4 fractures). The angles between the major fractures and the maximum horizontal in situ stress are 30°-45°, and fracture networks are located at the intersections of major multi-branch fractures. Short natural fractures rarely led to the formation of fracture networks. Thus, the interaction between hydraulic fractures and short natural fractures has little engineering significance. The conclusions are important for field applications and for gaining a deeper understanding of the formation process of volumetric fractures.

  3. Determination of Fracture System Geometry from Well Testing

    International Nuclear Information System (INIS)

    Doe, T.W.

    1994-01-01

    In this paper, the research and development for the description of the hydraulic geometry of fracture networks are discussed. The studies on fracture networks have developed on the premise that the structural geological information on fracture geometries could be used to develop the realistic models of flow. It has been widely recognized that a relatively small portion of natural fracture networks controls a major portion of groundwater flow. The key to efficient network modeling is to identify that portion of networks. It is the main purpose of this paper to discuss the methods for characterizing the hydraulic geometry of fracture flow systems. The methods described in this paper cover three approaches for defining the hydraulic geometry of fracture networks, that is, the determination of conductive fracture frequency in boreholes, the use of transient pressure and flow responses in single holes, and the use of cross hole test to assess connectivity. The information which can be obtained by each test is shown. Flow logging, well test distribution and conductive fracture frequency are discussed. The transient analysis of single hole well test and the cross hole analysis of well test for fracture network geometry are reported. The data taken by various methods together can provide network characterization. (K.I.)

  4. Geometry, mechanics and transmissivity of rock fractures

    International Nuclear Information System (INIS)

    Lanaro, F.

    2001-04-01

    This thesis work investigates methods and tools for characterising, testing and modelling the behaviour of rock fractures. Using a 3D-laser-scanning technique, the topography of the surfaces and their position with respect to one another are measured. From the fracture topography, fracture roughness, angularity and aperture are quantified; the major features used for characterisation. The standard deviations for the asperity heights, surface slopes and aperture are determined. These statistical parameters usually increase/decrease according to power laws of the sampling size, and sometimes reach a sill beyond which they become constant. Also the number of contact spots with a certain area decreases according to a power-law function of the area. These power-law relations reveal the self affine fractal nature of roughness and aperture. Roughness is 'persistent' while aperture varies between 'persistent' and 'anti-persistent' probably depending on the degree of match of the fracture walls. The fractal models for roughness, aperture and contact area are used to develop a constitutive model, based on contact mechanics, for describing the fracture normal and shear deformability. The experimental testing results of normal deformability are simulated well by the model whereas fracture shear deformability is not as well modelled. The model predicts well fracture dilation but is too stiff compared to rock samples. A mathematical description of the aperture pattern during shearing is also formulated. The mean value and covariance of the aperture in shearing is calculated and verifies reported observations. The aperture map of samples is inserted in a numerical program for flow calculation. The 'integral transform method' is used for solving the Reynolds' equation; it transforms the fracture transmissivity pattern into a frequency-based function. This closely resembles the power laws that describe fractals. This function can be described directly from the fractal properties of

  5. Proximal Femoral Geometry and the Risk of Fractures: Literature Review

    Directory of Open Access Journals (Sweden)

    N.V. Grygorieva

    2016-02-01

    Full Text Available This article presents the literature review of the impact of the upper third of the femur geometry (hip axis length, femoral neck angle, inter-trochanteric length, horizontal offset, thickness of the cortical bone, etc. on the risk of fractures. The article demonstrates the capabilities of techniques for measurement of hip geometry, namely conventional X-ray of pelvic bones, dual-energy X-ray absorptiometry, computed tomography. Possible correlation is shown between some genetic markers and features of the geometry of the upper third of the femur. Also, there are presented the results of own researches of age and sex characteristics of proximal hip geometry parameters in patients without fractures, as well as in patients of older age groups with internal and extraarticular femoral fractures.

  6. On the geometry of fracture and frustration

    NARCIS (Netherlands)

    Koning, Vinzenz

    2014-01-01

    Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical,

  7. Interpretation of fracture system geometry using well test data

    International Nuclear Information System (INIS)

    Doe, T.W.; Geier, J.E.

    1990-11-01

    This report presents three methods of determining fracture geometry and interconnection from well test information. Method 1 uses evidence for boundary effects in the well test to determine the distance to and type of fracture boundary. Method 2 uses the spatial dimension of the well test to infer the geometry of the fracture-conduit system. Method 3 obtains information of the spacing and transmissivity distribution of individual conductive fractures from fixed-interval-length (FIL) well tests. The three methods are applied to data from the Site Characterization and Validation (SCV) at the 360 m level of the Stripa Mine. The focus of the technology development is the constant-pressure welltest, although the general approaches apply to constant-rate well test, and to a much lesser extent slug or pulse test, which are relatively insensitive to boundaries and spatial dimension. Application of the techniques to the N and W holes in the SCV area shows that there is little evidence for boundary effects in the well test results. There is, on the other hand, considerable variation in the spatial dimension of the well test data ranging from sub-linear (fractures which decrease in conductivity with distance from the hole) to spherical, for three-dimensional fracture systems. The absence of boundary effects suggest that the rock mass in the SCV area contains a well connected fracture system. Major uncertainties in the analysis of well test data limit the use of single borehole measurements. Without assuming the value of specific storage, one can reliably determine only the spatial dimension, and, for two dimensional flow only, the transmissivity. Among the uncertainties are the effective well radius, the degree to which the fracture conduits fill the n-dimensional space in which flow occurs, and the cross-sectional area of the conduits at the wellbore. This report presents a complete development of constant-pressure well test methods for cylindrical flow and flow of arbitrary

  8. Comparison of surgical techniques of 111 medial malleolar fractures classified by fracture geometry.

    Science.gov (United States)

    Ebraheim, Nabil A; Ludwig, Todd; Weston, John T; Carroll, Trevor; Liu, Jiayong

    2014-05-01

    Evaluation of operative techniques used for medial malleolar fractures by classifying fracture geometry has not been well documented. One hundred eleven patients with medial malleolar fractures (transverse n = 63, oblique n = 29, vertical n = 7, comminuted n = 12) were included in this study. Seventy-two patients had complicating comorbidities. All patients were treated with buttress plate, lag screw, tension band, or K-wire fixation. Treatment outcomes were evaluated on the basis of radiological outcome (union, malunion, delayed union, or nonunion), need for operative revision, presence of postoperative complications, and AOFAS Ankle-Hindfoot score. For transverse fractures, tension band fixation showed the highest rate of union (79%), highest average AOFAS score (86), lowest revision rate (5%), and lowest complication rate (16%). For oblique fractures, lag screws showed the highest rate of union (71%), highest average AOFAS score (80), lowest revision rate (19%), and lowest complication rate (33%) of the commonly used fixation techniques. For vertical fractures, buttress plating was used in every case but 1, achieving union (whether normal or delayed) in all cases with an average AOFAS score of 84, no revisions, and a 17% complication rate. Comminuted fractures had relatively poor outcomes regardless of fixation method. The results of this study suggest that both tension bands and lag screws result in similar rates of union for transverse fractures of the medial malleolus, but that tension band constructs are associated with less need for revision surgery and fewer complications. In addition, our data demonstrate that oblique fractures were most effectively treated with lag screws and that vertical fractures attained superior outcomes with buttress plating. Level III, retrospective comparative series.

  9. Fracture network modelling: an integrated approach for realisation of complex fracture network geometries

    International Nuclear Information System (INIS)

    Srivastava, R.M.

    2007-01-01

    In its efforts to improve geological support of the safety case, Ontario Power Generation's Deep Geologic Repository Technology Programme (DGRTP) has developed a procedure (Srivastava, 2002) for creating realistic 3-D fracture network models (FNMs) that honor information typically available at the time of preliminary site characterisation: By accommodating all of the these various pieces of 'hard' and 'soft' data, these FNMs provide a single, coherent and consistent model that can serve the needs of many preliminary site characterisation studies. The detailed, complex and realistic models of 3-D fracture geometry produced by this method can serve as the basis for developing rock property models to be used in flow and transport studies. They can also be used for exploring the suitability of a proposed site by providing quantitative assessments of the probability that a proposed repository with a specified geometry will be intersected by fractures. When integrated with state-of-the-art scientific visualisation, these models can also help in the planning of additional data gathering activities by identifying critical fractures that merit further detailed investigation. Finally, these FNMs can serve as one of the central elements of the presentation and explanation of the Descriptive Conceptual Geosphere Model (DCM) to other interested parties, including non-technical audiences. In addition to being ideally suited to preliminary site characterisation, the approach also readily incorporates field data that may become available during subsequent site investigations, including ground reconnaissance, borehole programmes and other subsurface studies. A single approach can therefore serve the needs of the site characterisation from its inception through several years of data collection and more detailed site-specific investigations, accommodating new data as they become available and updating the FNMs accordingly. The FNMs from this method are probabilistic in the sense that

  10. Influence of bone mineral density and hip geometry on the different types of hip fracture.

    Science.gov (United States)

    Li, Yizhong; Lin, Jinkuang; Cai, Siqing; Yan, Lisheng; Pan, Yuancheng; Yao, Xuedong; Zhuang, Huafeng; Wang, Peiwen; Zeng, Yanjun

    2016-01-01

    The aim of this study was to assess the influence of bone mineral density and hip geometry on the fragility fracture of femoral neck and trochanteric region. There were 95 menopausal females of age ≥ 50 years with fragility fracture of hip, including 55 cases of femoral neck fracture and 40 cases of trochanteric fracture. Another 63 non-fractured females with normal bone mineral density (BMD) were chosen as control. BMD, hip axis length, neck-shaft angle and structural parameters including cross surface area, cortical thickness and buckling ratio were detected and compared. Compared with control group, the patients with femoral neck fracture or trochanteric fractures had significantly lower BMD of femoral neck, as well as lower cross surface area and cortical thickness and higher buckling ratio in femoral neck and trochanteric region. There were no significant differences of BMD and structural parameters in the femoral neck fracture group and intertrochanteric fracture group. Hip axis length and neck-shaft angle were not significantly different among three groups. The significant changes of BMD and proximal femur geometry were present in the fragility fracture of femoral neck and trochanteric region. The different types of hip fractures cannot be explained by these changes.

  11. Influence of bone mineral density and hip geometry on the different types of hip fracture

    Directory of Open Access Journals (Sweden)

    Yizhong Li

    2016-01-01

    Full Text Available The aim of this study was to assess the influence of bone mineral density and hip geometry on the fragility fracture of femoral neck and trochanteric region. There were 95 menopausal females of age ≥ 50 years with fragility fracture of hip, including 55 cases of femoral neck fracture and 40 cases of trochanteric fracture. Another 63 non-fractured females with normal bone mineral density (BMD were chosen as control. BMD, hip axis length, neck-shaft angle and structural parameters including cross surface area, cortical thickness and buckling ratio were detected and compared. Compared with control group, the patients with femoral neck fracture or trochanteric fractures had significantly lower BMD of femoral neck, as well as lower cross surface area and cortical thickness and higher buckling ratio in femoral neck and trochanteric region. There were no significant differences of BMD and structural parameters in the femoral neck fracture group and intertrochanteric fracture group. Hip axis length and neck-shaft angle were not significantly different among three groups. The significant changes of BMD and proximal femur geometry were present in the fragility fracture of femoral neck and trochanteric region. The different types of hip fractures cannot be explained by these changes.

  12. Analytical, numerical and experimental investigations of transverse fracture propagation from horizontal wells

    Energy Technology Data Exchange (ETDEWEB)

    Rahman, M.M.; Hossain, M.M.; Crosby, D.G.; Rahman, M.K.; Rahman, S.S. [School of Petroleum Engineering, The University of New South Wales, 2052 Sydney (Australia)

    2002-08-01

    This paper presents results of a comprehensive study involving analytical, numerical and experimental investigations into transverse fracture propagation from horizontal wells. The propagation of transverse hydraulic fractures from horizontal wells is simulated and investigated in the laboratory using carefully designed experimental setups. Closed-form analytical theories for Mode I (opening) stress intensity factors for idealized fracture geometries are reviewed, and a boundary element-based model is used herein to investigate non-planar propagation of fractures. Using the mixed mode fracture propagation criterion of the model, a reasonable agreement is found with respect to fracture geometry, net fracture pressures and fracture propagation paths between the modeled fractures and the laboratory tested fractures. These results suggest that the propagation of multiple fractures requires higher net pressures than a single fracture, the underlying reason of which is theoretically justified on the basis of local stress distribution.

  13. Size and geometry of apical sesamoid fracture fragments as a determinant of prognosis in Thoroughbred racehorses.

    Science.gov (United States)

    Kamm, J L; Bramlage, L R; Schnabel, L V; Ruggles, A J; Embertson, R M; Hopper, S A

    2011-07-01

    Analysis was performed to examine a method for refining the preoperative prognosis for horses that had surgery to remove apical fractures of the proximal sesamoid bones (PSBs). To determine if: 1) there was a difference in size or configuration of apical fractures between the different anatomical locations of the PSBs, which have been shown to affect the prognosis; and 2) the size or configuration could predict the prognosis for racehorses with these fractures. The study included 110 weanlings and yearlings and 56 training racehorses that underwent surgery to remove apical PSB fractures. Radiographs of the fractures were used for measurement of the abaxial and axial proportion and the abaxial to axial ratio, and race records were used to determine average earnings per start (AEPS) and total post operative starts. Analysis of variance and regression statistics were used to compare the fragment sizes between the specific PSBs on each of the limbs and compare size and configuration of the fractures to prognosis. There was a significantly larger abaxial to axial ratio (more transverse fracture) for the forelimb medial sesamoids than for all other sesamoids in untrained racehorses (P = 0.03). There were no other significant differences in size. There was no relationship between fracture size or configuration and AEPS nor total post operative starts. Apical fractures in weanlings and yearlings tend to be more transverse in the forelimb medial PSBs than the other PSBs. Apical fracture size and geometry does not determine prognosis for apical sesamoid fractures. Horses that undergo surgery to remove larger apical fractures of the PSBs do not have a worse outcome than those horses with smaller fractures. © 2010 EVJ Ltd.

  14. Effect of sized and specimen geometry on the initiation and propagation of the ductile fracture

    International Nuclear Information System (INIS)

    Frund, J.M.; Marini, B.; Bethmont, M.

    1994-02-01

    Strength to the fracture of the pipe in PWR has to be justified with mechanical analyses. These tests are based on the strength to ductile fracture of steels which are tested in lab. The values of resistance to fracture are obtained through tensile tests on CT specimens (determination of J-R curves). The purpose of this study is to justify the sizes of the specimens which have to be used to characterize the strength to ductile fracture of steel in secondary pipes. Tests were conducted on 0,5T-CT, 1T-CT and 2T-CT specimens. Two materials with different suffer contents were studied. The test results show that the JO,2 values gotten from the different specimens are similar. But the strength to ductile fracture in 2T-CT specimens in lower than the one measured in 0,5t-CT and 1T-CT specimens. The surface of fracture of the different specimens displays splits perpendicular to the notch and parallel to the sheet surface. These splits are produced by the separation of the manganese sulfur inclusions. The effect notes on the J-R curves seems to be relevant to these splits. The reason why these splits might be responsible for a decrease of the tearing modulus are not clearly defined up to this point. The results which have been published show the importance of the geometry effects (presence or not of lateral notches...) and the loading mode on the strength to ductile fracture. We note that the curves determined from tests on CT specimens are conservative. A few preliminary studies showed that the geometry effects on resistance to fracture can be studied and explained by using local approach methods. The Rousselier modeling is useful to explain the behaviour of ferritic steels in ductile fracture. (authors). 20 refs., 7 figs., 5 tabs

  15. Vibrational modes of hydraulic fractures: Inference of fracture geometry from resonant frequencies and attenuation

    Science.gov (United States)

    Lipovsky, Bradley P.; Dunham, Eric M.

    2015-02-01

    Oscillatory seismic signals arising from resonant vibrations of hydraulic fractures are observed in many geologic systems, including volcanoes, glaciers and ice sheets, and hydrocarbon and geothermal reservoirs. To better quantify the physical dimensions of fluid-filled cracks and properties of the fluids within them, we study wave motion along a thin hydraulic fracture waveguide. We present a linearized analysis, valid at wavelengths greater than the fracture aperture, that accounts for quasi-static elastic deformation of the fracture walls, as well as fluid viscosity, inertia, and compressibility. In the long-wavelength limit, anomalously dispersed guided waves known as crack or Krauklis waves propagate with restoring force from fracture wall elasticity. At shorter wavelengths, the waves become sound waves within the fluid channel. Wave attenuation in our model is due to fluid viscosity, rather than seismic radiation from crack tips or fracture wall roughness. We characterize viscous damping at both low frequencies, where the flow is always fully developed, and at high frequencies, where the flow has a nearly constant velocity profile away from viscous boundary layers near the fracture walls. Most observable seismic signals from resonating fractures likely arise in the boundary layer crack wave limit, where fluid-solid coupling is pronounced and attenuation is minimal. We present a method to estimate the aperture and length of a resonating hydraulic fracture using both the seismically observed quality factor and characteristic frequency. Finally, we develop scaling relations between seismic moment and characteristic frequency that might be useful when interpreting the statistics of hydraulic fracture events.

  16. Femoral Geometry in Male Patients with Atraumatic Hip Fracture - Original Investigation

    Directory of Open Access Journals (Sweden)

    Gülten Tan

    2007-03-01

    Full Text Available Aims: Hip fracture is the most serious complication of osteoporosis and the most disabling type of fracture. In this study, we aimed to compare femoral geometry in hip fractured male patients aged more than 65 years old with age matched controls. Patients and Methods: 20 male patients with a history of nontraumatic hip fracture and 19 age-matched healthy controls were included in this study. Bone mineral density of neck and trochanter of hip were measured by DEXA. In addition to BMD, an experienced radiologist measured proximal femur geometric parameters potentially involved in bone strength. Results: Mean BMDs of trochanteric region were not significantly different between groups, but mean BMDs of neck region were statistically significantly lower in the hip fractured group. Neck shaft angle and femur shaft width were the geometric parameters found to be significantly higher in the hip fractured group. The correlation between femur geometric and the anthropometric measurements was present only in the kontrol group. Conclusion: We concluded that besides femur geometric measurements, correlation between these measurements might be an important factors for the fracture risk. (From the World of Osteoporosis 2007;13:15-8

  17. Geometry-coupled reactive fluid transport at the fracture scale -Application to CO 2 geologic storage

    KAUST Repository

    Kim, Seunghee

    2015-08-19

    Water acidification follows CO2 injection and leads to reactive fluid transport through pores and rock fractures, with potential implications to reservoirs and wells in CO2 geologic storage and enhanced oil recovery. Kinetic rate laws for dissolution reactions in calcite and anorthite are combined with Navier-Stokes law and advection-diffusion transport to perform geometry-coupled numerical simulations in order to study the evolution of chemical reactions, species concentration and fracture morphology. Results are summarized as a function of two dimensionless parameters: the Damköhler number Da which is the ratio between advection and reaction times, and the transverse Peclet number Pe defined as the ratio between the time for diffusion across the fracture and the time for advection along the fracture. Reactant species are readily consumed near the inlet in a carbonate reservoir when the flow velocity is low (low transverse Peclet number and Da>10-1). At high flow velocities, diffusion fails to homogenize the concentration field across the fracture (high transverse Peclet number Pe>10-1). When the reaction rate is low as in anorthite reservoirs (Da<10-1) reactant species are more readily transported towards the outlet. At a given Peclet number, a lower Damköhler number causes the flow channel to experience a more uniform aperture enlargement along the length of the fracture. When the length-to-aperture ratio is sufficiently large, say l/d>30, the system response resembles the solution for 1-D reactive fluid transport. A decreased length-to-aperture ratio slows the diffusive transport of reactant species to the mineral fracture surface, and analyses of fracture networks must take into consideration both the length and slenderness of individual fractures in addition to Pe and Da numbers.

  18. Geometry-coupled reactive fluid transport at the fracture scale -Application to CO 2 geologic storage

    KAUST Repository

    Kim, Seunghee; Santamarina, Carlos

    2015-01-01

    Water acidification follows CO2 injection and leads to reactive fluid transport through pores and rock fractures, with potential implications to reservoirs and wells in CO2 geologic storage and enhanced oil recovery. Kinetic rate laws for dissolution reactions in calcite and anorthite are combined with Navier-Stokes law and advection-diffusion transport to perform geometry-coupled numerical simulations in order to study the evolution of chemical reactions, species concentration and fracture morphology. Results are summarized as a function of two dimensionless parameters: the Damköhler number Da which is the ratio between advection and reaction times, and the transverse Peclet number Pe defined as the ratio between the time for diffusion across the fracture and the time for advection along the fracture. Reactant species are readily consumed near the inlet in a carbonate reservoir when the flow velocity is low (low transverse Peclet number and Da>10-1). At high flow velocities, diffusion fails to homogenize the concentration field across the fracture (high transverse Peclet number Pe>10-1). When the reaction rate is low as in anorthite reservoirs (Da<10-1) reactant species are more readily transported towards the outlet. At a given Peclet number, a lower Damköhler number causes the flow channel to experience a more uniform aperture enlargement along the length of the fracture. When the length-to-aperture ratio is sufficiently large, say l/d>30, the system response resembles the solution for 1-D reactive fluid transport. A decreased length-to-aperture ratio slows the diffusive transport of reactant species to the mineral fracture surface, and analyses of fracture networks must take into consideration both the length and slenderness of individual fractures in addition to Pe and Da numbers.

  19. Scattering Of Nonplanar Acoustic Waves

    Science.gov (United States)

    Gillman, Judith M.; Farassat, F.; Myers, M. K.

    1995-01-01

    Report presents theoretical study of scattering of nonplanar acoustic waves by rigid bodies. Study performed as part of effort to develop means of predicting scattering, from aircraft fuselages, of noise made by rotating blades. Basic approach was to model acoustic scattering by use of boundary integral equation to solve equation by the Galerkin method.

  20. Geometries

    CERN Document Server

    Sossinsky, A B

    2012-01-01

    The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

  1. Geometry

    Indian Academy of Sciences (India)

    . In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

  2. Studies of fracture network geometry of reservoir outcrop analogues from terrestrial lidar data: attempts to quantify spatial variations of fracture characteristics

    Science.gov (United States)

    Vsemirnova, E. A.; Jones, R. R.; McCaffrey, K. J. W.

    2012-04-01

    We describe studies analysing terrestrial lidar datasets of fracture systems from a range of reservoir analogues in clastic and carbonate lithologies that represent geological analogues of offshore hydrocarbon reservoirs for the UK continental shelf. As fracture networks (observed here from centimetre to kilometre scale) can significantly affect the permeability of a fractured reservoir, the definition of fracture network geometry at various scales has become an important goal of structural analysis. The main aim of the study has been to extend the investigation of fracture networks in order to quantify spatial variations in fracture parameters in a variety of lithologies. The datasets were pre-processed using RiSCAN PRO software, and then re-sampled and filtered to derive characteristics which are traditionally measured from outcrops, including size distributions, fracture spacing and clustering statistics. This type of analysis can significantly reduce the uncertainty associated with some field fracture network measurements. The digitised fracture networks datasets are then used to investigate various aspects of spatial heterogeneity. A series of fracture maps (joints and faults) were generated at different scales, and fracture trends were studied to test scale dependency of fracture orientations. Multiscale trend analysis was then applied to describe the trend structure of the fracture networks.

  3. Validation of favor code linear elastic fracture solutions for finite-length flaw geometries

    International Nuclear Information System (INIS)

    Dickson, T.L.; Keeney, J.A.; Bryson, J.W.

    1995-01-01

    One of the current tasks within the US Nuclear Regulatory Commission (NRC)-funded Heavy Section Steel Technology Program (HSST) at Oak Ridge National Laboratory (ORNL) is the continuing development of the FAVOR (Fracture, analysis of Vessels: Oak Ridge) computer code. FAVOR performs structural integrity analyses of embrittled nuclear reactor pressure vessels (RPVs) with stainless steel cladding, to evaluate compliance with the applicable regulatory criteria. Since the initial release of FAVOR, the HSST program has continued to enhance the capabilities of the FAVOR code. ABAQUS, a nuclear quality assurance certified (NQA-1) general multidimensional finite element code with fracture mechanics capabilities, was used to generate a database of stress-intensity-factor influence coefficients (SIFICs) for a range of axially and circumferentially oriented semielliptical inner-surface flaw geometries applicable to RPVs with an internal radius (Ri) to wall thickness (w) ratio of 10. This database of SIRCs has been incorporated into a development version of FAVOR, providing it with the capability to perform deterministic and probabilistic fracture analyses of RPVs subjected to transients, such as pressurized thermal shock (PTS), for various flaw geometries. This paper discusses the SIFIC database, comparisons with other investigators, and some of the benchmark verification problem specifications and solutions

  4. Evidence for tectonic, lithologic, and thermal controls on fracture system geometries in an andesitic high-temperature geothermal field

    Science.gov (United States)

    Massiot, Cécile; Nicol, Andrew; McNamara, David D.; Townend, John

    2017-08-01

    Analysis of fracture orientation, spacing, and thickness from acoustic borehole televiewer (BHTV) logs and cores in the andesite-hosted Rotokawa geothermal reservoir (New Zealand) highlights potential controls on the geometry of the fracture system. Cluster analysis of fracture orientations indicates four fracture sets. Probability distributions of fracture spacing and thickness measured on BHTV logs are estimated for each fracture set, using maximum likelihood estimations applied to truncated size distributions to account for sampling bias. Fracture spacing is dominantly lognormal, though two subordinate fracture sets have a power law spacing. This difference in spacing distributions may reflect the influence of the andesitic sequence stratification (lognormal) and tectonic faults (power law). Fracture thicknesses of 9-30 mm observed in BHTV logs, and 1-3 mm in cores, are interpreted to follow a power law. Fractures in thin sections (˜5 μm thick) do not fit this power law distribution, which, together with their orientation, reflect a change of controls on fracture thickness from uniform (such as thermal) controls at thin section scale to anisotropic (tectonic) at core and BHTV scales of observation. However, the ˜5% volumetric percentage of fractures within the rock at all three scales suggests a self-similar behavior in 3-D. Power law thickness distributions potentially associated with power law fluid flow rates, and increased connectivity where fracture sets intersect, may cause the large permeability variations that occur at hundred meter scales in the reservoir. The described fracture geometries can be incorporated into fracture and flow models to explore the roles of fracture connectivity, stress, and mineral precipitation/dissolution on permeability in such andesite-hosted geothermal systems.

  5. Geometry

    CERN Document Server

    Prasolov, V V

    2015-01-01

    This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

  6. Fracture Anisotropy and Toughness in the Mancos Shale: Implications for crack-growth geometry

    Science.gov (United States)

    Chandler, M. R.; Meredith, P. G.; Brantut, N.; Crawford, B. R.

    2013-12-01

    the other two orientations. This anisotropy and variability in fracture properties is seen to cause deviation of the fracture direction during experiments on Arrester and Short-Transverse oriented samples, and can be expected to influence the geometry of propagating fractures. A comparison between the anisotropic tensile strength of the material and the crack-tip stress field in a transversely isotropic material has been used to develop a crack-tip deflection criterion in terms of the elasticity theory of cracks. This criterion suggests that a small perturbation in the incident angle of a mode-I crack propagating perpendicular to the bedding is likely to lead to a substantial deflection towards bedding-parallel (Short-Transverse) propagation. Further experimental work is currently underway on anisotropic Fracture Toughness measurements at elevated pressures and temperatures, simulating conditions in Shale Gas reservoirs at depths up to around 4km.

  7. Bone geometry, strength, and muscle size in runners with a history of stress fracture.

    Science.gov (United States)

    Popp, Kristin L; Hughes, Julie M; Smock, Amanda J; Novotny, Susan A; Stovitz, Steven D; Koehler, Scott M; Petit, Moira A

    2009-12-01

    Our primary aim was to explore differences in estimates of tibial bone strength, in female runners with and without a history of stress fractures. Our secondary aim was to explore differences in bone geometry, volumetric density, and muscle size that may explain bone strength outcomes. A total of 39 competitive distance runners aged 18-35 yr, with (SFX, n = 19) or without (NSFX, n = 20) a history of stress fracture were recruited for this cross-sectional study. Peripheral quantitative computed tomography (XCT 3000; Orthometrix, White Plains, NY) was used to assess volumetric bone mineral density (vBMD, mg x mm(-3)), bone area (ToA, mm(2)), and estimated compressive bone strength (bone strength index (BSI) = ToA x total volumetric density (ToD(2))) at the distal tibia (4%). Total (ToA, mm(2)) and cortical (CoA, mm(2)) bone area, cortical vBMD, and estimated bending strength (strength-strain index (SSIp), mm(3)) were measured at the 15%, 25%, 33%, 45%, 50%, and 66% sites. Muscle cross-sectional area (MCSA) was measured at the 50% and 66% sites. Participants in the SFX group had significantly smaller (7%-8%) CoA at the 45%, 50%, and 66% sites (P stress fracture. However, the lower strength was appropriate for the smaller muscle size, suggesting that interventions to reduce stress fracture risk might be aimed at improving muscle size and strength.

  8. Laboratory studies of groundwater degassing in replicas of natural fractured rock for linear flow geometry

    International Nuclear Information System (INIS)

    Geller, J.T.

    1998-02-01

    Laboratory experiments to simulate two-phase (gas and water) flow in fractured rock evolving from groundwater degassing were conducted in transparent replicas of natural rock fractures. These experiments extend the work by Geller et al. (1995) and Jarsjo and Geller (1996) that tests the hypothesis that groundwater degassing caused observed flow reductions in the Stripa Simulated Drift Experiment (SDE). Understanding degassing effects over a range of gas contents is needed due to the uncertainty in the gas contents of the water at the SDE. The main objectives of this study were to: (1) measure the effect of groundwater degassing on liquid flow rates for lower gas contents than the values used in Geller for linear flow geometry in the same fracture replicas of Geller; (2) provide a data set to develop a predictive model of two-phase flow in fractures for conditions of groundwater degassing; and (3) improve the certainty of experimental gas contents (this effort included modifications to the experimental system used by Geller et al. and separate gas-water equilibration tests). The Stripa site is being considered for a high-level radioactive waste repository

  9. Fracture geometries consistent with tiltmeter data and pressure and tracer communication in the GLISP I-1 stimulation

    Energy Technology Data Exchange (ETDEWEB)

    Palmer, I.D.; Moschovidis, Z.A. (Amoco Production Co., Tulsa, OK (USA))

    The goal of this paper is to examine the consistency of three totally independent diagnostic observations of fracturing (tiltmeters, pressure, and tracer communication). The Gregoire Lake In-Situ Steam Pilot (GLISP) in the Athabasca tar sands, includes three producing wells surrounding an injection well. The authors modeled tiltmeter records of the fracturing treatment of the central injection well, and pressure and tracer communication from the central injection well to the producing wells, and investigated how these analyses support various fracture geometry scenarios. Several different fracture geometry scenarios have been examined. Theoretical surface tiltmeter vectors for these scenarios are compared with observed vectors. Also, theoretical time delays based on propagation of pressure transients and tracer material have been predicted for these scenarios, and compared with observed delays. The results of these comparisons are expressed in the form of a range of fracture geometries that are most consistent with measured tiltmeter data in the field, and pressure and tracer time delays in the three production wells. Interpretations within this range include complex fracture systems with one or two fracture components rising steeply from the base of the McMurray Formation into the overlying depleted zone. Dominant horizontal fracturing does not appear to occur. The three independent sets of observations (pressure transient delays, tracer delays, and tiltmeter vectors) support this hypothesis. 9 refs., 20 figs., 3 tabs.

  10. A casting and imaging technique for determining void geometry and relative permeability behavior of a single fracture specimen

    Energy Technology Data Exchange (ETDEWEB)

    Cox, B.L.; Pruess, K.; Persoff, P.

    1990-01-01

    A casting technique has been developed for making translucent replicas of the void space of natural rock fractures. Attenuation of light shined through the cast combined with digital image analysis provides a pointwise definition of fracture apertures. The technique has been applied to a fracture specimen from Dixie Valley, Nevada, and the measured void space geometry has been used to develop theoretical predictions of two-phase relative permeability. A strong anisotropy in relative permeabilities has been found, which is caused by highly anisotropic spatial correlations among fracture apertures. 16 refs., 6 figs.

  11. Rib Geometry Explains Variation in Dynamic Structural Response: Potential Implications for Frontal Impact Fracture Risk.

    Science.gov (United States)

    Murach, Michelle M; Kang, Yun-Seok; Goldman, Samuel D; Schafman, Michelle A; Schlecht, Stephen H; Moorhouse, Kevin; Bolte, John H; Agnew, Amanda M

    2017-09-01

    The human thorax is commonly injured in motor vehicle crashes, and despite advancements in occupant safety rib fractures are highly prevalent. The objective of this study was to quantify the ability of gross and cross-sectional geometry, separately and in combination, to explain variation of human rib structural properties. One hundred and twenty-two whole mid-level ribs from 76 fresh post-mortem human subjects were tested in a dynamic frontal impact scenario. Structural properties (peak force and stiffness) were successfully predicted (p rib cross-sectional geometry obtained via direct histological imaging (total area, cortical area, and section modulus) and were improved further when utilizing a combination of cross-sectional and gross geometry (robusticity, whole bone strength index). Additionally, preliminary application of a novel, adaptive thresholding technique, allowed for total area and robusticity to be measured on a subsample of standard clinical CT scans with varied success. These results can be used to understand variation in individual rib response to frontal loading as well as identify important geometric parameters, which could ultimately improve injury criteria as well as the biofidelity of anthropomorphic test devices (ATDs) and finite element (FE) models of the human thorax.

  12. Change of manufacturing technique for the W7-X nonplanar coil cases

    International Nuclear Information System (INIS)

    Gehring, M.; Schaefer, P.; Herrmann, K.D.; Scheller, H.

    2001-01-01

    The geometry of the coil cases of the nonplanar coil system for the Wendelstein 7-X (W7-X) experiment (Sapper, The superconducting magnet system for the W7-X stellarator. Proceedings 12th Topical Meeting on the Fusion Technology) was changed to a more complex shape compared to the DEMO Coil case (Kronhardt et al., 1998. Proceedings of the 20th SOFT (1998) 731-734). Therefore the manufacturing technique developed for the DEMO Coil case cannot be used for the series production of 50 coils. For the final design of the coil cases, investigations were performed to find a technique suitable for manufacturing the cases within the required geometrical tolerances and mechanical characteristics. In order to qualify the manufacturing technique a complete half case was cast and machined afterwards. The casting procedure was optimised with respect to the geometrical accuracy and the mechanical characteristics at 4.2 K. Measurements of the yield strength, the tensile strength, the elongation, and the Young's modulus were performed at room- and cryo-temperature (4 and 7 K). The influence of the heat treatment, the annealing temperature and the size of the casting on the mechanical values is shown. The requirements on the stainless steel are a yield strength of 800 MPa at 4 K and an elongation at fracture of >25%. The magnetic permeability has to be <1.01. Furthermore the welding properties of the case material were investigated. The development program showed that casting of complete case half shells is a feasible manufacturing technique for the series production of the Wendelstein 7-X nonplanar coil cases

  13. Geometry

    CERN Document Server

    Pedoe, Dan

    1988-01-01

    ""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

  14. Non-planar ABJ theory and parity

    International Nuclear Information System (INIS)

    Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos

    2009-01-01

    While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this Letter we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance. For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account.

  15. Non-planar ABJ Theory and Parity

    DEFF Research Database (Denmark)

    Caputa, Pawel; Kristjansen, Charlotte; Zoubos, Konstantinos

    2009-01-01

    we derive the non-planar part of the two-loop dilatation generator of ABJ theory in its SU(2)xSU(2) sub-sector. Applying the dilatation generator to short operators, we explicitly demonstrate that, for operators carrying excitations on both spin chains, the non-planar part breaks parity invariance......While the ABJ Chern-Simons-matter theory and its string theory dual manifestly lack parity invariance, no sign of parity violation has so far been observed on the weak coupling spin chain side. In particular, the planar two-loop dilatation generator of ABJ theory is parity invariant. In this letter....... For operators with only one type of excitation, however, parity remains conserved at the non-planar level. We furthermore observe that, as for ABJM theory, the degeneracy between planar parity pairs is lifted when non-planar corrections are taken into account....

  16. Laboratory investigation of shale rock to identify fracture propagation in vertical direction to bedding

    Science.gov (United States)

    Peng, Tan; Yan, Jin; Bing, Hou; Yingcao, Zhou; Ruxin, Zhang; Zhi, Chang; Meng, Fan

    2018-06-01

    Affected by beddings and natural fractures, fracture geometry in the vertical plane is complex in shale formation, which differs from a simple fracture in homogeneous sandstone reservoirs. However, the propagation mechanism of a hydraulic fracture in the vertical plane has not been well understood. In this paper, a true tri-axial pressure machine was deployed for shale horizontal well fracturing simulation experiments of shale outcrops. The effects of multiple factors on hydraulic fracture vertical propagation were studied. The results revealed that hydraulic fracture initiation and propagation displayed four basic patterns in the vertical plane of laminated shale formation. A hydraulic fracture would cross the beddings under the high vertical stress difference between a vertical stress and horizontal minimum stress of 12 MPa, while a hydraulic fracture propagates along the beddings under a low vertical stress difference of 3 MPa. Four kinds of fracture geometry, including a single main fracture, a nonplanar fracture, a complex fracture, and a complex fracture network, were observed due to the combined effects of flow rate and viscosity. Due to the influence of binding strength (or cementing strength) on the fracture communication effects between a hydraulic fracture and the beddings, the opening region of the beddings takes the shape of an ellipse.

  17. Planar and nonplanar ion acoustic shock waves in relativistic degenerate astrophysical electron-positron-ion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Ata-ur-Rahman,; Qamar, A. [Institute of Physics and Electronics, University of Peshawar, Peshawar 25000 (Pakistan); National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan)

    2013-04-15

    We have studied the propagation of ion acoustic shock waves involving planar and non-planar geometries in an unmagnetized plasma, whose constituents are non-degenerate ultra-cold ions, relativistically degenerate electrons, and positrons. By using the reductive perturbation technique, Korteweg-deVries Burger and modified Korteweg-deVries Burger equations are derived. It is shown that only compressive shock waves can propagate in such a plasma system. The effects of geometry, the ion kinematic viscosity, and the positron concentration are examined on the ion acoustic shock potential and electric field profiles. It is found that the properties of ion acoustic shock waves in a non-planar geometry significantly differ from those in planar geometry. The present study has relevance to the dense plasmas, produced in laboratory (e.g., super-intense laser-dense matter experiments) and in dense astrophysical objects.

  18. Nonplanar tertiary amides in rigid chiral tricyclic dilactams. Peptide group distortions and vibrational optical activity.

    Science.gov (United States)

    Pazderková, Markéta; Profant, Václav; Hodačová, Jana; Sebestík, Jaroslav; Pazderka, Tomáš; Novotná, Pavlína; Urbanová, Marie; Safařík, Martin; Buděšínský, Miloš; Tichý, Miloš; Bednárová, Lucie; Baumruk, Vladimír; Maloň, Petr

    2013-08-22

    We investigate amide nonplanarity in vibrational optical activity (VOA) spectra of tricyclic spirodilactams 5,8-diazatricyclo[6,3,0,0(1,5)]undecan-4,9-dione (I) and its 6,6',7,7'-tetradeuterio derivative (II). These rigid molecules constrain amide groups to nonplanar geometries with twisted pyramidal arrangements of bonds to amide nitrogen atoms. We have collected a full range vibrational circular dichroism (VCD) and Raman optical activity (ROA) spectra including signals of C-H and C-D stretching vibrations. We report normal-mode analysis and a comparison of calculated to experimental VCD and ROA. The data provide band-to-band assignment and offer a possibility to evaluate roles of constrained nonplanar tertiary amide groups and rigid chiral skeletons. Nonplanarity shows as single-signed VCD and ROA amide I signals, prevailing the couplets expected to arise from the amide-amide interaction. Amide-amide coupling dominates amide II (mainly C'-N stretching, modified in tertiary amides by the absence of a N-H bond) transitions (strong couplet in VCD, no significant ROA) probably due to the close proximity of amide nitrogen atoms. At lower wavenumbers, ROA spectra exhibit another likely manifestation of amide nonplanarity, showing signals of amide V (δ(oop)(N-C) at ~570 cm(-1)) and amide VI (δ(oop)(C'═O) at ~700 cm(-1) and ~650 cm(-1)) vibrations.

  19. Evaluation of the conditions imposed by the fracture surface geometry on water seepage through fractured porous media

    International Nuclear Information System (INIS)

    Fuentes, Nestor O.; Faybishenko, B.

    2003-01-01

    In order to determine the geometric patterns of the fracture surfaces that imposes conditions on the fluid flow through fractured porous media, a series a fracture models have been analyzed using the RIMAPS technique and the variogram method. Results confirm that the main paths followed by the fluid channels are determined by the surface topography and remain constant during water seepage evolution. Characteristics scale lengths of both situations: fracture surface and the flow of water, are also found. There exists a relationship between the scale lengths corresponding to each situation. (author)

  20. FRACTURE GEOMETRY ANALYSIS FOR THE STRATIGRAPHIC UNITS OF THE REPOSITORY HOST HORIZON

    International Nuclear Information System (INIS)

    Hardin, E.

    2000-01-01

    The purpose of this Analysis and Model Report (AMR) is to evaluate the geometry of the primary joint sets (i.e., fractures belonging to a group demonstrating a preferential orientation) associated with the lithostratigraphic units of the Repository Host Horizon (RHH). Specifically, the analysis is limited to examining joint sets occurring within the upper lithophysal (Tptpul), middle nonlithophysal (Tptpmn), lower lithophysal (Tptpll), and lower non-lithophysal (Tptpln) zones of the crystal-poor member of the Topopah Spring Tuff. The results of this AMR supply the geometric input parameters for the joint sets used as input to the acquired software code DRKBA V3.3 (CRWMS M and O 2000i; hereafter DRKBA), which is used in the determination of key block sizes and distributions within the ''Drift Degradation Analysis'' AMR (CRWMS M and O 2000b). Additionally, the results of this AMR provide input for selecting the orientation of the emplacement drifts used in layout design work for the potential repository

  1. Strain and the optoelectronic properties of nonplanar phosphorene monolayers

    Science.gov (United States)

    Mehboudi, Mehrshad; Utt, Kainen; Terrones, Humberto; Harriss, Edmund O.; Pacheco SanJuan, Alejandro A.; Barraza-Lopez, Salvador

    2015-01-01

    Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene––a new 2D atomic material––in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum. PMID:25918413

  2. Influence of fracture geometry on bone healing under locking plate fixations: A comparison between oblique and transverse tibial fractures.

    Science.gov (United States)

    Miramini, Saeed; Zhang, Lihai; Richardson, Martin; Mendis, Priyan; Ebeling, Peter R

    2016-10-01

    Mechano-regulation plays a crucial role in bone healing and involves complex cellular events. In this study, we investigate the change of mechanical microenvironment of stem cells within early fracture callus as a result of the change of fracture obliquity, gap size and fixation configuration using mechanical testing in conjunction with computational modelling. The research outcomes show that angle of obliquity (θ) has significant effects on interfragmentary movement (IFM) which influences mechanical microenvironment of the callus cells. Axial IFM at near cortex of fracture decreases with θ, while shear IFM significantly increases with θ. While a large θ can increase shear IFM by four-fold compared to transverse fracture, it also result in the tension-stress effect at near cortex of fracture callus. In addition, mechanical stimuli for cell differentiation within the callus are found to be strongly negatively correlated to angle of obliquity and gap size. It is also shown that a relatively flexible fixation could enhance callus formation in presence of a large gap but could lead to excessive callus strain and interstitial fluid flow when a small transverse fracture gap is present. In conclusion, there appears to be an optimal fixation configuration for a given angle of obliquity and gap size. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

  3. Field and numerical descriptions of fracture geometries and terminations in chalk containing chert layers and inclusions; implications for groundwater flow in Danish chalk aquifers

    Science.gov (United States)

    Seyum, S.

    2017-12-01

    conditions that reproduce measured fracture geometries. The results of this study provide predictive, field-supported fracture geometries for flow models and, with appropriate changes to the parameters, the methodology is applicable to describing fracture geometries in chalk hydrocarbon systems.

  4. Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada: proceedings

    International Nuclear Information System (INIS)

    Barton, C.C.; Larsen, E.

    1985-01-01

    Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs

  5. Nonplanar ion acoustic waves with kappa-distributed electrons

    International Nuclear Information System (INIS)

    Sahu, Biswajit

    2011-01-01

    Using the standard reductive perturbation technique, nonlinear cylindrical and spherical Kadomtsev-Petviashvili equations are derived for the propagation of ion acoustic solitary waves in an unmagnetized collisionless plasma with kappa distributed electrons and warm ions. The influence of kappa-distributed electrons and the effects caused by the transverse perturbation on cylindrical and spherical ion acoustic waves (IAWs) are investigated. It is observed that increase in the kappa distributed electrons (i.e., decreasing κ) decreases the amplitude of the solitary electrostatic potential structures. The numerical results are presented to understand the formation of ion acoustic solitary waves with kappa-distributed electrons in nonplanar geometry. The present investigation may have relevance in the study of propagation of IAWs in space and laboratory plasmas.

  6. Bone Geometry as a Predictor of Tissue Fragility and Stress Fracture Risk

    Science.gov (United States)

    2004-10-01

    eferences ........................................................................ 11 A ppendices ...School of Medicine, New York NY Stress fractures occur among persons with normal bones, no acute injury, and are most common among elite runners and

  7. Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria

    Czech Academy of Sciences Publication Activity Database

    Malíková, L.; Veselý, V.; Seitl, Stanislav

    2016-01-01

    Roč. 89, AUG (2016), s. 99-107 ISSN 0142-1123. [International Conference on Characterisation of Crack Tip Fields /3./. Urbino, 20.04.2015-22.04.2015] Institutional support: RVO:68081723 Keywords : Near-crack-tip fields * Mixed mode * Crack propagation direction * Multi-parameter fracture criteria * Finite element analysis Subject RIV: JL - Materials Fatigue, Friction Mechanics Impact factor: 2.899, year: 2016

  8. On size and geometry effects on the brittle fracture of ferritic and tempered martensitic steels

    Science.gov (United States)

    Odette, G. R.; Chao, B. L.; Lucas, G. E.

    1992-09-01

    A finite element computation of nonsingular crack tip fields was combined with a weakest link statistics model of cleavage fracture. Model predictions for three point bend specimens with various widths and crack depth to width ratios are qualitatively consistent with a number of trends observed in a 12 Cr martensitic stainless steel. The toughness “benefits” of small sizes and shallow cracks are primarily reflected in strain limits rather than net section stress capacities, which is significant to fusion structures subject to large secondary stresses.

  9. Three-dimensional elastic--plastic stress and strain analyses for fracture mechanics: complex geometries

    International Nuclear Information System (INIS)

    Bellucci, H.J.

    1975-11-01

    The report describes the continuation of research into capability for three-dimensional elastic-plastic stress and strain analysis for fracture mechanics. A computer program, MARC-3D, has been completed and was used to analyze a cylindrical pressure vessel with a nozzle insert. A method for generating crack tip elements was developed and a model was created for a cylindrical pressure vessel with a nozzle and an imbedded flaw at the inside nozzle corner. The MARC-3D program was again used to analyze this flawed model. Documentation for the use of the MARC-3D computer program has been included as an appendix

  10. Influence of the geometry of curved artificial canals on the fracture of rotary nickel-titanium instruments subjected to cyclic fatigue tests.

    Science.gov (United States)

    Lopes, Hélio P; Vieira, Márcia V B; Elias, Carlos N; Gonçalves, Lucio S; Siqueira, José F; Moreira, Edson J L; Vieira, Victor T L; Souza, Letícia C

    2013-05-01

    This study evaluated the influence of different features of canal curvature geometry on the number of cycles to fracture of a rotary nickel-titanium endodontic instrument subjected to a cyclic fatigue test. BioRaCe BR4C instruments (FKG Dentaire, La Chaux-de Fonds, Switzerland) were tested in 4 grooves simulating curved metallic artificial canals, each one measuring 1.5 mm in width, 20 mm in total length, and 3.5 mm in depth with a U-shaped bottom. The parameters of curvature including the radius and arc lengths and the position of the arc differed in the 4 canal designs. Fractured surfaces and helical shafts of the separated instruments were analyzed by scanning electron microscopy. The Student's t test showed that a significantly lower number of cycles to fracture values were observed for instruments tested in canals with the smallest radius, the longest arc, and the arc located in the middle portion of the canal. Scanning electron microscopic analysis of the fracture surfaces revealed morphologic characteristics of ductile fracture. Plastic deformation was not observed in the helical shaft of the fractured instruments. Curvature geometry including the radius and arc lengths and the position of the arc along the root canal influence the number of cycles to fracture of rotary nickel-titanium instruments subjected to flexural load. Copyright © 2013 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

  11. A three-dimensional analysis of fracture mechanics test pieces of different geometries part 2 - Constraint and material variations

    Energy Technology Data Exchange (ETDEWEB)

    Tkach, Y., E-mail: Yuri.Tkach@WGIM.com [Department of Civil and Structural Engineering, School of MACE, UMIST/University of Manchester, PO Box 88, Manchester M60 1QD (United Kingdom); Burdekin, F.M., E-mail: mburdekin@aol.com [Department of Civil and Structural Engineering, School of MACE, UMIST/University of Manchester, PO Box 88, Manchester M60 1QD (United Kingdom)

    2012-05-15

    This paper reports the second stage of an extensive series of detailed three-dimensional elastic-plastic finite element analyses on the influence of fracture mechanics test specimen geometry and different material properties on constraint and triaxiality in the near crack tip region. The specimens studied were pre-cracked plain-sided and side-grooved Charpy sized specimens, plain-sided and side-grooved compact tension specimens of thickness B = 25 mm and plain-sided compact tension specimens of thickness B = 100 mm all with the ratio of the crack length to the specimen width a/W = 0.5. Stress-strain curves of materials of different yield strength and strain hardening behaviour spanning the range of practical interest for typical structural steels were implemented into the finite element models. The level of constraint in the specimens modelled has been characterised in terms of both the Q-stress parameter and the ratio of hydrostatic to the equivalent stress components. It has been established that in-plane constraint in the fracture toughness test pieces is significantly affected by the absolute ligament size of the specimen. It has also been shown that the strain hardening behaviour is one of the major material parameters defining constraint level in the fracture toughness specimen. - Highlights: Black-Right-Pointing-Pointer 3D FE analyses on plain and side-grooved Charpy sized and CT specimens of two sizes. Black-Right-Pointing-Pointer Crack tip constraint analysed for Q-stress and hydrostatic/equivalent stress ratio. Black-Right-Pointing-Pointer In-plane constraint is significantly affected by the absolute ligament size. Black-Right-Pointing-Pointer Constraint level is significantly affected by material strain hardening behaviour.

  12. A three-dimensional analysis of fracture mechanics test pieces of different geometries part 2 - Constraint and material variations

    International Nuclear Information System (INIS)

    Tkach, Y.; Burdekin, F.M.

    2012-01-01

    This paper reports the second stage of an extensive series of detailed three-dimensional elastic-plastic finite element analyses on the influence of fracture mechanics test specimen geometry and different material properties on constraint and triaxiality in the near crack tip region. The specimens studied were pre-cracked plain-sided and side-grooved Charpy sized specimens, plain-sided and side-grooved compact tension specimens of thickness B = 25 mm and plain-sided compact tension specimens of thickness B = 100 mm all with the ratio of the crack length to the specimen width a/W = 0.5. Stress–strain curves of materials of different yield strength and strain hardening behaviour spanning the range of practical interest for typical structural steels were implemented into the finite element models. The level of constraint in the specimens modelled has been characterised in terms of both the Q-stress parameter and the ratio of hydrostatic to the equivalent stress components. It has been established that in-plane constraint in the fracture toughness test pieces is significantly affected by the absolute ligament size of the specimen. It has also been shown that the strain hardening behaviour is one of the major material parameters defining constraint level in the fracture toughness specimen. - Highlights: ► 3D FE analyses on plain and side-grooved Charpy sized and CT specimens of two sizes. ► Crack tip constraint analysed for Q-stress and hydrostatic/equivalent stress ratio. ► In-plane constraint is significantly affected by the absolute ligament size. ► Constraint level is significantly affected by material strain hardening behaviour.

  13. Effect of strain rate and notch geometry on tensile properties and fracture mechanism of creep strength enhanced ferritic P91 steel

    Science.gov (United States)

    Pandey, Chandan; Mahapatra, M. M.; Kumar, Pradeep; Saini, N.

    2018-01-01

    Creep strength enhanced ferritic (CSEF) P91 steel were subjected to room temperature tensile test for quasi-static (less than 10-1/s) strain rate by using the Instron Vertical Tensile Testing Machine. Effect of different type of notch geometry, notch depth and angle on mechanical properties were also considered for different strain rate. In quasi-static rates, the P91 steel showed a positive strain rate sensitivity. On the basis of tensile data, fracture toughness of P91 steel was also calculated numerically. For 1 mm notch depth (constant strain rate), notch strength and fracture toughness were found to be increased with increase in notch angle from 45° to 60° while the maximum value attained in U-type notch. Notch angle and notch depth has found a minute effect on P91 steel strength and fracture toughness. The fracture surface morphology was studied by field emission scanning electron microscopy (FESEM).

  14. BMD T-score discriminates trochanteric fractures from unfractured controls, whereas geometry discriminates cervical fracture cases from unfractured controls of similar BMD.

    Science.gov (United States)

    Pulkkinen, P; Partanen, J; Jalovaara, P; Jämsä, T

    2010-07-01

    The ability of bone mineral density (BMD) to discriminate cervical and trochanteric hip fractures was studied. Since the majority of fractures occur among people who are not diagnosed as having osteoporosis, we also examined this population to elucidate whether geometrical risk factors can yield additional information on hip fracture risk beside BMD. The study showed that the T-score criterion was able to discriminate fracture patients from controls in the cases of trochanteric fractures, whereas geometrical measures may discriminate cervical fracture cases in patients with T-score >-2.5. Low bone mineral density (BMD) is a well-established risk factor for hip fracture. However, majority of fractures occur among people not diagnosed as having osteoporosis. We studied the ability of BMD to discriminate cervical and trochanteric hip fractures. Furthermore, we examined whether geometrical measures can yield additional information on the assessment of hip fracture risk in the fracture cases in subjects with T-score >-2.5. Study group consisted of postmenopausal females with non-pathologic cervical (n = 39) or trochanteric (n = 18) hip fracture (mean age 74.2 years) and 40 age-matched controls. BMD was measured at femoral neck, and femoral neck axis length, femoral neck and shaft cortex thicknesses (FNC and FSC), and femoral neck-shaft angle (NSA) were measured from radiographs. BMD T-score threshold of -2.5 was able to discriminate trochanteric fractures from controls (p trochanteric fractures occurred in individuals with T-score fractures. Twenty of these fractures (51.3%) occurred in individuals with BMD in osteoporotic range and 19 (48.7%) in individuals with T-score >-2.5. Within these non-osteoporotic cervical fracture patients (N = 19) and non-osteoporotic controls (N = 35), 83.3% were classified correctly based on a model including NSA and FNC (p trochanteric fractures could be discriminated based on a BMD T-score fracture cases would remain under-diagnosed if

  15. Development of a Marine Propeller With Nonplanar Lifting Surfaces

    DEFF Research Database (Denmark)

    Andersen, Poul; Friesch, Jürgen; Kappel, Jens J.

    2005-01-01

    The principle of non-planar lifting surfaces is applied to the design of modern aircraft wings to obtain better lift to drag ratios. Whereas a pronounced fin or winglet at the wingtip has been developed for aircraft, the application of the nonplanar principle to marine propellers, dealt...... with in this paper, has led to the KAPPEL propeller with blades curved toward the suction side integrating the fin or winglet into the propeller blade. The combined theoretical, experimental, and practical approach to develop and design marine propellers with nonplanar lifting surfaces has resulted in propellers...

  16. 2015 Accomplishments-Tritium aging studies on stainless steel. Effects of hydrogen isotopes, crack orientation, and specimen geometry on fracture toughness

    Energy Technology Data Exchange (ETDEWEB)

    Morgan, Michael J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2016-01-01

    This study reports on the effects of hydrogen isotopes, crack orientation, and specimen geometry on the fracture toughness of stainless steels. Fracture toughness variability was investigated for Type 21-6-9 stainless steel using the 7K0004 forging. Fracture toughness specimens were cut from the forging in two different geometric configurations: arc shape and disc shape. The fracture toughness properties were measured at ambient temperature before and after exposure to hydrogen gas and compared to prior studies. There are three main conclusions that can be drawn from the results. First, the fracture toughness properties of actual reservoir forgings and contemporary heats of steel are much higher than those measured in earlier studies that used heats of steel from the 1980s and 1990s and forward extruded forgings which were designed to simulate reservoir microstructures. This is true for as-forged heats as well as forged heats exposed to hydrogen gas. Secondly, the study confirms the well-known observation that cracks oriented parallel to the forging grain flow will propagate easier than those oriented perpendicular to the grain flow. However, what was not known, but is shown here, is that this effect is more pronounced, particularly after hydrogen exposures, when the forging is given a larger upset. In brick forgings, which have a relatively low amount of upset, the fracture toughness variation with specimen orientation is less than 5%; whereas, in cup forgings, the fracture toughness is about 20% lower than that forging to show how specimen geometry affects fracture toughness values. The American Society for Testing Materials (ASTM) specifies minimum specimen section sizes for valid fracture toughness values. However, sub-size specimens have long been used to study tritium effects because of the physical limitation of diffusing hydrogen isotopes into stainless steel at mild temperatures so as to not disturb the underlying forged microstructure. This study shows

  17. The impact of in-situ stress and outcrop-based fracture geometry on hydraulic aperture and upscaled permeability in fractured reservoirs

    DEFF Research Database (Denmark)

    Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid

    2016-01-01

    explicitly, we quantify equivalent permeability, i.e. combined matrix and stress-dependent fracture flow. Fracture networks extracted from a large outcropping pavement form the basis of these models. The results show that the angle between fracture strike and σ 1 has a controlling impact on aperture...

  18. Yangian-type symmetries of non-planar leading singularities

    Energy Technology Data Exchange (ETDEWEB)

    Frassek, Rouven [Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom); Meidinger, David [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, 12489 Berlin (Germany)

    2016-05-18

    We take up the study of integrable structures behind non-planar contributions to scattering amplitudes in N = 4 super Yang-Mills theory. Focusing on leading singularities, we derive the action of the Yangian generators on color-ordered subsets of the external states. Each subset corresponds to a single boundary of the non-planar on-shell diagram. While Yangian invariance is broken, we find that higher-level Yangian generators still annihilate the non-planar on-shell diagram. For a given diagram, the number of these generators is governed by the degree of non-planarity. Furthermore, we present additional identities involving integrable transfer matrices. In particular, for diagrams on a cylinder we obtain a conservation rule similar to the Yangian invariance condition of planar on-shell diagrams. To exemplify our results, we consider a five-point MHV on-shell function on a cylinder.

  19. Height gain of vertebral bodies and stabilization of vertebral geometry over one year after vertebroplasty of osteoporotic vertebral fractures

    International Nuclear Information System (INIS)

    Pitton, Michael B.; Morgen, Nadine; Herber, Sascha; Dueber, Christoph; Drees, Philipp; Boehm, Bertram

    2008-01-01

    The height gain of vertebral bodies after vertebroplasty and geometrical stability was evaluated over a one-year period. Osteoporotic fractures were treated with vertebroplasty. The vertebral geometry and disc spaces were analysed using reformatted computed tomography (CT) images: heights of the anterior, posterior, and lateral vertebral walls, disc spaces, endplate angles, and minimal endplate distances. Vertebrae were assigned to group I [severe compression (anterior height/posterior height) 0.75). A total of 102 vertebral bodies in 40 patients (12 men, 28 women, age 70.3 ± 9.5) were treated with vertebroplasty and prospectively followed for 12 months. Group I showed a greater benefit compared with group II with respect to anterior height gain (+2.1 ± 1.9 vs +0.7 ± 1.6 mm, P < 0.001), reduction of endplate angle (-3.6 ± 4.2 vs -0.8 ± 2.3 , P < 0.001), and compression index (+0.09 ± 0.11 vs +0.01 ± 0.06, P < 0.001). At one-year follow-up, group I demonstrated preserved anterior height gain (+1.5 ± 2.8 mm, P < 0.015) and improved endplate angle (-3.4 ± 4.9 , P < 0.001). In group II, the vertebral heights returned to and were fixed at the pre-interventional levels. Vertebroplasty provided vertebral height gain over one year, particularly in cases with severe compression. Vertebrae with moderate compression were fixed and stabilized at the pre-treatment level over one year. (orig.)

  20. Planar and nonplanar electron-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution

    International Nuclear Information System (INIS)

    Han, Jiu-Ning; Luo, Jun-Hua; Sun, Gui-Hua; Liu, Zhen-Lai; Ge, Su-Hong; Wang, Xin-Xing; Li, Jun-Xiu

    2014-01-01

    The nonlinear dynamics of nonplanar (cylindrical and spherical) electron-acoustic solitary wave structures in an unmagnetized, collisionless plasma composed of stationary ions, cold fluid electrons and hot q-nonextensive distributed electrons are theoretically studied. We discuss the effects of the nonplanar geometry, nonextensivity of hot electrons and ‘hot’ to ‘cold’ electron number density ratio on the time evolution characters of cylindrical and spherical solitary waves. Moreover, the effects of plasma parameters on the nonlinear structure induced by the interaction between two planar solitary waves are also investigated. It is found that these plasma parameters have significant influences on the properties of the above-mentioned nonlinear structures. Our theoretical study may be useful to understand the nonlinear features of electron-acoustic wave structures in astrophysical plasma systems. (paper)

  1. A new technique for determining orientation and motion of a 2-D, non-planar magnetopause

    Directory of Open Access Journals (Sweden)

    A. Blagau

    2010-03-01

    Full Text Available For a four-point mission like Cluster, the differences in position and time when the satellites detect the magnetopause or any other discontinuity, can be used to infer the discontinuity local orientation, thickness and motion. This timing technique, commonly assuming a planar geometry, offers an independent check for various single-spacecraft techniques. In the present paper we propose an extension of the timing method, capable of determining in a self-consistent way the macroscopic parameters of a two-dimensional, non-planar discontinuity. Such a configuration can be produced by a local bulge or indentation in the magnetopause, or by a large amplitude wave traveling on this surface, and is recognized in Cluster data when the single spacecraft techniques provide different individual normals contained roughly in the same plane. The model we adopted for the magnetopause assumes a layer of constant thickness of either cylindrical or parabolic shape, which has one or two degrees of freedom for the motion in the plane of the individual normals. The method was further improved by incorporating in a self-consistent way the requirement of minimum magnetic field variance along the magnetopause normal. An additional assumption, required in a previously proposed non-planar technique, i.e. that the non-planarity has negligible effects on the minimum variance analysis, is thus avoided. We applied the method to a magnetopause transition for which the various planar techniques provided inconsistent results. By contrast, the solutions obtained from the different implementations of the new 2-D method were consistent and stable, indicating a convex shape for the magnetopause. These solutions perform better than the planar solutions from the normal magnetic field variance perspective. The magnetopause dynamics and the presence of a non-zero normal magnetic field component in the analyzed event are discussed.

  2. History matching of large scale fractures to production data; Calage de la geometrie des reseaux de fractures aux donnees hydrodynamiques de production d'un champ petrolier

    Energy Technology Data Exchange (ETDEWEB)

    Jenni, S.

    2005-01-01

    Object based models are very helpful to represent complex geological media such as fractured reservoirs. For building realistic fracture networks, these models have to be constrained to both static (seismic, geomechanics, geology) and dynamic data (well tests and production history). In this report we present a procedure for the calibration of large-scale fracture networks to production history. The history matching procedure includes a realistic geological modeling, a parameterization method coherent with the geological model and allowing an efficient optimization. Fluid flow modeling is based on a double medium approach. The calibration procedure was applied to a semi-synthetic case based on a real fractured reservoir. The calibration to water-cut data was performed. (author)

  3. Comparison of plantar flexor musculotendinous stiffness, geometry, and architecture in male runners with and without a history of tibial stress fracture.

    Science.gov (United States)

    Pamukoff, Derek N; Blackburn, J Troy

    2015-02-01

    Greater lower extremity joint stiffness may be related to the development of tibial stress fractures in runners. Musculotendinous stiffness is the largest contributor to joint stiffness, but it is unclear what factors contribute to musculotendinous stiffness. The purpose of this study was to compare plantar flexor musculotendinous stiffness, architecture, geometry, and Achilles tendon stiffness between male runners with and without a history of tibial stress fracture. Nineteen healthy runners (age = 21 ± 2.7 years; mass = 68.2 ± 9.3 kg; height = 177.3 ± 6.0 cm) and 19 runners with a history of tibial stress fracture (age = 21 ± 2.9 years; mass = 65.3 ± 6.0 kg; height = 177.2 ± 5.2 cm) were recruited from community running groups and the university's varsity and club cross-country teams. Plantar flexor musculotendinous stiffness was estimated from the damped frequency of oscillatory motion about the ankle follow perturbation. Ultrasound imaging was used to measure architecture and geometry of the medial gastrocnemius. Dependent variables were compared between groups via one-way ANOVAs. Previously injured runners had greater plantar flexor musculotendinous stiffness (P < .001), greater Achilles tendon stiffness (P = .004), and lesser Achilles tendon elongation (P = .003) during maximal isometric contraction compared with healthy runners. No differences were found in muscle thickness, pennation angle, or fascicle length.

  4. Heritability of prevalent vertebral fracture and volumetric bone mineral density and geometry at the lumbar spine in three generations of the Framingham study.

    Science.gov (United States)

    Liu, Ching-Ti; Karasik, David; Zhou, Yanhua; Hsu, Yi-Hsiang; Genant, Harry K; Broe, Kerry E; Lang, Thomas F; Samelson, Elizabeth J; Demissie, Serkalem; Bouxsein, Mary L; Cupples, L Adrienne; Kiel, Douglas P

    2012-04-01

    Genetic factors likely contribute to the risk for vertebral fractures; however, there are few studies on the genetic contributions to vertebral fracture (VFrx), vertebral volumetric bone mineral density (vBMD), and geometry. Also, the heritability (h(2)) for VFrx and its genetic correlation with phenotypes contributing to VFrx risk have not been established. This study aims to estimate the h(2) of vertebral fracture, vBMD, and cross-sectional area (CSA) derived from quantitative computed tomography (QCT) scans and to estimate the extent to which they share common genetic association in adults of European ancestry from three generations of Framingham Heart Study (FHS) families. Members of the FHS families were assessed for VFrx by lateral radiographs or QCT lateral scout views at 13 vertebral levels (T(4) to L(4)) using Genant's semiquantitative (SQ) scale (grades 0 to 3). Vertebral fracture was defined as having at least 25% reduction in height of any vertebra. We also analyzed QCT scans at the L(3) level for integral (In.BMD) and trabecular (Tb.BMD) vBMD and CSA. Heritability estimates were calculated, and bivariate genetic correlation analysis was performed, adjusting for various covariates. For VFrx, we analyzed 4099 individuals (148 VFrx cases) including 2082 women and 2017 men from three generations. Estimates of crude and multivariable-adjusted h(2) were 0.43 to 0.69 (p < 1.1 × 10(-2)). A total of 3333 individuals including 1737 men and 1596 women from two generations had VFrx status and QCT-derived vBMD and CSA information. Estimates of crude and multivariable-adjusted h(2) for vBMD and CSA ranged from 0.27 to 0.51. In a bivariate analysis, there was a moderate genetic correlation between VFrx and multivariable-adjusted In.BMD (-0.22) and Tb.BMD (-0.29). Our study suggests vertebral fracture, vertebral vBMD, and CSA in adults of European ancestry are heritable, underscoring the importance of further work to identify the specific variants underlying

  5. Nonplanar loops leave the Veneziano model photon massless

    NARCIS (Netherlands)

    Foda, O.

    1987-01-01

    The absence of a pole at p2=0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found.

  6. Nonplanar loops leave the Veneziano model photon massless

    International Nuclear Information System (INIS)

    Foda, O.

    1987-01-01

    The absence of a pole at p 2 =0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found. (orig.)

  7. Nonplanar loops leave the Veneziano model photon massless

    Energy Technology Data Exchange (ETDEWEB)

    Foda, O.

    1987-04-16

    The absence of a pole at p/sup 2/=0 in the orientable nonplanar one-loop photon self-energy in the Veneziano model is verified. Thus the photon remains massless, and spontaneous symmetry breaking - at least as reported in this context in the literature - is not found.

  8. Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

    Science.gov (United States)

    Salazar, R.; Tellez, G.

    2012-01-01

    We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

  9. Geometry reconstruction method for patient-specific finite element models for the assessment of tibia fracture risk in osteogenesis imperfecta.

    Science.gov (United States)

    Caouette, Christiane; Ikin, Nicole; Villemure, Isabelle; Arnoux, Pierre-Jean; Rauch, Frank; Aubin, Carl-Éric

    2017-04-01

    Lower limb deformation in children with osteogenesis imperfecta (OI) impairs ambulation and may lead to fracture. Corrective surgery is based on empirical assessment criteria. The objective was to develop a reconstruction method of the tibia for OI patients that could be used as input of a comprehensive finite element model to assess fracture risks. Data were obtained from three children with OI and tibia deformities. Four pQCT scans were registered to biplanar radiographs, and a template mesh was deformed to fit the bone outline. Cortical bone thickness was computed. Sensitivity of the model to missing slices of pQCT was assessed by calculating maximal von Mises stress for a vertical hopping load case. Sensitivity of the model to ±5 % of cortical thickness measurements was assessed by calculating loads at fracture. Difference between the mesh contour and bone outline on the radiographs was below 1 mm. Removal of one pQCT slice increased maximal von Mises stress by up to 10 %. Simulated ±5 % variation of cortical bone thickness leads to variations of up to 4.1 % on predicted fracture loads. Using clinically available tibia imaging from children with OI, the developed reconstruction method allowed the building of patient-specific finite element models.

  10. Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria

    Czech Academy of Sciences Publication Activity Database

    Malíková, L.; Veselý, V.; Seitl, Stanislav

    2015-01-01

    Roč. 9, č. 33 (2015), s. 25-32 ISSN 1971-8993 Institutional support: RVO:68081723 Keywords : Near-crack-tip fields * Williams expansion * Crack propagation direction * Multi-parameter fracture criteria * Finite element analysis Subject RIV: JL - Materials Fatigue, Friction Mechanics

  11. Simplified nonplanar wafer bonding for heterogeneous device integration

    Science.gov (United States)

    Geske, Jon; Bowers, John E.; Riley, Anton

    2004-07-01

    We demonstrate a simplified nonplanar wafer bonding technique for heterogeneous device integration. The improved technique can be used to laterally integrate dissimilar semiconductor device structures on a lattice-mismatched substrate. Using the technique, two different InP-based vertical-cavity surface-emitting laser active regions have been integrated onto GaAs without compromising the quality of the photoluminescence. Experimental and numerical simulation results are presented.

  12. Some remarks on non-planar Feynman diagrams

    International Nuclear Information System (INIS)

    Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz

    2013-12-01

    Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

  13. Some remarks on non-planar Feynman diagrams

    Energy Technology Data Exchange (ETDEWEB)

    Bielas, Krzysztof; Dubovyk, Ievgen; Gluza, Janusz [Silesia Univ., Katowice (Poland). Inst. of Physics; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2013-12-15

    Two criteria for planarity of a Feynman diagram upon its propagators (momentum ows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.

  14. From large N nonplanar anomalous dimensions to open spring theory

    Energy Technology Data Exchange (ETDEWEB)

    Mello Koch, Robert de, E-mail: robert@neo.phys.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa); Kemp, Garreth, E-mail: Garreth.Kemp@students.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa); Smith, Stephanie, E-mail: Stephanie.Smith@students.wits.ac.za [National Institute for Theoretical Physics, Department of Physics and Centre for Theoretical Physics University of Witwatersrand, Wits, 2050 (South Africa)

    2012-05-23

    In this Letter we compute the nonplanar one-loop anomalous dimension of restricted Schur polynomials that have a bare dimension of O(N). This is achieved by mapping the restricted Schur polynomials into states of a specific U(p) irreducible representation. In this way the dilatation operator is mapped into a u(p) valued operator and, as a result, can easily be diagonalized. The resulting spectrum is reproduced by a model of springs between masses.

  15. Conformal, planarizing and bridging AZ5214-E layers deposited by a 'draping' technique on non-planar III V substrates

    Science.gov (United States)

    Eliás, P.; Strichovanec, P.; Kostic, I.; Novák, J.

    2006-12-01

    A draping technique was tested for the deposition of positive-tone AZ5214-E photo-resist layers on non-planar (1 0 0)-oriented III-V substrates, which had a variety of three-dimensional (3D) topographies micromachined in them that consisted, e.g., of mesa ridges confined to side facets with variable tilt, inverted pyramidal holes and stubs confined to perpendicular side facets. All objects were sharp-edged. In each draping experiment, an AZ5214-E sheet was (1) formed floating on the water surface, (2) lowered onto a non-planar substrate and (3) draped over it during drying to form either self-sustained, or conformal, or planarizing layers over the non-planar substrates. The draping process is based on the depression of the glass transition temperature Tg of AZ5214-E material induced by penetrant water molecules that interact with AZ5214-E. During the process, the molecules are initially trapped under an AZ5214-E sheet and then transported out through the sheet via permeation. The water-AZ5214-E interaction modifies the stiffness κ of the sheet. The magnitude of the effect depends on temperature T and on partial water vapour pressure difference p(T, P, κ): the net effect is that Tg = f(C(T, P), p(T, P, κ)) is lowered as the concentration C of water increases with T and p, where P is the permeability of the sheet. The interaction depressed the Tg of the sheets as low as or lower than 53 °C for 6 µm thick sheets. At room temperature T Tg, the sheet becomes rubbery and mouldable by adhesion and capillary forces. As a result, it can either contour or planarize the topography depending on its geometry and thickness of the sheet.

  16. Spinning geometry = Twisted geometry

    International Nuclear Information System (INIS)

    Freidel, Laurent; Ziprick, Jonathan

    2014-01-01

    It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)

  17. Midterm Follow-Up of Vertebral Geometry and Remodeling of the Vertebral Bidisk Unit (VDU) After Percutaneous Vertebroplasty of Osteoporotic Vertebral Fractures

    International Nuclear Information System (INIS)

    Pitton, Michael Bernhard; Koch, Ulrike; Drees, Philip; Dueber, Christoph

    2009-01-01

    The purpose of this study was to investigate geometrical stability and preservation of height gain of vertebral bodies after percutaneous vertebroplasty during 2 years' follow-up and to elucidate the geometric remodeling process of the vertebral bidisk unit (VDU) of the affected segment. Patients with osteoporotic vertebral compression fractures with pain resistant to analgetic drugs were treated with polymethylmethacrylate vertebroplasty. Mean ± standard error cement volume was 5.1 ± 2.0 ml. Vertebral geometry was documented by sagittal and coronal reformations from multidetector computed tomography data sets: anterior, posterior, and lateral vertebral heights, end plate angles, and compression index (CI = anterior/posterior height). Additionally, the VDU (vertebral bodies plus both adjacent disk spaces) was calculated from the multidetector computed tomography data sets: anterior, posterior, and both lateral aspects. Patients were assigned to two groups: moderate compression with CI of >0.75 (group 1) and severe compression with CI of o vs. -1.0 ± 2.7 o , P o , P < 0.01) and compression indices (+0.11 ± 0.15, P < 0.01). Thus, posterior height loss of vertebrae and adjacent intervertebral disk spaces contributed to a remodeling of the VDU, resulting in some compensation of the kyphotic malposition of the affected vertebral segment. Vertebroplasty improved vertebral geometry during midterm follow-up. In severe vertebral compression, significant height gain and improvement of end plate angles were achieved. The remodeling of the VDUs contributes to reduction of kyphosis and an overall improvement of the statics of the spine.

  18. Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

    Science.gov (United States)

    Leser, Patrick E.; Newman, John A.; Warner, James E.; Leser, William P.; Hochhalter, Jacob D.; Yuan, Fuh-Gwo

    2016-01-01

    Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis data from sources such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-based damage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed high-fidelity crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. The model is flexible in that only the expensive computation of the crack driving forces is replaced by the surrogate models, leaving the remaining parameters accessible for uncertainty quantification. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified, edge-notched, aluminum tensile specimen. Predictions of remaining useful life are made over time for five updates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.

  19. Investigation of nonplanar modular coil systems for stellarator fusion reactors

    International Nuclear Information System (INIS)

    Harmeyer, E.

    1988-12-01

    Steady-state stellarators constitute an important option for a future fusion reactor. The helical magnetic field required for plasma confinement can be produced by means of a set of modular nonplanar coils. In order to achieve optimum power density of the plasma, the magnetic flux density inside the torus is made as high as possible. State-of-the-art estimates allow values of the magnetic flux density on axis of B 0 = 4-7 T. The present report is concerned with investigations on modular nonplanar stellarator coil systems. Coil systems with poloidal periodicity l=2 and a coil system of the W VII-AS type with superposed l=0, 1, 2, 3 terms are treated. Furthermore, the parameters are simultaneously varied while keeping constant the ratios of certain magnitudes. In the parameter space of the geometric values and coil number the following quantities are evaluated: maximum magnetic flux density in the coil domain, stored magnetic energy of the coil system, magnetic force density distribution or magnetic forces, and mechanical stress distribution in the coils. Numerical methods are applied in the programme systems used for these calculations. The aim of the study is to determine an optimum regime for the above parameters. The numerical results are compared with those of analytical approximation solutions. (orig.)

  20. Top-forms of leading singularities in nonplanar multi-loop amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Baoyi; Cheung, Yeuk-Kwan E.; Xie, Ruofei; Xin, Yuan [Nanjing University, Department of Physics, Nanjing (China); Chen, Gang [Zhejiang Normal University, Department of Physics, Jinhua (China); Nanjing University, Department of Physics, Nanjing (China)

    2018-02-15

    The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW bridges to a planar diagram whose top-form is well known now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW bridges in an inverse order as discussed in our former paper (Chen et al. in Eur Phys J C 77(2):80 2017). To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint in the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes of N = 4 Super Yang-Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes. (orig.)

  1. KAPPEL Propeller. Development of a Marine Propeller with Non-planar Lifting Surfaces

    DEFF Research Database (Denmark)

    Kappel, J.; Andersen, Poul

    2002-01-01

    The principle of non-planar lifting surfaces is applied to the design of modern aircraft wings to obtain better lift to drag ratios. Whereas a pronounced fin or "winglet" at the wingtip has been developed for aircraft, the application of the non-planar principle to marine propellers, dealt...... with in this paper, has led to the KAPPEL propeller with blades curved towards the suction side integrating the fin or winglet into the propeller blade. The combined theoretical, experimental and practical approach to develop and design marine propellers with non-planar lifting surfaces has resulted in propellers...

  2. Method for brazing together planar and nonplanar metal members

    International Nuclear Information System (INIS)

    Hammersand, F.G.; Witkowski, A.J.

    1985-01-01

    The invention relates to a method and apparatus for brazing two metal members together, at least one of which is nonplanar, in a brazing furnace using a substantially pure brazing material. The method comprises the steps of utilizing a brazing fixture to hold the two metal members in tangential relation to one another along a portion of each member so that a cavity is formed adjacent to the contacting portions. A braze material is then positioned within the cavity. The braze fixture, the metal members, and the braze material are then placed in a brazing furnace. A heat shield is then placed over the braze fixture, the metal members, and the braze material to shield the braze material from direct furnace radiation. The furnace temperature is linearly increased at a rate of about 180 0 C. per hour until a temperature of 350 0 C. is achieved. Heat is transferred by conduction from the metal members to the braze material to cause the braze material to melt. Some material from the metal members slowly diffuses into the braze material forming a braze joint. The furnace is rapidly cooled to room temperature using nitrogen gas. The brazed assemblies made according to this method are superior to assemblies formed by heliarc welding

  3. Multi-projector auto-calibration and placement optimization for non-planar surfaces

    Science.gov (United States)

    Li, Dong; Xie, Jinghui; Zhao, Lu; Zhou, Lijing; Weng, Dongdong

    2015-10-01

    Non-planar projection has been widely applied in virtual reality and digital entertainment and exhibitions because of its flexible layout and immersive display effects. Compared with planar projection, a non-planar projection is more difficult to achieve because projector calibration and image distortion correction are difficult processes. This paper uses a cylindrical screen as an example to present a new method for automatically calibrating a multi-projector system in a non-planar environment without using 3D reconstruction. This method corrects the geometric calibration error caused by the screen's manufactured imperfections, such as an undulating surface or a slant in the vertical plane. In addition, based on actual projection demand, this paper presents the overall performance evaluation criteria for the multi-projector system. According to these criteria, we determined the optimal placement for the projectors. This method also extends to surfaces that can be parameterized, such as spheres, ellipsoids, and paraboloids, and demonstrates a broad applicability.

  4. Nonplanar spiral states of the t-J model with classical spins

    International Nuclear Information System (INIS)

    Hamada, M.; Shimahara, H.; Mori, H.

    1995-01-01

    The spiral state in the two-dimensional t-J model is studied by numerical diagonalization of an effective Hamiltonian. We examine all possibilities of the spiral spin states including the nonplanar states. It is found that nonplanar spiral states occur, but the deviations from the planar spiral state in the nonplanar spiral states are small for small hole concentrations where our effective Hamiltonian is valid. The modulation of the spin configuration increases continuously from the antiferromagnetic order as the hole concentration increases, and discontinuously changes at a critical hole concentration. Then the state undergoes the first-order phase transition either to the (π,0) phase or to the ferromagnetic phase, depending on the value of J/t

  5. Hyperbolic geometry

    CERN Document Server

    Iversen, Birger

    1992-01-01

    Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

  6. Beam model for non-planar orbits in synchrotrons

    International Nuclear Information System (INIS)

    Month, M.

    1984-01-01

    A framework has been developed for a beam model in the case of synchrotron orbits not confined to a plane. An appropriate moving reference system for the analysis of beam stability has been introduced. As examples of strong perturbations to median plane symmetry, two geometries for the overpass for the Tevatron collider are considered

  7. Twistor geometry

    NARCIS (Netherlands)

    van den Broek, P.M.

    1984-01-01

    The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

  8. Linkages of fracture network geometry and hydro-mechanical properties to spatio-temporal variations of seismicity in Koyna-Warna Seismic Zone

    Science.gov (United States)

    Selles, A.; Mikhailov, V. O.; Arora, K.; Ponomarev, A.; Gopinadh, D.; Smirnov, V.; Srinu, Y.; Satyavani, N.; Chadha, R. K.; Davulluri, S.; Rao, N. P.

    2017-12-01

    Well logging data and core samples from the deep boreholes in the Koyna-Warna Seismic Zone (KWSZ) provided a glimpse of the 3-D fracture network responsible for triggered earthquakes in the region. The space-time pattern of earthquakes during the last five decades show strong linkage of favourably oriented fractures system deciphered from airborne LiDAR and borehole structural logging to the seismicity. We used SAR interferometry data on surface displacements to estimate activity of the inferred faults. The failure in rocks at depths is largely governed by overlying lithostatic and pore fluid pressure in the rock matrix which are subject to change in space and time. While lithostatic pressure tends to increase with depth pore pressure is prone to fluctuations due to any change in the hydrological regime. Based on the earthquake catalogue data, the seasonal variations in seismic activity associated with annual fluctuations in the reservoir water level were analyzed over the time span of the entire history of seismological observations in this region. The regularities in the time changes in the structure of seasonal variations are revealed. An increase in pore fluid pressure can result in rock fracture and oscillating pore fluid pressures due to a reservoir loading and unloading cycles can cause iterative and cumulative damage, ultimately resulting in brittle failure under relatively low effective mean stress conditions. These regularities were verified by laboratory physical modeling. Based on our observations of main trends of spatio-temporal variations in seismicity as well as the spatial distribution of fracture network a conceptual model is presented to explain the triggered earthquakes in the KWSZ. The work was supported under the joint Russian-Indian project of the Russian Science Foundation (RSF) and the Department of Science and Technology (DST) of India (RSF project no. 16-47-02003 and DST project INT/RUS/RSF/P-13).

  9. Transition of W7-X non-planar coils from manufacturing to assembly

    Energy Technology Data Exchange (ETDEWEB)

    Ehrke, G. [Max-Planck-Institut fuer Plasmaphysik (IPP), EURATOM Association, Wendelsteinstrasse 1, D-17491 Greifswald (Germany)], E-mail: gunnar.ehrke@ipp.mpg.de

    2009-06-15

    The main magnetic field of Wendelstein 7-X fusion experiment (W7-X) at Max-Planck-Institut fuer Plasmaphysik Greifswald, Germany will be provided by 50 non-planar coils and supported by 20 planar coils. The non-planar coils were delivered by a consortium (CON) consisting of Babcock Noell GmbH Germany (BNG) and ASG Superconductors S.p.A. Italy (ASG). The coil production ended with the delivery of the last non-planar coil in March 2008 at the manufacturing branch of BNG in Zeitz, Germany. The construction of the coils was characterised by design changes, many rework actions and resulting time delays. Due to these numerous adjustments and changes a continuous improvement process was needed. This paper will give an overview about the transition of the non-planar coils from the acceptance tests at the manufacturer site to the beginning of the assembly at IPP. Furthermore this report will highlight technical interfaces in the period of transition.

  10. Structural templating in a nonplanar phthalocyanine using single crystal copper iodide

    OpenAIRE

    Rochford, L. A. (Luke A.); Ramadan, Alexandra J.; Keeble, Dean S.; Ryan, Mary P.; Heutz, Sandrine; Jones, T. S. (Tim S.)

    2015-01-01

    Solution-grown copper iodide crystals are used as substrates for the templated growth of the nonplanar vanadyl phthalocyanine using organic molecular beam deposition. Structural characterization reveals a single molecular orientation produced by the (111) Miller plane of the copper iodide crystals. These fundamental measurements show the importance of morphology and structure in templating interactions for organic electronics applications.

  11. Nonplanar Tertiary Amides in Rigid Chiral Tricyclic Dilactams. Peptide Group Distortions and Vibrational Optical Activity

    Czech Academy of Sciences Publication Activity Database

    Pazderková, Markéta; Profant, V.; Hodačová, J.; Šebestík, Jaroslav; Pazderka, T.; Novotná, P.; Urbanová, M.; Šafařík, Martin; Buděšínský, Miloš; Tichý, Miloš; Bednárová, Lucie; Baumruk, V.; Maloň, Petr

    2013-01-01

    Roč. 117, č. 33 (2013), s. 9626-9642 ISSN 1520-6106 R&D Projects: GA ČR GAP205/10/1276 Institutional support: RVO:61388963 Keywords : spirodilactams * amide bond * vibrational circular dichroism * non-planarity * Raman optical activity Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.377, year: 2013

  12. Non-planar corrections to the Pomeron and reggeons in the dual unitarity scheme

    International Nuclear Information System (INIS)

    Uschersohn, J.

    1976-03-01

    A special class of non-planar diagrams is studied, those in which the produced clusters are crossed. Insertion of these diagrams in the reggeon propagators accounts for exchange degeneracy breaking. The even signature reggeons get their intercept promoted to a larger value, while the odd signature ones are left unchanged. (author)

  13. Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0

    International Nuclear Information System (INIS)

    Dubovyk, Ievgen; Gluza, Janusz; Riemann, Tord

    2016-04-01

    We introduce the Mellin-Barnes representation of general Feynman integrals and discuss their evaluation. The Mathematica package AMBRE has been recently extended in order to cover consistently non-planar Feynman integrals with two loops. Prospects for the near future are outlined. This write-up is an introduction to new results which have also been presented elsewhere.

  14. Planar and non-planar nucleus-acoustic shock structures in self-gravitating degenerate quantum plasma systems

    Science.gov (United States)

    Zaman, D. M. S.; Amina, M.; Dip, P. R.; Mamun, A. A.

    2017-11-01

    The basic properties of planar and non-planar (spherical and cylindrical) nucleus-acoustic (NA) shock structures (SSs) in a strongly coupled self-gravitating degenerate quantum plasma system (containing strongly coupled non-relativistically degenerate heavy nuclear species, weakly coupled non-relativistically degenerate light nuclear species, and inertialess non-/ultra-relativistically degenerate electrons) have been investigated. The generalized quantum hydrodynamic model and the reductive perturbation method have been used to derive the modified Burgers equation. It is shown that the strong correlation among heavy nuclear species acts as the source of dissipation and is responsible for the formation of the NA SSs with positive (negative) electrostatic (self-gravitational) potential. It is also observed that the effects of non-/ultra-relativistically degenerate electron pressure, dynamics of non-relativistically degenerate light nuclear species, spherical geometry, etc., significantly modify the basic features of the NA SSs. The applications of our results in astrophysical compact objects like white dwarfs and neutron stars are briefly discussed.

  15. Lunar floor-fractured craters as magmatic intrusions: Geometry, modes of emplacement, associated tectonic and volcanic features, and implications for gravity anomalies

    Science.gov (United States)

    Jozwiak, Lauren M.; Head, James W.; Wilson, Lionel

    2015-03-01

    Lunar floor-fractured craters are a class of 170 lunar craters with anomalously shallow, fractured floors. Two end-member processes have been proposed for the floor formation: viscous relaxation, and subcrater magmatic intrusion and sill formation. Recent morphometric analysis with new Lunar Reconnaissance Orbiter Laser Altimeter (LOLA) and image (LROC) data supports an origin related to shallow magmatic intrusion and uplift. We find that the distribution and characteristics of the FFC population correlates strongly with crustal thickness and the predicted frequency distribution of overpressurization values of magmatic dikes. For a typical nearside lunar crustal thickness, dikes with high overpressurization values favor surface effusive eruptions, medium values favor intrusion and sill formation, and low values favor formation of solidified dikes concentrated lower in the crust. We develop a model for this process, make predictions for the morphologic, morphometric, volcanic, and geophysical consequences of the process and then compare these predictions with the population of observed floor-fractured craters. In our model, the process of magmatic intrusion and sill formation begins when a dike propagates vertically towards the surface; as the dike encounters the underdense brecciated region beneath the crater, the magmatic driving pressure is insufficient to continue vertical propagation, but pressure in the stalled dike exceeds the local lithostatic pressure. The dike then begins to propagate laterally forming a sill which does not propagate past the crater floor region because increased overburden pressure from the crater wall and rim crest pinch off the dike at this boundary; the sill then continues to inflate, further raising and fracturing the brittle crater floor. When the intrusion diameter to intrusion depth ratio is smaller than a critical value, the intrusion assumes a laccolith shape with a domed central region. When the ratio exceeds a critical value

  16. Molecular geometry

    CERN Document Server

    Rodger, Alison

    1995-01-01

    Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

  17. Hydraulic fracture propagation modeling and data-based fracture identification

    Science.gov (United States)

    Zhou, Jing

    Successful shale gas and tight oil production is enabled by the engineering innovation of horizontal drilling and hydraulic fracturing. Hydraulically induced fractures will most likely deviate from the bi-wing planar pattern and generate complex fracture networks due to mechanical interactions and reservoir heterogeneity, both of which render the conventional fracture simulators insufficient to characterize the fractured reservoir. Moreover, in reservoirs with ultra-low permeability, the natural fractures are widely distributed, which will result in hydraulic fractures branching and merging at the interface and consequently lead to the creation of more complex fracture networks. Thus, developing a reliable hydraulic fracturing simulator, including both mechanical interaction and fluid flow, is critical in maximizing hydrocarbon recovery and optimizing fracture/well design and completion strategy in multistage horizontal wells. A novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple nonplanar fractures' propagation in both homogeneous and heterogeneous reservoirs with or without pre-existing natural fractures. Initiation, growth, and coalescence of the microcracks will lead to the generation of macroscopic fractures, which is explicitly mimicked by failure and removal of bonds between particles from the discrete element network. This physics-based modeling approach leads to realistic fracture patterns without using the empirical rock failure and fracture propagation criteria required in conventional continuum methods. Based on this model, a sensitivity study is performed to investigate the effects of perforation spacing, in-situ stress anisotropy, rock properties (Young's modulus, Poisson's ratio, and compressive strength), fluid properties, and natural fracture properties on hydraulic fracture propagation. In addition, since reservoirs are buried thousands of feet below the surface, the

  18. Optical geometry

    International Nuclear Information System (INIS)

    Robinson, I.; Trautman, A.

    1988-01-01

    The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

  19. Architectural geometry

    KAUST Repository

    Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

    2014-01-01

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  20. Architectural geometry

    KAUST Repository

    Pottmann, Helmut

    2014-11-26

    Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

  1. Beautiful geometry

    CERN Document Server

    Maor, Eli

    2014-01-01

    If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

  2. The non-planar single-frequency ring laser with variable output coupling

    Science.gov (United States)

    Wu, Ke-ying; Yang, Su-hui; Wei, Guang-hui

    2002-03-01

    We put forward a novel non-planar single-frequency ring laser, which consists of a corner cube prism and a specially cut Porro prism made by Nd:YAG crystal. The relative angle between the corner cube and the Porro prism could be adjusted to control the output coupling of the laser resonator and the polarization-state of the output laser. A 1.06 μm single-frequency laser with 1 W output has been obtained.

  3. Ambient mass spectrometry: From the planar to the non-planar surface analysis

    Czech Academy of Sciences Publication Activity Database

    Rejšek, Jan; Vrkoslav, Vladimír; Cvačka, Josef

    2017-01-01

    Roč. 15, č. 1 (2017), s. 31 ISSN 2336-7202. [Mezioborové setkání mladých biologů, biochemiků a chemiků /17./. 30.05.2017-01.06.2017, Milovy] Institutional support: RVO:61388963 Keywords : ambient mass spectrometry * thin layer chromatography * non-planar surface analysis Subject RIV: CB - Analytical Chemistry, Separation

  4. Film formation of non-planar phthalocyanines on copper(i) iodide

    OpenAIRE

    Ramadan, A. J.; Fearn, S.; Jones, T. S. (Tim S.); Heutz, S.; Rochford, L. A. (Luke A.)

    2016-01-01

    Structural templating is frequently used in organic photovoltaic devices to control the properties of the functional layers and therefore improve efficiencies. Modification of the substrate temperatures has also been shown to impact the structure and morphology of phthalocyanine thin films. Here we combine templating by copper iodide and high substrate temperature growth and study its effect on the structure and morphology of two different non-planar phthalocyanines, chloroaluminium (ClAlPc) ...

  5. Fracture Mechanics

    International Nuclear Information System (INIS)

    Jang, Dong Il; Jeong, Gyeong Seop; Han, Min Gu

    1992-08-01

    This book introduces basic theory and analytical solution of fracture mechanics, linear fracture mechanics, non-linear fracture mechanics, dynamic fracture mechanics, environmental fracture and fatigue fracture, application on design fracture mechanics, application on analysis of structural safety, engineering approach method on fracture mechanics, stochastic fracture mechanics, numerical analysis code and fracture toughness test and fracture toughness data. It gives descriptions of fracture mechanics to theory and analysis from application of engineering.

  6. An Automatic Multi-Target Independent Analysis Framework for Non-Planar Infrared-Visible Registration.

    Science.gov (United States)

    Sun, Xinglong; Xu, Tingfa; Zhang, Jizhou; Zhao, Zishu; Li, Yuankun

    2017-07-26

    In this paper, we propose a novel automatic multi-target registration framework for non-planar infrared-visible videos. Previous approaches usually analyzed multiple targets together and then estimated a global homography for the whole scene, however, these cannot achieve precise multi-target registration when the scenes are non-planar. Our framework is devoted to solving the problem using feature matching and multi-target tracking. The key idea is to analyze and register each target independently. We present a fast and robust feature matching strategy, where only the features on the corresponding foreground pairs are matched. Besides, new reservoirs based on the Gaussian criterion are created for all targets, and a multi-target tracking method is adopted to determine the relationships between the reservoirs and foreground blobs. With the matches in the corresponding reservoir, the homography of each target is computed according to its moving state. We tested our framework on both public near-planar and non-planar datasets. The results demonstrate that the proposed framework outperforms the state-of-the-art global registration method and the manual global registration matrix in all tested datasets.

  7. Silica-based microstructures on nonplanar substrates by femtosecond laser-induced nonlinear lithography

    International Nuclear Information System (INIS)

    Mizoshiri, M; Nishiyama, H; Hirata, Y; Nishii, J

    2009-01-01

    We developed a technique for the formation of nonplanar surfaces of inorganic optical materials by a combined process of nonlinear lithography and plasma etching. This technique can be used to fabricate structures even on non-flat substrates, which is difficult using current semiconductor technology. Three-dimensional patterns were written directly inside a positive-tone photoresist using femtosecond laser-induced nonlinear optical absorption. The patterns were then transferred to underlying nonplanar substrates by the ion beam etching technique. For the lithographic process, we obtained a minimum feature size of 900 nm, which is below the diffraction limit. We demonstrated the fabrication of silica-based hybrid diffractive-refractive lenses. Fresnel zone plates with smooth surfaces were obtained on convex microlenses. When a 633-nm-wavelength He-Ne laser was coupled normally to the hybrid lens, the primary focal length was measured as 630 μm. This hybridization shifted the focal length by 200 μm, which agreed with the theoretical value. Our process is useful for the precise fabrication of nonplanar structures based on inorganic materials.

  8. Analytische Geometrie

    Science.gov (United States)

    Kemnitz, Arnfried

    Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.

  9. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  10. Information geometry

    CERN Document Server

    Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

    2017-01-01

    The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

  11. Nonplanar property study of antifungal agent tolnaftate-spectroscopic approach

    Science.gov (United States)

    Arul Dhas, D.; Hubert Joe, I.; Roy, S. D. D.; Balachandran, S.

    2011-09-01

    Vibrational analysis of the thionocarbamate fungicide tolnaftate which is antidermatophytic, antitrichophytic and antimycotic agent, primarily inhibits the ergosterol biosynthesis in the fungus, was carried out using NIR FT-Raman and FTIR spectroscopic techniques. The equilibrium geometry, various bonding features, harmonic vibrational wavenumbers and torsional potential energy surface (PES) scan studies have been computed using density functional theory method. The detailed interpretation of the vibrational spectra has been carried out with the aid of VEDA.4 program. Vibrational spectra, natural bonding orbital (NBO) analysis and optimized molecular structure show the clear evidence for electronic interaction of thionocarbamate group with aromatic ring. Predicted electronic absorption spectrum from TD-DFT calculation has been compared with the UV-vis spectrum. The Mulliken population analysis on atomic charges and the HOMO-LUMO energy were also calculated. Vibrational analysis reveals that the simultaneous IR and Raman activation of the C-C stretching mode in the phenyl and naphthalene ring provide evidence for the charge transfer interaction between the donor and acceptor groups and is responsible for its bioactivity as a fungicide.

  12. Relationships between fractures

    Science.gov (United States)

    Peacock, D. C. P.; Sanderson, D. J.; Rotevatn, A.

    2018-01-01

    Fracture systems comprise many fractures that may be grouped into sets based on their orientation, type and relative age. The fractures are often arranged in a network that involves fracture branches that interact with one another. Interacting fractures are termed geometrically coupled when they share an intersection line and/or kinematically coupled when the displacements, stresses and strains of one fracture influences those of the other. Fracture interactions are characterised in terms of the following. 1) Fracture type: for example, whether they have opening (e.g., joints, veins, dykes), closing (stylolites, compaction bands), shearing (e.g., faults, deformation bands) or mixed-mode displacements. 2) Geometry (e.g., relative orientations) and topology (the arrangement of the fractures, including their connectivity). 3) Chronology: the relative ages of the fractures. 4) Kinematics: the displacement distributions of the interacting fractures. It is also suggested that interaction can be characterised in terms of mechanics, e.g., the effects of the interaction on the stress field. It is insufficient to describe only the components of a fracture network, with fuller understanding coming from determining the interactions between the different components of the network.

  13. Mathematical modelling of ultrasonic testing of components with defects close to a non-planar surface

    International Nuclear Information System (INIS)

    Westlund, Jonathan; Bostroem, Anders

    2011-05-01

    Nondestructive testing with ultrasound is a standard procedure in the nuclear power industry. To develop and qualify the methods extensive experimental work with test blocks is usually required. This can be very time-consuming and costly and it also requires a good physical intuition of the situation. A reliable mathematical model of the testing situation can, therefore, be very valuable and cost-effective as it can reduce experimental work significantly. A good mathematical model enhances the physical intuition and is very useful for parametric studies, as a pedagogical tool, and for the qualification of procedures and personnel. The aim of the present report is to describe work that has been performed to model ultrasonic testing of components that contain a defect close to a nonplanar surface. For nuclear power applications this may be a crack or other defect on the inside of a pipe with a diameter change or connection. This is an extension of the computer program UTDefect, which previously only admits a planar back surface (which is often applicable also to pipes if the pipe diameter is large enough). The problems are investigated in both 2D and 3D, and in 2D both the simpler anti-plane (SH) and the in-plane (P-SV) problem are studied. The 2D investigations are primarily solved to get a 'feeling' for the solution procedure, the discretizations, etc. In all cases an integral equation approach with a Green's function in the kernel is taken. The nonplanar surface is treated by the boundary element method (BEM) where a division of the surface is made in small elements. The defects are mainly cracks, strip-like (in 2D) or rectangular (in 3D), and these are treated with more analytical methods. In 2D also more general defects are treated with the help of their transition (T) matrix. As in other parts of UTDefect the ultrasonic probes in transmission and reception are included in the model. In 3D normalization by a side drilled hole is possible. Some numerical results

  14. Analytic geometry

    CERN Document Server

    Burdette, A C

    1971-01-01

    Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st

  15. Geometry Revealed

    CERN Document Server

    Berger, Marcel

    2010-01-01

    Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,

  16. Vector geometry

    CERN Document Server

    Robinson, Gilbert de B

    2011-01-01

    This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom

  17. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  18. Projective Geometry

    Indian Academy of Sciences (India)

    mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.

  19. Geometry -----------~--------------RESONANCE

    Indian Academy of Sciences (India)

    Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.

  20. Non-planar ion-acoustic solitary waves and their head-on collision in a plasma with nonthermal electrons and warm adiabatic ions

    Energy Technology Data Exchange (ETDEWEB)

    Han Jiuning; He Yonglin; Chen Yan; Zhang Kezhi; Ma Baohong [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China)

    2013-01-15

    By using the model of Cairns et al.[Geophys. Rev. Lett. 22, 2709 (1995)], the head-on collision of cylindrical/spherical ion-acoustic solitary waves in an unmagnetized non-planar plasma consisting of warm adiabatic ions and nonthermally distributed electrons is investigated. The extended Poincare-Lighthill-Kuo perturbation method is used to derive the modified Korteweg-de Vries equations for ion-acoustic solitary waves in this plasma system. The effects of the plasma geometry m, the ion to electron temperature ratio {sigma}, and the nonthermality of the electron distribution {alpha} on the interaction of the colliding solitary waves are studied. It is found that the plasma geometries have a big impact on the phase shifts of solitary waves. Also it is important to note that the phase shifts induced by the collision of compressive and rarefactive solitary waves are very different. We point out that this study is useful to the investigations about the observations of electrostatic solitary structures in astrophysical as well as in experimental plasmas with nonthermal energetic electrons.

  1. Massive planar and non-planar double box integrals for light N f contributions to

    Science.gov (United States)

    von Manteuffel, Andreas; Studerus, Cedric

    2013-10-01

    We present the master integrals needed for the light fermionic two-loop corrections to top quark pair production in the gluon fusion channel. Via the method of differential equations we compute the results in terms of multiple polylogarithms in a Laurent series about d = 4, where d is the space-time dimension. The most involved topology is a non-planar double box with one internal mass. We employ the coproduct-augmented symbol calculus and show that significant simplifications are possible for selected results using an optimised set of multiple polylogarithms.

  2. Riemannian geometry

    CERN Document Server

    Petersen, Peter

    2016-01-01

    Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

  3. Special geometry

    International Nuclear Information System (INIS)

    Strominger, A.

    1990-01-01

    A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)

  4. A Novel Non-Planar Transverse Stretching Process for Micro-Porous PTFE Membranes and Resulting Characteristics

    KAUST Repository

    Chang, Y.-H.

    2018-02-26

    Polytetrafluoroethylene (PTFE) micro-porous membranes were prepared from PTFE fine powder through extruding, rolling, and uniaxial longitudinally stretching. In contrast to conventional planar transverse stretching, a novel 3D mold design of non-planar transverse stretching process was employed in this study to produce micro-porous structure. The morphology, membrane thickness, mean pore size, and porosity of the PTFE membrane were investigated. The results show that the non-planar transverse stretched membranes exhibit more uniform average pore diameter with thinner membrane thickness. Morphological changes induced by planar and non-planar transverse stretching for pore characteristics were investigated. The stretching conditions, stretching temperature and rate, affect the stretched membrane. Increasing temperature facilitated the uniformity of pore size and uniformity of membrane thickness. Moreover, increase in stretching rate resulted in finer pore size and thinner membrane.

  5. General Geometry and Geometry of Electromagnetism

    OpenAIRE

    Shahverdiyev, Shervgi S.

    2002-01-01

    It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

  6. Covalent functionalization of octagraphene with magnetic octahedral B6- and non-planar C6- clusters

    Science.gov (United States)

    Chigo-Anota, E.; Cárdenas-Jirón, G.; Salazar Villanueva, M.; Bautista Hernández, A.; Castro, M.

    2017-10-01

    The interaction between the magnetic boron octahedral (B6-) and non-planar (C6-) carbon clusters with semimetal nano-sheet of octa-graphene (C64H24) in the gas phase is studied by means of DFT calculations. These results reveal that non-planar-1 (anion) carbon cluster exhibits structural stability, low chemical reactivity, magnetic (1.0 magneton bohr) and semiconductor behavior. On the other hand, there is chemisorption phenomena when the stable B6- and C6- clusters are absorbed on octa-graphene nanosheets. Such absorption generates high polarity and the low-reactivity remains as on the individual pristine cases. Electronic charge transference occurs from the clusters toward the nanosheets, producing a reduction of the work function for the complexes and also induces a magnetic behavior on the functionalized sheets. The quantum descriptors obtained for these systems reveal that they are feasible candidates for the design of molecular circuits, magnetic devices, and nano-vehicles for drug delivery.

  7. Novel nonplanar triphenylamine-centered oligofluorenes: Synthesis, thermal, photophysical and electrochemical properties

    International Nuclear Information System (INIS)

    Zhang Yujian; Ouyang Mi; Yu Chunhui; Hu Bin; Lou Qianping; Zhang Cheng

    2011-01-01

    A series of fluorene derivatives containing a triphenylamine (TPA) derivative core and two oligofluorene peripheries was effectively synthesized. These compounds are fluorescent and emission color ranges from blue to red. The spiro-skeleton molecular structure leads to excellent glass transition temperatures and weak intermolecular interactions. Simultaneously, novel nonplanar triphenylamine-centered oligofluorenes solve the spectral stability problem and hole-injection issue for fluorene-based materials. The photophysical properties of 6 and 7 are investigated in solvents with different polarities, which reveal the existence of the Charge Transfer (CT) excited-state in these molecules. - Highlights: → Novel nonplanar oligofluorenes consisting of triphenylamine (TPA) derivatives as the core and oligofluorenes as the peripheries were facilely prepared via CF 3 SO 3 H-promoted Friedel-Crafts and Suzuki cross-coupling reactions. → These as-prepared compounds effectively solve the spectral stability problem and hole-injection issue for fluorene-based materials. → The ability of hole-injection and emission color could be fine tuned by R substituent at the C4 position of TPA.

  8. Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Verheest, Frank [Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B–9000 Gent (Belgium); School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000 (South Africa); Hellberg, Manfred A. [School of Chemistry and Physics, University of KwaZulu-Natal, Durban 4000 (South Africa)

    2016-06-15

    More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions.

  9. Chaotic non-planar vibrations of the thin elastica. Part I: Experimental observation of planar instability

    Science.gov (United States)

    Cusumano, J. P.; Moon, F. C.

    1995-01-01

    In this two-part paper, the results of an investigation into the non-linear dynamics of a flexible cantilevered rod (the elastica) with a thin rectangular cross-section are presented. An experimental examination of the dynamics of the elastica over a broad parameter range forms the core of Part I. In Part II, the experimental work is related to a theoretical study of the mechanics of the elastica, and the study of a two-degree-of-freedom model obtained by modal projection. The experimental system used in this investigation is a rod with clamped-free boundary conditions, forced by sinusoidally displacing the clamped end. Planar periodic motions of the driven elastica are shown to lose stability at distinct resonant wedges, and the resulting motions are shown in general to be non-planar, chaotic, bending-torsion oscillations. Non-planar motions in all resonances exhibit energy cascading and dynamic two-well phenomena, and a family of asymmetric, bending-torsion non-linear modes is discovered. Correlation dimension calculations are used to estimate the number of active degrees of freedom in the system.

  10. Differential geometry

    CERN Document Server

    Ciarlet, Philippe G

    2007-01-01

    This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

  11. Nonplanar machines

    International Nuclear Information System (INIS)

    Ritson, D.

    1989-05-01

    This talk examines methods available to minimize, but never entirely eliminate, degradation of machine performance caused by terrain following. Breaking of planar machine symmetry for engineering convenience and/or monetary savings must be balanced against small performance degradation, and can only be decided on a case-by-case basis. 5 refs

  12. Flow characteristics through a single fracture of artificial fracture system

    International Nuclear Information System (INIS)

    Park, Byoung Yoon; Bae, Dae Seok; Kim, Chun Soo; Kim, Kyung Su; Koh, Young Kwon; Jeon, Seok Won

    2001-04-01

    Fracture flow in rock masses is one of the most important issues in petroleum engineering, geology, and hydrogeology. Especially, in case of the HLW disposal, groundwater flow in fractures is an important factor in the performance assessment of the repository because the radionuclides move along the flowing groundwater through fractures. Recently, the characterization of fractures and the modeling of fluid flow in fractures are studied by a great number of researchers. Among those studies, the hydraulic behavior in a single fracture is one of the basic issues for understanding of fracture flow in rockmass. In this study, a fluid flow test in the single fracture made of transparent epoxy replica was carried out to obtain the practical exponent values proposed from the Cubic law and to estimate the flow rates through a single fracture. Not only the relationship between flow rates and the geometry of fracture was studied, but also the various statistical parameters of fracture geometry were compared to the effective transmissivity data obtained from computer simulation.

  13. Printing line/space patterns on nonplanar substrates using a digital micromirror device-based point-array scanning technique

    Science.gov (United States)

    Kuo, Hung-Fei; Kao, Guan-Hsuan; Zhu, Liang-Xiu; Hung, Kuo-Shu; Lin, Yu-Hsin

    2018-02-01

    This study used a digital micromirror device (DMD) to produce point-array patterns and employed a self-developed optical system to define line-and-space patterns on nonplanar substrates. First, field tracing was employed to analyze the aerial images of the lithographic system, which comprised an optical system and the DMD. Multiobjective particle swarm optimization was then applied to determine the spot overlapping rate used. The objective functions were set to minimize linewidth and maximize image log slope, through which the dose of the exposure agent could be effectively controlled and the quality of the nonplanar lithography could be enhanced. Laser beams with 405-nm wavelength were employed as the light source. Silicon substrates coated with photoresist were placed on a nonplanar translation stage. The DMD was used to produce lithographic patterns, during which the parameters were analyzed and optimized. The optimal delay time-sequence combinations were used to scan images of the patterns. Finally, an exposure linewidth of less than 10 μm was successfully achieved using the nonplanar lithographic process.

  14. Application of Young-Michelson and Brown-Twiss interferometers for determining geometric parameters of nonplanar rough objects

    NARCIS (Netherlands)

    Mandrosov, V. I.

    The possibility of using Young-Michelson and Brown-Twiss interferometers for measuring the angular dimensions and parameters of the surface shape of remote passively scattering and self-luminous nonplanar rough objects by optical radiation propagating from them is substantiated. The analysis is

  15. Sodium-cutting: a new top-down approach to cut open nanostructures on nonplanar surfaces on a large scale.

    Science.gov (United States)

    Chen, Wei; Deng, Da

    2014-11-11

    We report a new, low-cost and simple top-down approach, "sodium-cutting", to cut and open nanostructures deposited on a nonplanar surface on a large scale. The feasibility of sodium-cutting was demonstrated with the successfully cutting open of ∼100% carbon nanospheres into nanobowls on a large scale from Sn@C nanospheres for the first time.

  16. Application of MCD spectroscopy and TD-DFT to a highly non-planar porphyrinoid ring system. New insights on red-shifted porphyrinoid spectral bands.

    Science.gov (United States)

    Mack, John; Asano, Yoshiaki; Kobayashi, Nagao; Stillman, Martin J

    2005-12-21

    The first magnetic circular dichroism (MCD) spectra are reported for tetraphenyltetraacenaphthoporphyrin (TPTANP). The impact on the electronic structure of steric interactions between the fused acenaphthalene rings and the meso-tetraphenyl substituents is explored based on an analysis of the optical spectra of the Zn(II) complex (ZnTPTANP) and the free base dication species ([H4TPTANP]2+). In the case of ZnTPTANP, significant folding of the porphyrinoid ligand induces a highly unusual MCD-sign reversal providing the first direct spectroscopic evidence of ligand nonplanarity. Density functional theory (DFT) geometry optimizations for a wide range of Zn(II) porphyrinoids based on the B3LYP functional and TD-DFT calculations of the associated UV-visible absorption spectra are reported, allowing a complete assessment of the MCD data. TPTANP complexes are found to fall into a class of cyclic polyenes, termed as soft MCD chromophores by Michl (J. Pure Appl. Chem. 1980, 52, 1549.), since the signs of the Faraday A1 terms observed in the MCD spectrum are highly sensitive to slight structural changes. The origin of an unusually large red shift of the main B (or Soret) band of MTPTANP (the most red shifted ever reported for fused-ring-expanded metal porphines) and of similar red shifts observed in the spectra of other peripherally crowded porphyrinoid complexes is also explored and explained on this basis.

  17. Nonplanar nanoselective area growth of InGaAs/InP

    DEFF Research Database (Denmark)

    Kuznetsova, Nadezda; Colman, Pierre; Semenova, Elizaveta

    2014-01-01

    In this study, we have investigated metal-organic vapor phase epitaxial nano-patterned selective area growth of InGaAs/InP on non-planar (001) InP surfaces. Due to high etching resistance and the small molecular size of negative tone electron beam HSQ resist, the protection mask formed in HSQ has...... small feature sizes in ten nanometers scale and allow realization of in-situ etching. As was observed in the SAG regime, in-situ etching of InP by carbon tetrabromide leads to formation of self-limited structures. By altering etching time, the groove shape can be changed from a triangular trench...... to anistropic or isotropic character of etching. The investigated technique of nano-patterned selective area growth allows obtaining different profiles of structures and different quantum structures such as quantum well or wires in the same growth run. To investigate the shape and crystalline quality...

  18. Non-planar dislocations: 3D models and thermally-activated glide processes

    International Nuclear Information System (INIS)

    Ngan, A.H.W.

    2005-01-01

    In recent years, there has been a renewed interest in studying the cross-slip of screw dislocations in the simple face-centred cubic (FCC) structure. This paper serves to address parallel developments in modelling the cross-slip of screw dislocations in the body-centred cubic (BCC) structure and the ordered L1 2 structure. In the latter two cases, the dislocation cores have non-planar spreading offering high intrinsic Peierls stresses. The flow behaviours of these materials, such as the non-Schmid behaviour and temperature-dependence of flow stress, are largely due to the behaviours of single dislocations. 3D atomistic modelling of the minimum-energy path for the glide processes in these cases is performed with an aim to reconcile with experimentally determined activation energies for slip

  19. Nanopatterning of tools for replication of non-planar polymer surfaces

    DEFF Research Database (Denmark)

    Cech, Jiri

    in the order of expected lifetime in descending order: aluminum, titanium, and nickel. The second problem addressed is the forming of a nanostructured surface on a non-planar substrate. We used the hydrostatic nanoimprinting technique, with the HSQ films deposited by spin-coating and spray-coating methods...... with nanostructured surfaces, we need to fabricate molds facing the same problem. In this work, we address this problem. At first, we need to verify if the previously reported monolayer adhesion-reducing coating (FDTS) can be used under different conditions during actual injection molding. Such coatings are critical...... to facilitate de-molding of the nanopatterned parts. We analyzed the coated surfaces of aluminum, titanium, and nickel molds before and after 500 molding cycles, using X-ray photoelectron spectroscopy, AFM and contact angle measurements. We show that the contact angle and that the fluorine concentration...

  20. Iterative reconstruction with attenuation compensation from cone-beam projections acquired via nonplanar orbits

    International Nuclear Information System (INIS)

    Zeng, G.L.; Weng, Y.; Gullberg, G.T.

    1997-01-01

    Single photon emission computed tomography (SPECT) imaging with cone-beam collimators provides improved sensitivity and spatial resolution for imaging small objects with large field-of-view detectors. It is known that Tuy's cone-beam data sufficiency condition must be met to obtain artifact-free reconstructions. Even though Tuy's condition was derived for an attenuation-free situation, the authors hypothesize that an artifact-free reconstruction can be obtained even if the cone-beam data are attenuated, provided the imaging orbit satisfies Tuy's condition and the exact attenuation map is known. In the authors' studies, emission data are acquired using nonplanar circle-and-line orbits to acquire cone-beam data for tomographic reconstructions. An extended iterative ML-EM (maximum likelihood-expectation maximization) reconstruction algorithm is derived and used to reconstruct projection data with either a pre-acquired or assumed attenuation map. Quantitative accuracy of the attenuation corrected emission reconstruction is significantly improved

  1. Two-Loop Master Integrals for $\\gamma^{*} \\to 3$ Jets the Non-Planar Topologies

    CERN Document Server

    Gehrmann, T

    2001-01-01

    The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in $\\e=(4-d)/2$, where $d$ is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

  2. Hydrologic behavior of fracture networks

    International Nuclear Information System (INIS)

    Long, J.C.S.; Endo, H.K.; Karasaki, K.; Pyrak, L.; MacLean, P.; Witherspoon, P.A.

    1985-01-01

    This paper reviews recent research on the nature of flow and transport in discontinuous fracture networks. The hydrologic behavior of these networks has been examined using two- and three-dimensional numerical models. The numerical models represent random realizations of fracture networks based on statistical field measurements of fracture geometry and equivalent hydraulic aperture. The authors have compared the flux and mechanical transported behavior of these networks to the behavior of equivalent continua. In this way they were able to determine whether a given fracture network could be modeled as an equivalent porous media in both flux and advective transport studies. They have examined departures from porous media behavior both as a function of interconnectivity and heterogeneity. Parameter studies have revealed behavior patterns such as: given a fracture frequency that can be measured in the field, porous media like behavior and the magnitude of permeability are both enhanced if the fractures are longer and the standard deviation of fracture permeabilities is smaller. The behavior of well tests in fractured networks has been modeled and compared to a new analytical well test solution which accounts for the early time dominance of the fractures intersecting the well. Finally, a three-dimensional fracture flow model has been constructed which assumes fractures are randomly located discs. This model has been constructed which assumes fractures are randomly located discs. This model uses a semi-analytical solution for flow such that it is relatively easy to use the model as a tool for stochastic analysis. 13 references, 12 figures

  3. Rock fracture processes in chemically reactive environments

    Science.gov (United States)

    Eichhubl, P.

    2015-12-01

    Rock fracture is traditionally viewed as a brittle process involving damage nucleation and growth in a zone ahead of a larger fracture, resulting in fracture propagation once a threshold loading stress is exceeded. It is now increasingly recognized that coupled chemical-mechanical processes influence fracture growth in wide range of subsurface conditions that include igneous, metamorphic, and geothermal systems, and diagenetically reactive sedimentary systems with possible applications to hydrocarbon extraction and CO2 sequestration. Fracture processes aided or driven by chemical change can affect the onset of fracture, fracture shape and branching characteristics, and fracture network geometry, thus influencing mechanical strength and flow properties of rock systems. We are investigating two fundamental modes of chemical-mechanical interactions associated with fracture growth: 1. Fracture propagation may be aided by chemical dissolution or hydration reactions at the fracture tip allowing fracture propagation under subcritical stress loading conditions. We are evaluating effects of environmental conditions on critical (fracture toughness KIc) and subcritical (subcritical index) fracture properties using double torsion fracture mechanics tests on shale and sandstone. Depending on rock composition, the presence of reactive aqueous fluids can increase or decrease KIc and/or subcritical index. 2. Fracture may be concurrent with distributed dissolution-precipitation reactions in the hostrock beyond the immediate vicinity of the fracture tip. Reconstructing the fracture opening history recorded in crack-seal fracture cement of deeply buried sandstone we find that fracture length growth and fracture opening can be decoupled, with a phase of initial length growth followed by a phase of dominant fracture opening. This suggests that mechanical crack-tip failure processes, possibly aided by chemical crack-tip weakening, and distributed solution-precipitation creep in the

  4. Oxidative stress and apoptosis of Carassius auratus lymphocytes induced by nonplanar (PCB153) and coplanar (PCB169) polychlorinated biphenyl congeners in vitro

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jian-ying; ZHANG Hang-jun; NI Wan-min

    2009-01-01

    and the coplanar congener was more cytotoxic than nonplanar congener. This study suggests that cytotoxicity mechanisms of the PCB congeners on fish lymphocytes depend on their planarity and chemical structures.

  5. Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

    Energy Technology Data Exchange (ETDEWEB)

    Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua; Nan, Ya-Gong; Han, Zhen-Hai; Dong, Guang-Xing [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Duan, Wen-Shan [College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China); Li, Jun-Xiu [College of Civil Engineering, Hexi University, Zhangye 734000 (China)

    2014-01-15

    With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.

  6. Seismic Characterizations of Fractures: Dynamic Diagnostics

    Science.gov (United States)

    Pyrak-Nolte, L. J.

    2017-12-01

    Fracture geometry controls fluid flow in a fracture, affects mechanical stability and influences energy partitioning that affects wave scattering. Our ability to detect and monitor fracture evolution is controlled by the frequency of the signal used to probe a fracture system, i.e. frequency selects the scales. No matter the frequency chosen, some set of discontinuities will be optimal for detection because different wavelengths sample different subsets of fractures. The select subset of fractures is based on the stiffness of the fractures which in turn is linked to fluid flow. A goal is obtaining information from scales outside the optimal detection regime. Fracture geometry trajectories are a potential approach to drive a fracture system across observation scales, i.e. moving systems between effective medium and scattering regimes. Dynamic trajectories (such as perturbing stress, fluid pressure, chemical alteration, etc.) can be used to perturb fracture geometry to enhance scattering or give rise to discrete modes that are intimately related to the micro-structural evolution of a fracture. However, identification of these signal features will require methods for identifying these micro-structural signatures in complicated scattered fields. Acknowledgment: This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program under Award Number (DE-FG02-09ER16022).

  7. Complex analysis and geometry

    CERN Document Server

    Silva, Alessandro

    1993-01-01

    The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

  8. Non-Riemannian geometry

    CERN Document Server

    Eisenhart, Luther Pfahler

    2005-01-01

    This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

  9. Geometry of the Universe

    International Nuclear Information System (INIS)

    Gurevich, L.Eh.; Gliner, Eh.B.

    1978-01-01

    Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

  10. Studies of urea geometry by means of ab initio methods and computer simulations of liquids

    OpenAIRE

    Cirino, José Jair Vianna; Bertran, Celso Aparecido

    2002-01-01

    A study was carried out on the urea geometries using ab initio calculation and Monte Carlo computational simulation of liquids. The ab initio calculated results showed that urea has a non-planar conformation in the gas phase in which the hydrogen atoms are out of the plane formed by the heavy atoms. Free energies associated to the rotation of the amino groups of urea in water were obtained using the Monte Carlo method in which the thermodynamic perturbation theory is implemented. The magnitud...

  11. Hip Fracture

    Science.gov (United States)

    ... hip fractures in people of all ages. In older adults, a hip fracture is most often a result of a fall from a standing height. In people with very weak bones, a hip fracture can occur simply by standing on the leg and twisting. Risk factors The rate of hip fractures increases substantially with ...

  12. Manufactoring the non-planar coils for the Wendelstein 7-X experiment

    International Nuclear Information System (INIS)

    Scheller, H.; Theisen, E.; Heyn, K.

    2005-01-01

    Because of the conditions associated with is use, nuclear fusion is a highly promising future energy supply option. The current objective of research worldwide is to demonstrate the feasibility of fusion power plants. The Wendelstein 7-X experiment at present under construction in Greifswald by the Max Planck Institute for Plasma Physics (IPP) is to demonstrate this feasibility for the stellarator concept. Babcock Noell Nuclear (BNN) in a consortium with Ansaldo Superconduttori, Genoa (ASG) has been commissioned by IPP to build the fifty superconducting non-planar coils constituting the magnet cage of the Wendelstein 7-X experiment. The coils will be assembled at the Zeitz manufacturing plant of BNM, a subsidiary of BNN. Manufacturing such a complex system is possible with the proper europeanwide network of subcontractors contributing special components. Thus, the superconductors were made by the German-Italian consortium, EAS, Hanau, and OCSI, Fornaci di Barga, Italy; the stainless steel housings are cast be Oesterby Gjutery AB in Sweden, the winding packs for BNN are produced by ABB, Neusaess, and mechanical finishing and final 3D measurement is performed by C-CON in Germany. (orig.)

  13. Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

    International Nuclear Information System (INIS)

    Singh, L.P.; Ram, S.D.; Singh, D.B.

    2011-01-01

    Highlights: → An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. → The density ahead of the shock is taken as a power of the position from the origin of the shock wave. → For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. → The solution obtained for the planer, and cylindrically symmetric flow is new one. → The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

  14. Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits

    International Nuclear Information System (INIS)

    Kudo, Hiroyuki; Saito, Tsuneo

    1994-01-01

    Smith and Grangeat derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's, they have similar overall structures to each other. The contribution of this paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam backprojection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3-D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies

  15. Color-suppression of non-planar diagrams in bosonic bound states

    Science.gov (United States)

    Alvarenga Nogueira, J. H.; Ji, Chueng-Ryong; Ydrefors, E.; Frederico, T.

    2018-02-01

    We study the suppression of non-planar diagrams in a scalar QCD model of a meson system in 3 + 1 space-time dimensions due to the inclusion of the color degrees of freedom. As a prototype of the color-singlet meson, we consider a flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark with equal masses exchanging a scalar-gluon of a different mass, which is investigated within the framework of the homogeneous Bethe-Salpeter equation. The equation is solved by using the Nakanishi representation for the manifestly covariant bound-state amplitude and its light-front projection. The resulting non-singular integral equation is solved numerically. The damping of the impact of the cross-ladder kernel on the binding energies are studied in detail. The color-suppression of the cross-ladder effects on the light-front wave function and the elastic electromagnetic form factor are also discussed. As our results show, the suppression appears significantly large for Nc = 3, which supports the use of rainbow-ladder truncations in practical non-perturbative calculations within QCD.

  16. Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

    Directory of Open Access Journals (Sweden)

    Marte Gutierrez

    2015-12-01

    Full Text Available Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses due to their relatively lower stiffness and shear strength than those of the rock matrix. Understanding the effects of fracture geometrical distribution, such as length, spacing, persistence and orientation, is important for quantifying the mechanical behavior of fractured rock masses. The relation between fracture geometry and the mechanical characteristics of the fractured rock mass is complicated due to the fact that the fracture geometry and mechanical behaviors of fractured rock mass are strongly dependent on the length scale. In this paper, a comprehensive study was conducted to determine the effects of fracture distribution on the equivalent continuum elastic compliance of fractured rock masses over a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, three different simulation techniques involving Oda's elastic compliance tensor, Monte Carlo simulation (MCS, and suitable probability density functions (PDFs were employed to represent the elastic compliance of fractured rock masses. To yield geologically realistic results, parameters for defining fracture distributions were obtained from different geological fields. The influence of the key fracture parameters and their relations to the overall elastic behavior of the fractured rock mass were studied and discussed. A detailed study was also carried out to investigate the validity of the use of a representative element volume (REV in the equivalent continuum representation of fractured rock masses. A criterion was also proposed to determine the appropriate REV given the fracture distribution of the rock mass.

  17. Dynamic earthquake rupture simulations on nonplanar faults embedded in 3D geometrically complex, heterogeneous elastic solids

    Energy Technology Data Exchange (ETDEWEB)

    Duru, Kenneth, E-mail: kduru@stanford.edu [Department of Geophysics, Stanford University, Stanford, CA (United States); Dunham, Eric M. [Department of Geophysics, Stanford University, Stanford, CA (United States); Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA (United States)

    2016-01-15

    Dynamic propagation of shear ruptures on a frictional interface in an elastic solid is a useful idealization of natural earthquakes. The conditions relating discontinuities in particle velocities across fault zones and tractions acting on the fault are often expressed as nonlinear friction laws. The corresponding initial boundary value problems are both numerically and computationally challenging. In addition, seismic waves generated by earthquake ruptures must be propagated for many wavelengths away from the fault. Therefore, reliable and efficient numerical simulations require both provably stable and high order accurate numerical methods. We present a high order accurate finite difference method for: a) enforcing nonlinear friction laws, in a consistent and provably stable manner, suitable for efficient explicit time integration; b) dynamic propagation of earthquake ruptures along nonplanar faults; and c) accurate propagation of seismic waves in heterogeneous media with free surface topography. We solve the first order form of the 3D elastic wave equation on a boundary-conforming curvilinear mesh, in terms of particle velocities and stresses that are collocated in space and time, using summation-by-parts (SBP) finite difference operators in space. Boundary and interface conditions are imposed weakly using penalties. By deriving semi-discrete energy estimates analogous to the continuous energy estimates we prove numerical stability. The finite difference stencils used in this paper are sixth order accurate in the interior and third order accurate close to the boundaries. However, the method is applicable to any spatial operator with a diagonal norm satisfying the SBP property. Time stepping is performed with a 4th order accurate explicit low storage Runge–Kutta scheme, thus yielding a globally fourth order accurate method in both space and time. We show numerical simulations on band limited self-similar fractal faults revealing the complexity of rupture

  18. Rib Fractures

    Science.gov (United States)

    ... Video) Achilles Tendon Tear Additional Content Medical News Rib Fractures By Thomas G. Weiser, MD, MPH, Associate Professor, ... Tamponade Hemothorax Injury to the Aorta Pulmonary Contusion Rib Fractures Tension Pneumothorax Traumatic Pneumothorax (See also Introduction to ...

  19. Root fractures

    DEFF Research Database (Denmark)

    Andreasen, Jens Ove; Christensen, Søren Steno Ahrensburg; Tsilingaridis, Georgios

    2012-01-01

    The purpose of this study was to analyze tooth loss after root fractures and to assess the influence of the type of healing and the location of the root fracture. Furthermore, the actual cause of tooth loss was analyzed....

  20. Stress Fractures

    Science.gov (United States)

    Stress fractures Overview Stress fractures are tiny cracks in a bone. They're caused by repetitive force, often from overuse — such as repeatedly jumping up and down or running long distances. Stress fractures can also arise from normal use of ...

  1. Slab1.0: A three-dimensional model of global subduction zone geometries

    Science.gov (United States)

    Hayes, Gavin P.; Wald, David J.; Johnson, Rebecca L.

    2012-01-01

    We describe and present a new model of global subduction zone geometries, called Slab1.0. An extension of previous efforts to constrain the two-dimensional non-planar geometry of subduction zones around the focus of large earthquakes, Slab1.0 describes the detailed, non-planar, three-dimensional geometry of approximately 85% of subduction zones worldwide. While the model focuses on the detailed form of each slab from their trenches through the seismogenic zone, where it combines data sets from active source and passive seismology, it also continues to the limits of their seismic extent in the upper-mid mantle, providing a uniform approach to the definition of the entire seismically active slab geometry. Examples are shown for two well-constrained global locations; models for many other regions are available and can be freely downloaded in several formats from our new Slab1.0 website, http://on.doi.gov/d9ARbS. We describe improvements in our two-dimensional geometry constraint inversion, including the use of ‘average’ active source seismic data profiles in the shallow trench regions where data are otherwise lacking, derived from the interpolation between other active source seismic data along-strike in the same subduction zone. We include several analyses of the uncertainty and robustness of our three-dimensional interpolation methods. In addition, we use the filtered, subduction-related earthquake data sets compiled to build Slab1.0 in a reassessment of previous analyses of the deep limit of the thrust interface seismogenic zone for all subduction zones included in our global model thus far, concluding that the width of these seismogenic zones is on average 30% larger than previous studies have suggested.

  2. Geometry and its applications

    CERN Document Server

    Meyer, Walter J

    2006-01-01

    Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

  3. Algebraic geometry in India

    Indian Academy of Sciences (India)

    algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.

  4. Spinorial Geometry and Branes

    International Nuclear Information System (INIS)

    Sloane, Peter

    2007-01-01

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  5. Spinorial Geometry and Branes

    Energy Technology Data Exchange (ETDEWEB)

    Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)

    2007-09-15

    We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)

  6. Compartmentalization analysis using discrete fracture network models

    Energy Technology Data Exchange (ETDEWEB)

    La Pointe, P.R.; Eiben, T.; Dershowitz, W. [Golder Associates, Redmond, VA (United States); Wadleigh, E. [Marathon Oil Co., Midland, TX (United States)

    1997-08-01

    This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.

  7. Quantum switching of π-electron rotations in a nonplanar chiral molecule by using linearly polarized UV laser pulses.

    Science.gov (United States)

    Mineo, Hirobumi; Yamaki, Masahiro; Teranishi, Yoshiaki; Hayashi, Michitoshi; Lin, Sheng Hsien; Fujimura, Yuichi

    2012-09-05

    Nonplanar chiral aromatic molecules are candidates for use as building blocks of multidimensional switching devices because the π electrons can generate ring currents with a variety of directions. We employed (P)-2,2'-biphenol because four patterns of π-electron rotations along the two phenol rings are possible and theoretically determine how quantum switching of the π-electron rotations can be realized. We found that each rotational pattern can be driven by a coherent excitation of two electronic states under two conditions: one is the symmetry of the electronic states and the other is their relative phase. On the basis of the results of quantum dynamics simulations, we propose a quantum control method for sequential switching among the four rotational patterns that can be performed by using ultrashort overlapped pump and dump pulses with properly selected relative phases and photon polarization directions. The results serve as a theoretical basis for the design of confined ultrafast switching of ring currents of nonplanar molecules and further current-induced magnetic fluxes of more sophisticated systems.

  8. Acetabular Fracture

    Directory of Open Access Journals (Sweden)

    Chad Correa

    2017-09-01

    Full Text Available History of present illness: A 77-year-old female presented to her primary care physician (PCP with right hip pain after a mechanical fall. She did not lose consciousness or have any other traumatic injuries. She was unable to ambulate post-fall, so X-rays were ordered by her PCP. Her X-rays were concerning for a right acetabular fracture (see purple arrows, so the patient was referred to the emergency department where a computed tomography (CT scan was ordered. Significant findings: The non-contrast CT images show a minimally displaced comminuted fracture of the right acetabulum involving the acetabular roof, medial and anterior walls (red arrows, with associated obturator muscle hematoma (blue oval. Discussion: Acetabular fractures are quite rare. There are 37 pelvic fractures per 100,000 people in the United States annually, and only 10% of these involve the acetabulum. They occur more frequently in the elderly totaling an estimated 4,000 per year. High-energy trauma is the primary cause of acetabular fractures in younger individuals and these fractures are commonly associated with other fractures and pelvic ring disruptions. Fractures secondary to moderate or minimal trauma are increasingly of concern in patients of advanced age.1 Classification of acetabular fractures can be challenging. However, the approach can be simplified by remembering the three basic types of acetabular fractures (column, transverse, and wall and their corresponding radiologic views. First, column fractures should be evaluated with coronally oriented CT images. This type of fracture demonstrates a coronal fracture line running caudad to craniad, essentially breaking the acetabulum into two halves: a front half and a back half. Secondly, transverse fractures should be evaluated by sagittally oriented CT images. By definition, a transverse fracture separates the acetabulum into superior and inferior halves with the fracture line extending from anterior to posterior

  9. Geometry essentials for dummies

    CERN Document Server

    Ryan, Mark

    2011-01-01

    Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

  10. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  11. Hydrologic behavior of fracture networks

    International Nuclear Information System (INIS)

    Long, J.C.S.; Endo, H.K.; Karasaki, K.; Pyrak, L.; MacLean, P.; Witherspoon, P.A.

    1984-10-01

    This paper reviews recent research on the nature of flow and transport in discontinuous fracture networks. The hydrologic behavior of these networks has been examined using two- and three-dimensional numerical models. The numerical models represent random realizations of fracture networks based on statistical field measurements of fracture geometry and equivalent hydraulic aperture. We have compared the flux and mechanical transport behavior of these networks to the behavior of equivalent continua. In this way we are able to determine whether a given fracture network can be modeled as an equivalent porous media in both flux and advective transport studies. We have examined departures from porous media behavior both as a function of interconnectivity and heterogeneity. Parameter studies have revealed behavior patterns such as: given a fracture frequency that can be measured in the field, porous media like behavior and the magnitude of permeability are both enhanced if the fractures are longer and the standard deviation of fracture permeabilities is smaller. Transport studies have shown that the ratio between flux and velocity is not necessarily constant when the direction of flow is changed in systems which do behave like a porous media for flux. Thus the conditions under which porous media analysis can be used in transport studies are more restrictive than the condition for flux studies. We have examined systems which do not behave like porous media and have shown how the in situ behavior varies as a function of scale of observation. The behavior of well tests in fractured networks has been modeled and compared to a new analytical well test solution which accounts for the early time dominance of the fractures intersecting the well. Finally, a three-dimensional fracture flow model has been constructed which assumes fractures are randomly located discs. 13 references, 12 figures

  12. An Embedded 3D Fracture Modeling Approach for Simulating Fracture-Dominated Fluid Flow and Heat Transfer in Geothermal Reservoirs

    Energy Technology Data Exchange (ETDEWEB)

    Johnston, Henry [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Wang, Cong [Colorado School of Mines; Winterfeld, Philip [Colorado School of Mines; Wu, Yu-Shu [Colorado School of Mines

    2018-02-14

    An efficient modeling approach is described for incorporating arbitrary 3D, discrete fractures, such as hydraulic fractures or faults, into modeling fracture-dominated fluid flow and heat transfer in fractured geothermal reservoirs. This technique allows 3D discrete fractures to be discretized independently from surrounding rock volume and inserted explicitly into a primary fracture/matrix grid, generated without including 3D discrete fractures in prior. An effective computational algorithm is developed to discretize these 3D discrete fractures and construct local connections between 3D fractures and fracture/matrix grid blocks of representing the surrounding rock volume. The constructed gridding information on 3D fractures is then added to the primary grid. This embedded fracture modeling approach can be directly implemented into a developed geothermal reservoir simulator via the integral finite difference (IFD) method or with TOUGH2 technology This embedded fracture modeling approach is very promising and computationally efficient to handle realistic 3D discrete fractures with complicated geometries, connections, and spatial distributions. Compared with other fracture modeling approaches, it avoids cumbersome 3D unstructured, local refining procedures, and increases computational efficiency by simplifying Jacobian matrix size and sparsity, while keeps sufficient accuracy. Several numeral simulations are present to demonstrate the utility and robustness of the proposed technique. Our numerical experiments show that this approach captures all the key patterns about fluid flow and heat transfer dominated by fractures in these cases. Thus, this approach is readily available to simulation of fractured geothermal reservoirs with both artificial and natural fractures.

  13. Experimental and Analytical Research on Fracture Processes in ROck

    Energy Technology Data Exchange (ETDEWEB)

    Herbert H.. Einstein; Jay Miller; Bruno Silva

    2009-02-27

    Experimental studies on fracture propagation and coalescence were conducted which together with previous tests by this group on gypsum and marble, provide information on fracturing. Specifically, different fracture geometries wsere tested, which together with the different material properties will provide the basis for analytical/numerical modeling. INitial steps on the models were made as were initial investigations on the effect of pressurized water on fracture coalescence.

  14. On time-dependent Hamiltonian realizations of planar and nonplanar systems

    Science.gov (United States)

    Esen, Oğul; Guha, Partha

    2018-04-01

    In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3 D systems. We illustrate our constructions with various examples.

  15. Mandible Fractures.

    Science.gov (United States)

    Pickrell, Brent B; Serebrakian, Arman T; Maricevich, Renata S

    2017-05-01

    Mandible fractures account for a significant portion of maxillofacial injuries and the evaluation, diagnosis, and management of these fractures remain challenging despite improved imaging technology and fixation techniques. Understanding appropriate surgical management can prevent complications such as malocclusion, pain, and revision procedures. Depending on the type and location of the fractures, various open and closed surgical reduction techniques can be utilized. In this article, the authors review the diagnostic evaluation, treatment options, and common complications of mandible fractures. Special considerations are described for pediatric and atrophic mandibles.

  16. The Geometry Conference

    CERN Document Server

    Bárány, Imre; Vilcu, Costin

    2016-01-01

    This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

  17. Facial Fractures.

    Science.gov (United States)

    Ghosh, Rajarshi; Gopalkrishnan, Kulandaswamy

    2018-06-01

    The aim of this study is to retrospectively analyze the incidence of facial fractures along with age, gender predilection, etiology, commonest site, associated dental injuries, and any complications of patients operated in Craniofacial Unit of SDM College of Dental Sciences and Hospital. This retrospective study was conducted at the Department of OMFS, SDM College of Dental Sciences, Dharwad from January 2003 to December 2013. Data were recorded for the cause of injury, age and gender distribution, frequency and type of injury, localization and frequency of soft tissue injuries, dentoalveolar trauma, facial bone fractures, complications, concomitant injuries, and different treatment protocols.All the data were analyzed using statistical analysis that is chi-squared test. A total of 1146 patients reported at our unit with facial fractures during these 10 years. Males accounted for a higher frequency of facial fractures (88.8%). Mandible was the commonest bone to be fractured among all the facial bones (71.2%). Maxillary central incisors were the most common teeth to be injured (33.8%) and avulsion was the most common type of injury (44.6%). Commonest postoperative complication was plate infection (11%) leading to plate removal. Other injuries associated with facial fractures were rib fractures, head injuries, upper and lower limb fractures, etc., among these rib fractures were seen most frequently (21.6%). This study was performed to compare the different etiologic factors leading to diverse facial fracture patterns. By statistical analysis of this record the authors come to know about the relationship of facial fractures with gender, age, associated comorbidities, etc.

  18. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  19. Revolutions of Geometry

    CERN Document Server

    O'Leary, Michael

    2010-01-01

    Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

  20. Fundamental concepts of geometry

    CERN Document Server

    Meserve, Bruce E

    1983-01-01

    Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

  1. Developments in special geometry

    International Nuclear Information System (INIS)

    Mohaupt, Thomas; Vaughan, Owen

    2012-01-01

    We review the special geometry of 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 discuss 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.

  2. Fracture sacrum.

    Directory of Open Access Journals (Sweden)

    Dogra A

    1995-04-01

    Full Text Available An extremely rare case of combined transverse and vertical fracture of sacrum with neurological deficit is reported here with a six month follow-up. The patient also had an L1 compression fracture. The patient has recovered significantly with conservative management.

  3. Fracture Mechanics

    CERN Document Server

    Zehnder, Alan T

    2012-01-01

    Fracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge. Alan Zehnder joined the faculty at Cornell University in 1988. Since then he has served in a number of leadership roles including Chair of the Department of Theoretical and Applied Mechanics, and Director of the Sibley School of Mechanical and Aerospace Engineering.  He teaches applied mechanics and his research t...

  4. Rigidifying Nonplanar Perylene Diimides by Ring Fusion Toward Geometry-Tunable Acceptors for High-Performance Fullerene-Free Solar Cells.

    Science.gov (United States)

    Zhong, Hongliang; Wu, Chen-Hao; Li, Chang-Zhi; Carpenter, Joshua; Chueh, Chu-Chen; Chen, Jung-Yao; Ade, Harald; Jen, Alex K-Y

    2016-02-03

    Rigid fused perylene diimide (PDI) dimers bridged with heterocycles exhibit superior photovoltaic performance compared to their unfused semiflexible analogues. Changing the chalcogen atoms in the aromatic bridges gradually increases the twist angles between the two PDI planes, leading to a varied morphology in which the one bridged by thiophene achieves a balance and shows the best efficiency of 6.72%. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  5. Application of Young-Michelson and Brown-Twiss interferometers for determining geometric parameters of nonplanar rough objects

    International Nuclear Information System (INIS)

    Mandrosov, V I

    2008-01-01

    The possibility of using Young-Michelson and Brown-Twiss interferometers for measuring the angular dimensions and parameters of the surface shape of remote passively scattering and self-luminous nonplanar rough objects by optical radiation propagating from them is substantiated. The analysis is based on the properties of approximate transverse functions of field coherence B t and B t ' and intensity coherence B ti and B ti ' formed by the time averaging of the products of fields and intensities taken at two points of a receiving aperture (the prime denotes self-luminous objects). The averaging time is set to be much longer than the coherence time of radiation propagating from an object. It is shown that for the radiation coherence length much smaller than the depth of the visible region of the object, the functions B t and B t ' are proportional to the Fourier transform of the intensity distribution in the image of a remote object, which is the generalisation of the Van Cittert-Zernicke theorem to the case of a nonplanar object, while functions B ti and B ti ' are proportional to the squares of the modulus of the Fourier transform of this distribution. It is also shown that the recording of functions B t and B t ' with a Young-Michelson interferometer gives only the angular dimensions of the visible region of objects, whereas the recording of functions B ti and B ti ' with a Brown-Twiss interferometer allows one to find these dimensions and the radius of curvature of the object surface. (laser radiation scattering)

  6. Geometry of multihadron production

    Energy Technology Data Exchange (ETDEWEB)

    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.

  7. Designs and finite geometries

    CERN Document Server

    1996-01-01

    Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.

  8. Geometry of multihadron production

    International Nuclear Information System (INIS)

    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

  9. The Beauty of Geometry

    Science.gov (United States)

    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. Evaluation of scale effects on hydraulic characteristics of fractured rock using fracture network model

    International Nuclear Information System (INIS)

    Ijiri, Yuji; Sawada, Atsushi; Uchida, Masahiro; Ishiguro, Katsuhiko; Umeki, Hiroyuki; Sakamoto, Kazuhiko; Ohnishi, Yuzo

    2001-01-01

    It is important to take into account scale effects on fracture geometry if the modeling scale is much larger than the in-situ observation scale. The scale effect on fracture trace length, which is the most scale dependent parameter, is investigated using fracture maps obtained at various scales in tunnel and dam sites. We found that the distribution of fracture trace length follows negative power law distribution in regardless of locations and rock types. The hydraulic characteristics of fractured rock is also investigated by numerical analysis of discrete fracture network (DFN) model where power law distribution of fracture radius is adopted. We found that as the exponent of power law distribution become larger, the hydraulic conductivity of DFN model increases and the travel time in DFN model decreases. (author)

  11. A Lorentzian quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Grotz, Andreas

    2011-10-07

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  12. Methods of information geometry

    CERN Document Server

    Amari, Shun-Ichi

    2000-01-01

    Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

  13. A Lorentzian quantum geometry

    International Nuclear Information System (INIS)

    Grotz, Andreas

    2011-01-01

    In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

  14. Geometry on the space of geometries

    International Nuclear Information System (INIS)

    Christodoulakis, T.; Zanelli, J.

    1988-06-01

    We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

  15. Simulation of complex fracture networks influenced by natural fractures in shale gas reservoir

    Directory of Open Access Journals (Sweden)

    Zhao Jinzhou

    2014-10-01

    Full Text Available When hydraulic fractures intersect with natural fractures, the geometry and complexity of a fracture network are determined by the initiation and propagation pattern which is affected by a number of factors. Based on the fracture mechanics, the criterion for initiation and propagation of a fracture was introduced to analyze the tendency of a propagating angle and factors affecting propagating pressure. On this basis, a mathematic model with a complex fracture network was established to investigate how the fracture network form changes with different parameters, including rock mechanics, in-situ stress distribution, fracture properties, and frac treatment parameters. The solving process of this model was accelerated by classifying the calculation nodes on the extending direction of the fracture by equal pressure gradients, and solving the geometrical parameters prior to the iteration fitting flow distribution. With the initiation and propagation criterion as the bases for the propagation of branch fractures, this method decreased the iteration times through eliminating the fitting of the fracture length in conventional 3D fracture simulation. The simulation results indicated that the formation with abundant natural fractures and smaller in-situ stress difference is sufficient conditions for fracture network development. If the pressure in the hydraulic fractures can be kept at a high level by temporary sealing or diversion, the branch fractures will propagate further with minor curvature radius, thus enlarging the reservoir stimulation area. The simulated shape of fracture network can be well matched with the field microseismic mapping in data point range and distribution density, validating the accuracy of this model.

  16. Instability of nonplanar modulated dust acoustic wave packets in a strongly coupled nonthermal dusty plasma

    Energy Technology Data Exchange (ETDEWEB)

    El-Labany, S. K., E-mail: skellabany@hotmail.com; Zedan, N. A., E-mail: nesreenplasma@yahoo.com [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 (Egypt); El-Taibany, W. F., E-mail: eltaibany@hotmail.com, E-mail: eltaibany@du.edu.eg [Department of Physics, Faculty of Science, Damietta University, New Damietta, P.O. 34517 (Egypt); Department of Physics, College of Science for Girls in Abha, King Khalid University, P.O. 960 Abha (Saudi Arabia)

    2015-07-15

    Cylindrical and spherical amplitude modulations of dust acoustic (DA) solitary wave envelopes in a strongly coupled dusty plasma containing nonthermal distributed ions are studied. Employing a reductive perturbation technique, a modified nonlinear Schrödinger equation including the geometrical effect is derived. The influences of nonthermal ions, polarization force, and the geometries on the modulational instability conditions are analyzed and the possible rogue wave structures are discussed in detail. It is found that the spherical DA waves are more structurally stable to perturbations than the cylindrical ones. Possible applications of these theoretical findings are briefly discussed.

  17. Fracture mechanics

    CERN Document Server

    Perez, Nestor

    2017-01-01

    The second edition of this textbook includes a refined presentation of concepts in each chapter, additional examples; new problems and sections, such as conformal mapping and mechanical behavior of wood; while retaining all the features of the original book. The material included in this book is based upon the development of analytical and numerical procedures pertinent to particular fields of linear elastic fracture mechanics (LEFM) and plastic fracture mechanics (PFM), including mixed-mode-loading interaction. The mathematical approach undertaken herein is coupled with a brief review of several fracture theories available in cited references, along with many color images and figures. Dynamic fracture mechanics is included through the field of fatigue and Charpy impact testing. Explains computational and engineering approaches for solving crack-related problems using straightforward mathematics that facilitate comprehension of the physical meaning of crack growth processes; Expands computational understandin...

  18. Fracture analysis

    International Nuclear Information System (INIS)

    Ueng, Tzoushin; Towse, D.

    1991-01-01

    Fractures are not only the weak planes of a rock mass, but also the easy passages for the fluid flow. Their spacing, orientation, and aperture will affect the deformability, strength, heat transmittal, and fluid transporting properties of the rock mass. To understand the thermomechanical and hydrological behaviors of the rock surrounding the heater emplacement borehole, the location, orientation, and aperture of the fractures of the rock mass should be known. Borehole television and borescope surveys were performed to map the location, orientation, and aperture of the fractures intersecting the boreholes drilled in the Prototype Engineered Barrier System Field Tests (PEBSFT) at G-Tunnel. Core logging was also performed during drilling. However, because the core was not oriented and the depth of the fracture cannot be accurately determined, the results of the core logging were only used as reference and will not be discussed here

  19. Facial Fractures.

    Science.gov (United States)

    Ricketts, Sophie; Gill, Hameet S; Fialkov, Jeffery A; Matic, Damir B; Antonyshyn, Oleh M

    2016-02-01

    After reading this article, the participant should be able to: 1. Demonstrate an understanding of some of the changes in aspects of facial fracture management. 2. Assess a patient presenting with facial fractures. 3. Understand indications and timing of surgery. 4. Recognize exposures of the craniomaxillofacial skeleton. 5. Identify methods for repair of typical facial fracture patterns. 6. Discuss the common complications seen with facial fractures. Restoration of the facial skeleton and associated soft tissues after trauma involves accurate clinical and radiologic assessment to effectively plan a management approach for these injuries. When surgical intervention is necessary, timing, exposure, sequencing, and execution of repair are all integral to achieving the best long-term outcomes for these patients.

  20. Complex and symplectic geometry

    CERN Document Server

    Medori, Costantino; Tomassini, Adriano

    2017-01-01

    This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

  1. Non-Euclidean geometry

    CERN Document Server

    Kulczycki, Stefan

    2008-01-01

    This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

  2. Pisiform fractures

    International Nuclear Information System (INIS)

    Fleege, M.A.; Jebson, P.J.; Renfrew, D.L.; El-Khoury, G.Y.; Steyers, C.M. Jr.

    1991-01-01

    Fractures of the pisiform are often missed due to improper radiographic evaluation and a tendency to focus on other, more obvious injuries. Delayed diagnosis may result in disabling sequelae. A high index of clinical suspicion and appropriate radiographic examination will establish the correct diagnosis. Ten patients with pisiform fracture are presented. The anatomy, mechanism of injury, clinical presentation, radiographic features, and evaluation of this injury are discussed. (orig.)

  3. Stress fractures

    International Nuclear Information System (INIS)

    Berquist, T.H.; Cooper, K.L.; Pritchard, D.J.

    1985-01-01

    The diagnosis of a stress fracture should be considered in patients presented with pain after a change in activity, especially if the activity is strenuous and the pain is in the lower extremities. Since evidence of the stress fracture may not be apparent for weeks on routine radiographs, proper use of other imaging techniques will allow an earlier diagnosis. Prompt diagnosis is especially important in the femur, where displacement may occur

  4. Influence of interface properties on fracture behaviour of concrete

    Indian Academy of Sciences (India)

    Interface; concrete; bond strength; fracture toughness; stiffness; ductility. 1. Introduction .... behaviour of concrete using sandwich, and direct rock-mortar compact specimens under mode I and mode II ... pulse velocity technique. 4.2 Geometry of ...

  5. Lectures on coarse geometry

    CERN Document Server

    Roe, John

    2003-01-01

    Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...

  6. Lectures on Symplectic Geometry

    CERN Document Server

    Silva, Ana Cannas

    2001-01-01

    The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...

  7. Complex algebraic geometry

    CERN Document Server

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  8. Geometry and Combinatorics

    DEFF Research Database (Denmark)

    Kokkendorff, Simon Lyngby

    2002-01-01

    The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

  9. The geometry of geodesics

    CERN Document Server

    Busemann, Herbert

    2005-01-01

    A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.

  10. Geometry and billiards

    CERN Document Server

    Tabachnikov, Serge

    2005-01-01

    Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...

  11. Introduction to tropical geometry

    CERN Document Server

    Maclagan, Diane

    2015-01-01

    Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...

  12. Rudiments of algebraic geometry

    CERN Document Server

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  13. Implosions and hypertoric geometry

    DEFF Research Database (Denmark)

    Dancer, A.; Kirwan, F.; Swann, A.

    2013-01-01

    The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....

  14. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  15. d-geometries revisited

    CERN Document Server

    Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio

    2013-01-01

    We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.

  16. Scaphoid Fracture

    Directory of Open Access Journals (Sweden)

    Esther Kim, BS

    2018-04-01

    Full Text Available History of present illness: A 25-year-old, right-handed male presented to the emergency department with left wrist pain after falling from a skateboard onto an outstretched hand two-weeks prior. He otherwise had no additional concerns, including no complaints of weakness or loss of sensation. On physical exam, there was tenderness to palpation within the anatomical snuff box. The neurovascular exam was intact. Plain films of the left wrist and hand were obtained. Significant findings: The anteroposterior (AP plain film of this patient demonstrates a full thickness fracture through the middle third of the scaphoid (red arrow, with some apparent displacement (yellow lines and subtle angulation of the fracture fragments (blue line. Discussion: The scaphoid bone is the most commonly fractured carpal bone accounting for 70%-80% of carpal fractures.1 Classically, it is sustained following a fall onto an outstretched hand (FOOSH. Patients should be evaluated for tenderness with palpation over the anatomical snuffbox, which has a sensitivity of 100% and specificity of 40%.2 Plain films are the initial diagnostic modality of choice and have a sensitivity of 70%, but are commonly falsely negative in the first two to six weeks of injury (false negative of 20%.3 The Mayo classification organizes scaphoid fractures as involving the proximal, mid, and distal portions of the scaphoid bone with mid-fractures being the most common.3 The proximal scaphoid is highly susceptible to vascular compromise because it depends on retrograde blood flow from the radial artery. Therefore, disruption can lead to serious sequelae including osteonecrosis, arthrosis, and functional impairment. Thus, a low threshold should be maintained for neurovascular evaluation and surgical referral. Patients with non-displaced scaphoid fractures should be placed in a thumb spica splint.3 Patients with even suspected scaphoid fractures should be placed in a thumb spica splint and re

  17. CMS geometry through 2020

    International Nuclear Information System (INIS)

    Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

    2014-01-01

    CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

  18. Software Geometry in Simulations

    Science.gov (United States)

    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).

  19. Introduction to combinatorial geometry

    International Nuclear Information System (INIS)

    Gabriel, T.A.; Emmett, M.B.

    1985-01-01

    The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity

  20. Near Wellbore Hydraulic Fracture Propagation from Perforations in Tight Rocks: The Roles of Fracturing Fluid Viscosity and Injection Rate

    Directory of Open Access Journals (Sweden)

    Seyed Hassan Fallahzadeh

    2017-03-01

    Full Text Available Hydraulic fracture initiation and near wellbore propagation is governed by complex failure mechanisms, especially in cased perforated wellbores. Various parameters affect such mechanisms, including fracturing fluid viscosity and injection rate. In this study, three different fracturing fluids with viscosities ranging from 20 to 600 Pa.s were used to investigate the effects of varying fracturing fluid viscosities and fluid injection rates on the fracturing mechanisms. Hydraulic fracturing tests were conducted in cased perforated boreholes made in tight 150 mm synthetic cubic samples. A true tri-axial stress cell was used to simulate real far field stress conditions. In addition, dimensional analyses were performed to correspond the results of lab experiments to field-scale operations. The results indicated that by increasing the fracturing fluid viscosity and injection rate, the fracturing energy increased, and consequently, higher fracturing pressures were observed. However, when the fracturing energy was transferred to a borehole at a faster rate, the fracture initiation angle also increased. This resulted in more curved fracture planes. Accordingly, a new parameter, called fracturing power, was introduced to relate fracture geometry to fluid viscosity and injection rate. Furthermore, it was observed that the presence of casing in the wellbore impacted the stress distribution around the casing in such a way that the fracture propagation deviated from the wellbore vicinity.

  1. A geometrically based method for predicting stress-induced fracture aperture and flow in discrete fracture networks

    DEFF Research Database (Denmark)

    Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid

    2016-01-01

    networks, digitized from outcropping pavements. These networks cover a wide range of possible geometries and spatial distributions. The geometrically based method predicts the average hydraulic aperture and equivalent permeability of fractured porous media with error margins of less than 5%....

  2. Characterization of fracture networks for fluid flow analysis

    International Nuclear Information System (INIS)

    Long, J.C.S.; Billaux, D.; Hestir, K.; Majer, E.L.; Peterson, J.; Karasaki, K.; Nihei, K.; Gentier, S.; Cox, L.

    1989-06-01

    The analysis of fluid flow through fractured rocks is difficult because the only way to assign hydraulic parameters to fractures is to perform hydraulic tests. However, the interpretation of such tests, or ''inversion'' of the data, requires at least that we know the geometric pattern formed by the fractures. Combining a statistical approach with geophysical data may be extremely helpful in defining the fracture geometry. Cross-hole geophysics, either seismic or radar, can provide tomograms which are pixel maps of the velocity or attenuation anomalies in the rock. These anomalies are often due to fracture zones. Therefore, tomograms can be used to identify fracture zones and provide information about the structure within the fracture zones. This structural information can be used as the basis for simulating the degree of fracturing within the zones. Well tests can then be used to further refine the model. Because the fracture network is only partially connected, the resulting geometry of the flow paths may have fractal properties. We are studying the behavior of well tests under such geometry. Through understanding of this behavior, it may be possible to use inverse techniques to refine the a priori assignment of fractures and their conductances such that we obtain the best fit to a series of well test results simultaneously. The methodology described here is under development and currently being applied to several field sites. 4 refs., 14 figs

  3. Global aspects of complex geometry

    CERN Document Server

    Catanese, Fabrizio; Huckleberry, Alan T

    2006-01-01

    Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.

  4. Fracture modelling of a high performance armour steel

    Science.gov (United States)

    Skoglund, P.; Nilsson, M.; Tjernberg, A.

    2006-08-01

    The fracture characteristics of the high performance armour steel Armox 500T is investigated. Tensile mechanical experiments using samples with different notch geometries are used to investigate the effect of multi-axial stress states on the strain to fracture. The experiments are numerically simulated and from the simulation the stress at the point of fracture initiation is determined as a function of strain and these data are then used to extract parameters for fracture models. A fracture model based on quasi-static experiments is suggested and the model is tested against independent experiments done at both static and dynamic loading. The result show that the fracture model give reasonable good agreement between simulations and experiments at both static and dynamic loading condition. This indicates that multi-axial loading is more important to the strain to fracture than the deformation rate in the investigated loading range. However on-going work will further characterise the fracture behaviour of Armox 500T.

  5. Sources of hyperbolic geometry

    CERN Document Server

    Stillwell, John

    1996-01-01

    This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Po...

  6. Generalizing optical geometry

    International Nuclear Information System (INIS)

    Jonsson, Rickard; Westman, Hans

    2006-01-01

    We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity

  7. Trochanteric fractures

    International Nuclear Information System (INIS)

    Herrlin, K.; Stroemberg, T.; Lidgren, L.; Walloee, A.; Pettersson, H.; Lund Univ.

    1988-01-01

    Four hundred and thirty trochanteric factures operated upon with McLaughlin, Ender or Richard's osteosynthesis were divided into 6 different types based on their radiographic appearance before and immediately after reposition with special reference to the medial cortical support. A significant correlation was found between the fracture type and subsequent mechanical complications where types 1 and 2 gave less, and types 4 and 5 more complications. A comparison of the various osteosyntheses showed that Richard's had significantly fewer complications than either the Ender or McLaughlin types. For Richard's osteosynthesis alone no correlation to fracture type could be made because of the small number of complications in this group. (orig.)

  8. Fracture Blisters

    Directory of Open Access Journals (Sweden)

    Uebbing, Claire M

    2011-02-01

    Full Text Available Fracture blisters are a relatively uncommon complication of fractures in locations of the body, such as the ankle, wrist elbow and foot, where skin adheres tightly to bone with little subcutaneous fat cushioning. The blister that results resembles that of a second degree burn.These blisters significantly alter treatment, making it difficult to splint or cast and often overlying ideal surgical incision sites. Review of the literature reveals no consensus on management; however, most authors agree on early treatment prior to blister formation or delay until blister resolution before attempting surgical correction or stabilization. [West J Emerg Med. 2011;12(1;131-133.

  9. Geometry of thresholdless active flow in nematic microfluidics

    Science.gov (United States)

    Green, Richard; Toner, John; Vitelli, Vincenzo

    2017-10-01

    Active nematics are orientationally ordered but apolar fluids composed of interacting constituents individually powered by an internal source of energy. When activity exceeds a system-size-dependent threshold, spatially uniform active apolar fluids undergo a hydrodynamic instability leading to spontaneous macroscopic fluid flow. Here we show that a special class of spatially nonuniform configurations of such active apolar fluids display laminar (i.e., time-independent) flow even for arbitrarily small activity. We also show that two-dimensional active nematics confined on a surface of nonvanishing Gaussian curvature must necessarily experience a nonvanishing active force. This general conclusion follows from a key result of differential geometry: Geodesics must converge or diverge on surfaces with nonzero Gaussian curvature. We derive the conditions under which such curvature-induced active forces generate thresholdless flow for two-dimensional curved shells. We then extend our analysis to bulk systems and show how to induce thresholdless active flow by controlling the curvature of confining surfaces, external fields, or both. The resulting laminar flow fields are determined analytically in three experimentally realizable configurations that exemplify this general phenomenon: (i) toroidal shells with planar alignment, (ii) a cylinder with nonplanar boundary conditions, and (iii) a Frederiks cell that functions like a pump without moving parts. Our work suggests a robust design strategy for active microfluidic chips and could be tested with the recently discovered living liquid crystals.

  10. Computational synthetic geometry

    CERN Document Server

    Bokowski, Jürgen

    1989-01-01

    Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...

  11. Discrete and computational geometry

    CERN Document Server

    Devadoss, Satyan L

    2011-01-01

    Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...

  12. Geometry and Cloaking Devices

    Science.gov (United States)

    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. Lectures on discrete geometry

    CERN Document Server

    2002-01-01

    Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

  14. Complex differential geometry

    CERN Document Server

    Zheng, Fangyang

    2002-01-01

    The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...

  15. Geometry and symmetry

    CERN Document Server

    Yale, Paul B

    2012-01-01

    This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi

  16. Flexible Near-Field Nanopatterning with Ultrathin, Conformal Phase Masks on Nonplanar Substrates for Biomimetic Hierarchical Photonic Structures.

    Science.gov (United States)

    Kwon, Young Woo; Park, Junyong; Kim, Taehoon; Kang, Seok Hee; Kim, Hyowook; Shin, Jonghwa; Jeon, Seokwoo; Hong, Suck Won

    2016-04-26

    Multilevel hierarchical platforms that combine nano- and microstructures have been intensively explored to mimic superior properties found in nature. However, unless directly replicated from biological samples, desirable multiscale structures have been challenging to efficiently produce to date. Departing from conventional wafer-based technology, new and efficient techniques suitable for fabricating bioinspired structures are highly desired to produce three-dimensional architectures even on nonplanar substrates. Here, we report a facile approach to realize functional nanostructures on uneven microstructured platforms via scalable optical fabrication techniques. The ultrathin form (∼3 μm) of a phase grating composed of poly(vinyl alcohol) makes the material physically flexible and enables full-conformal contact with rough surfaces. The near-field optical effect can be identically generated on highly curved surfaces as a result of superior conformality. Densely packed nanodots with submicron periodicity are uniformly formed on microlens arrays with a radius of curvature that is as low as ∼28 μm. Increasing the size of the gratings causes the production area to be successfully expanded by up to 16 in(2). The "nano-on-micro" structures mimicking real compound eyes are transferred to flexible and stretchable substrates by sequential imprinting, facilitating multifunctional optical films applicable to antireflective diffusers for large-area sheet-illumination displays.

  17. Synthesis and Characterization of Sulfonated Poly(Phenylene Containing a Non-Planar Structure and Dibenzoyl Groups

    Directory of Open Access Journals (Sweden)

    Hohyoun Jang

    2016-02-01

    Full Text Available Polymers for application as sulfonated polyphenylene membranes were prepared by nickel-catalyzed carbon-carbon coupling reaction of bis(4-chlorophenyl-1,2-diphenylethylene (BCD and 1,4-dichloro-2,5-dibenzoylbenzene (DCBP. Conjugated cis/trans isomer (BCD had a non-planar conformation containing four peripheral aromatic rings that facilitate the formation of π–π interactions. 1,4-Dichloro-2,5-dibenzoylbenzene was synthesized from the oxidation reaction of 2,5-dichloro-p-xylene, followed by Friedel-Crafts reaction with benzene. DCBP monomer had good reactivity in polymerization affecting the activity of benzophenone as an electron-withdrawing group. The polyphenylene was sulfonated using concentrated sulfuric acid. These polymers without any ether linkages on the polymer backbone were protected from nucleophilic attack by hydrogen peroxide, hydroxide anion, and radicals generated by polymer electrolyte membrane fuel cell (PEMFC operation systems. The mole fraction of the sulfonic acid groups was controlled by varying the mole ratio of bis(4-chlorophenyl-1,2-diphenylethylene in the copolymer. In comparison with Nafion 211® membrane, these SBCDCBP membranes showed ion exchange capacity (IEC ranging from 1.04 to 2.07 meq./g, water uptake from 36.5% to 69.4%, proton conductivity from 58.7 to 101.9 mS/cm, and high thermal stability.

  18. Elbow Fractures

    Science.gov (United States)

    ... is also an important factor when treating elbow fractures. Casts are used more frequently in children, as their risk of developing elbow stiffness is small; however, in an adult, elbow stiffness is much more likely. Rehabilitation directed by your doctor is often used to ...

  19. Wrist Fractures

    Science.gov (United States)

    ... All Topics A-Z Videos Infographics Symptom Picker Anatomy Bones Joints Muscles Nerves Vessels Tendons About Hand Surgery What is a Hand Surgeon? What is a Hand Therapist? Media Find a Hand Surgeon Home Anatomy Wrist Fractures Email to a friend * required fields ...

  20. Shoulder Fractures

    Science.gov (United States)

    ... All Topics A-Z Videos Infographics Symptom Picker Anatomy Bones Joints Muscles Nerves Vessels Tendons About Hand Surgery What is a Hand Surgeon? What is a Hand Therapist? Media Find a Hand Surgeon Home Anatomy Shoulder Fractures Email to a friend * required fields ...

  1. Towards relativistic quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

    2015-12-17

    We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

  2. Multiplicity in difference geometry

    OpenAIRE

    Tomasic, Ivan

    2011-01-01

    We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.

  3. Spacetime and Euclidean geometry

    Science.gov (United States)

    Brill, Dieter; Jacobson, Ted

    2006-04-01

    Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

  4. Physics and geometry

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2009-01-01

    The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered

  5. Origami, Geometry and Art

    Science.gov (United States)

    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…

  6. Gravity is Geometry.

    Science.gov (United States)

    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)

  7. Towards a Nano Geometry?

    DEFF Research Database (Denmark)

    Booss-Bavnbek, Bernhelm

    2011-01-01

    This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...

  8. Diophantine geometry an introduction

    CERN Document Server

    Hindry, Marc

    2000-01-01

    This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

  9. Sliding vane geometry turbines

    Science.gov (United States)

    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.

  10. History of analytic geometry

    CERN Document Server

    Boyer, Carl B

    2012-01-01

    Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.

  11. Non-euclidean geometry

    CERN Document Server

    Coxeter, HSM

    1965-01-01

    This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

  12. Topics in Riemannian geometry

    International Nuclear Information System (INIS)

    Ezin, J.P.

    1988-08-01

    The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

  13. Geometry Euclid and beyond

    CERN Document Server

    Hartshorne, Robin

    2000-01-01

    In recent years, I have been teaching a junior-senior-level course on the classi­ cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa­ rately. The remainder of the book is an exploration of questions that arise natu­ rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...

  14. The effect of specimen and flaw dimensions on fracture toughness

    International Nuclear Information System (INIS)

    Nevalainen, M.J.

    1997-06-01

    The effect of the specimen size and geometry on fracture toughness has been investigated both by experimental tests and computational analyses. The methods for constraint description, namely T-stress, Q-parameter and Small-Scale Yielding Correction (SSYC) have been compared and applied for various geometries. A statistical treatment for the specimen thickness effect on cleavage fracture toughness has been investigated. Elliptical surface cracks were compared with straight-thickness cracks and a method for crack shape correction was presented. Based on the results, the differences in apparent fracture toughness values obtained from various specimen configurations can be better understood and taken into account

  15. Description of Fracture Systems for External Criticality Reports

    International Nuclear Information System (INIS)

    Nicot, Jean-Philippe

    2001-01-01

    The purpose of this Analysis/Model Report (AMR) is to describe probabilistically the main features of the geometry of the fracture system in the vicinity of the repository. They will be used to determine the quantity of fissile material that could accumulate in the fractured rock underneath a waste package as it degrades. This AMR is to feed the geochemical calculations for external criticality reports. This AMR is done in accordance with the technical work plan (BSC (Bechtel SAIC Company) 2001 b). The scope of this AMR is restricted to the relevant parameters of the fracture system. The main parameters of interest are fracture aperture and fracture spacing distribution parameters. The relative orientation of the different fracture sets is also important because of its impact on criticality, but they will be set deterministically. The maximum accumulation of material depends primarily on the fracture porosity, combination of the fracture aperture, and fracture intensity. However, the fracture porosity itself is not sufficient to characterize the potential for accumulation of a fracture system. The fracture aperture is also important because it controls both the flow through the fracture and the potential plugging of the system. Other features contributing to the void space such as lithophysae are also investigated. On the other hand, no analysis of the matrix porosity is done. The parameters will be used in sensitivity analyses of geochemical calculations providing actinide accumulations and in the subsequent Monte Carlo criticality analyses

  16. Effects of geometry and temperature on mode I interlaminar fracture ...

    Indian Academy of Sciences (India)

    Administrator

    explanation of the toughening mechanisms were made by comparing the impact properties with ... characteristics of this material are suitable for common ... qualitatively fine dispersion of the nanofiller within the ... may be too small to effectively interact with the propa- ... failure is examined by studying the structural changes.

  17. Bimalleolar ankle fracture with proximal fibular fracture

    NARCIS (Netherlands)

    Colenbrander, R. J.; Struijs, P. A. A.; Ultee, J. M.

    2005-01-01

    A 56-year-old female patient suffered a bimalleolar ankle fracture with an additional proximal fibular fracture. This is an unusual fracture type, seldom reported in literature. It was operatively treated by open reduction and internal fixation of the lateral malleolar fracture. The proximal fibular

  18. The causes of geometry effects in ductile tearing

    International Nuclear Information System (INIS)

    Dexter, R.J.; Griesbach, T.J.

    1993-01-01

    An adequate understanding of geometry effects in ductile tearing can only be achieved when the different causes of the effects are distinguished and these geometry effects are linked to particular micromechanical fracture processes or global deformation mechanisms. It is shown that the micromechanical process of ductile (fibrous) fracture is dependent on achieving a critical strain, which is only slightly dependent on the stress state for the range of triaxiality conditions in pressure vessels and through-cracked plates. Under certain conditions, the crack tip strain can be shown to scale with the value of the J integral and there is a direct connection between J and the underlying micro mechanical process. This connection is lost for significant crack extension or large-scale plasticity. Nevertheless the J integral may still be use on an empirical basis under some conditions. Under fully-plastic conditions the primary source of geometry dependence in the J-R curves is due to the geometry dependence of the shape and volume of the plastic region that develops around the uncracked ligament. This occurs because J is essentially proportional to the total plastic work done on the specimen. If it can be assured that the fracture mode in both the test specimen and the structure will remain fully fibrous, it is conservative to extrapolate J-R curves generated from small compact specimens for the analysis of pressure vessel crack stability. 132 refs., 12 figs., 3 tabs

  19. Intelligent Patching of Conceptual Geometry for CFD Analysis

    Science.gov (United States)

    Li, Wu

    2010-01-01

    the second surface. No two intersection relationships will result in a common intersection point of three surfaces. The output files of iPatch are IGES, d3m, and mapbc files that define the CFD geometry in VGRID format. The IGES file gives the NURBS definition of the outer mold line in the geometry. The d3m file defines how the outer mold line is broken into surface patches whose boundary curves are defined by points. The mapbc file specifies what the boundary condition is on each patch and the corresponding NURBS surface definition of each non-planar patch in the IGES file.

  20. Fracture mechanics

    International Nuclear Information System (INIS)

    Miannay, D.P.

    1995-01-01

    This book entitle ''Fracture Mechanics'', the first one of the monograph ''Materiologie'' is geared to design engineers, material engineers, non destructive inspectors and safety experts. This book covers fracture mechanics in isotropic homogeneous continuum. Only the monotonic static loading is considered. This book intended to be a reference with the current state of the art gives the fundamental of the issues under concern and avoids the developments too complicated or not yet mastered for not making reading cumbersome. The subject matter is organized as going from an easy to a more complicated level and thus follows the chronological evolution in the field. Similarly the microscopic scale is considered before the macroscopic scale, the physical understanding of phenomena linked to the experimental observation of the material preceded the understanding of the macroscopic behaviour of structures. In this latter field the relatively recent contribution of finite element computations with some analogy with the experimental observation is determining. However more sensitive analysis is not skipped

  1. Multivariate calculus and geometry

    CERN Document Server

    Dineen, Seán

    2014-01-01

    Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

  2. Transformational plane geometry

    CERN Document Server

    Umble, Ronald N

    2014-01-01

    Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...

  3. Multilevel geometry optimization

    Science.gov (United States)

    Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.

    2000-02-01

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.

  4. Multilevel geometry optimization

    Energy Technology Data Exchange (ETDEWEB)

    Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)

    2000-02-15

    Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.

  5. Geometry and Destiny

    OpenAIRE

    Krauss, Lawrence M.; Turner, Michael S.

    1999-01-01

    The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.

  6. Complex geometries in wood

    DEFF Research Database (Denmark)

    Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob

    2009-01-01

    The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....

  7. Electroweak vacuum geometry

    International Nuclear Information System (INIS)

    Lepora, N.; Kibble, T.

    1999-01-01

    We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)

  8. Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction II: Nonplanar Molecules.

    Science.gov (United States)

    Whittleton, Sarah R; Otero-de-la-Roza, A; Johnson, Erin R

    2017-11-14

    The crystal structure prediction (CSP) of a given compound from its molecular diagram is a fundamental challenge in computational chemistry with implications in relevant technological fields. A key component of CSP is the method to calculate the lattice energy of a crystal, which allows the ranking of candidate structures. This work is the second part of our investigation to assess the potential of the exchange-hole dipole moment (XDM) dispersion model for crystal structure prediction. In this article, we study the relatively large, nonplanar, mostly flexible molecules in the first five blind tests held by the Cambridge Crystallographic Data Centre. Four of the seven experimental structures are predicted as the energy minimum, and thermal effects are demonstrated to have a large impact on the ranking of at least another compound. As in the first part of this series, delocalization error affects the results for a single crystal (compound X), in this case by detrimentally overstabilizing the π-conjugated conformation of the monomer. Overall, B86bPBE-XDM correctly predicts 16 of the 21 compounds in the five blind tests, a result similar to the one obtained using the best CSP method available to date (dispersion-corrected PW91 by Neumann et al.). Perhaps more importantly, the systems for which B86bPBE-XDM fails to predict the experimental structure as the energy minimum are mostly the same as with Neumann's method, which suggests that similar difficulties (absence of vibrational free energy corrections, delocalization error,...) are not limited to B86bPBE-XDM but affect GGA-based DFT-methods in general. Our work confirms B86bPBE-XDM as an excellent option for crystal energy ranking in CSP and offers a guide to identify crystals (organic salts, conjugated flexible systems) where difficulties may appear.

  9. Detection of latent fingerprints using high-resolution 3D confocal microscopy in non-planar acquisition scenarios

    Science.gov (United States)

    Kirst, Stefan; Vielhauer, Claus

    2015-03-01

    In digitized forensics the support of investigators in any manner is one of the main goals. Using conservative lifting methods, the detection of traces is done manually. For non-destructive contactless methods, the necessity for detecting traces is obvious for further biometric analysis. High resolutional 3D confocal laser scanning microscopy (CLSM) grants the possibility for a detection by segmentation approach with improved detection results. Optimal scan results with CLSM are achieved on surfaces orthogonal to the sensor, which is not always possible due to environmental circumstances or the surface's shape. This introduces additional noise, outliers and a lack of contrast, making a detection of traces even harder. Prior work showed the possibility of determining angle-independent classification models for the detection of latent fingerprints (LFP). Enhancing this approach, we introduce a larger feature space containing a variety of statistical-, roughness-, color-, edge-directivity-, histogram-, Gabor-, gradient- and Tamura features based on raw data and gray-level co-occurrence matrices (GLCM) using high resolutional data. Our test set consists of eight different surfaces for the detection of LFP in four different acquisition angles with a total of 1920 single scans. For each surface and angles in steps of 10, we capture samples from five donors to introduce variance by a variety of sweat compositions and application influences such as pressure or differences in ridge thickness. By analyzing the present test set with our approach, we intend to determine angle- and substrate-dependent classification models to determine optimal surface specific acquisition setups and also classification models for a general detection purpose for both, angles and substrates. The results on overall models with classification rates up to 75.15% (kappa 0.50) already show a positive tendency regarding the usability of the proposed methods for LFP detection on varying surfaces in non-planar

  10. W-geometry

    International Nuclear Information System (INIS)

    Hull, C.M.

    1993-01-01

    The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)

  11. Integral geometry and valuations

    CERN Document Server

    Solanes, Gil

    2014-01-01

    Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented...

  12. CBM RICH geometry optimization

    Energy Technology Data Exchange (ETDEWEB)

    Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration

    2016-07-01

    The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.

  13. FROMS3D: New Software for 3-D Visualization of Fracture Network System in Fractured Rock Masses

    Science.gov (United States)

    Noh, Y. H.; Um, J. G.; Choi, Y.

    2014-12-01

    A new software (FROMS3D) is presented to visualize fracture network system in 3-D. The software consists of several modules that play roles in management of borehole and field fracture data, fracture network modelling, visualization of fracture geometry in 3-D and calculation and visualization of intersections and equivalent pipes between fractures. Intel Parallel Studio XE 2013, Visual Studio.NET 2010 and the open source VTK library were utilized as development tools to efficiently implement the modules and the graphical user interface of the software. The results have suggested that the developed software is effective in visualizing 3-D fracture network system, and can provide useful information to tackle the engineering geological problems related to strength, deformability and hydraulic behaviors of the fractured rock masses.

  14. Introducing geometry concept based on history of Islamic geometry

    Science.gov (United States)

    Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

    2018-01-01

    Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

  15. Fault geometry and earthquake mechanics

    Directory of Open Access Journals (Sweden)

    D. J. Andrews

    1994-06-01

    Full Text Available Earthquake mechanics may be determined by the geometry of a fault system. Slip on a fractal branching fault surface can explain: 1 regeneration of stress irregularities in an earthquake; 2 the concentration of stress drop in an earthquake into asperities; 3 starting and stopping of earthquake slip at fault junctions, and 4 self-similar scaling of earthquakes. Slip at fault junctions provides a natural realization of barrier and asperity models without appealing to variations of fault strength. Fault systems are observed to have a branching fractal structure, and slip may occur at many fault junctions in an earthquake. Consider the mechanics of slip at one fault junction. In order to avoid a stress singularity of order 1/r, an intersection of faults must be a triple junction and the Burgers vectors on the three fault segments at the junction must sum to zero. In other words, to lowest order the deformation consists of rigid block displacement, which ensures that the local stress due to the dislocations is zero. The elastic dislocation solution, however, ignores the fact that the configuration of the blocks changes at the scale of the displacement. A volume change occurs at the junction; either a void opens or intense local deformation is required to avoid material overlap. The volume change is proportional to the product of the slip increment and the total slip since the formation of the junction. Energy absorbed at the junction, equal to confining pressure times the volume change, is not large enongh to prevent slip at a new junction. The ratio of energy absorbed at a new junction to elastic energy released in an earthquake is no larger than P/µ where P is confining pressure and µ is the shear modulus. At a depth of 10 km this dimensionless ratio has th value P/µ= 0.01. As slip accumulates at a fault junction in a number of earthquakes, the fault segments are displaced such that they no longer meet at a single point. For this reason the

  16. Two lectures on D-geometry and noncommutative geometry

    International Nuclear Information System (INIS)

    Douglas, M.R.

    1999-01-01

    This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

  17. A new computer code for discrete fracture network modelling

    Science.gov (United States)

    Xu, Chaoshui; Dowd, Peter

    2010-03-01

    The authors describe a comprehensive software package for two- and three-dimensional stochastic rock fracture simulation using marked point processes. Fracture locations can be modelled by a Poisson, a non-homogeneous, a cluster or a Cox point process; fracture geometries and properties are modelled by their respective probability distributions. Virtual sampling tools such as plane, window and scanline sampling are included in the software together with a comprehensive set of statistical tools including histogram analysis, probability plots, rose diagrams and hemispherical projections. The paper describes in detail the theoretical basis of the implementation and provides a case study in rock fracture modelling to demonstrate the application of the software.

  18. Geometry of Quantum States

    International Nuclear Information System (INIS)

    Hook, D W

    2008-01-01

    A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and

  19. The application of positron emission tomography to the study of mass transfer in fractured rock

    International Nuclear Information System (INIS)

    Gilling, D.; Jefferies, N.L.; Fowles, P.; Hawkesworth, M.R.; Parker, D.J.

    1991-06-01

    Water flow in hard rocks takes place dominantly in fractures. In order to predict the transport of dissolved radioelements through a fractured rock it is necessary to determine both the geometry of the fracture network and the hydraulic properties of the individual fractures. This paper describes a technique for studying mass transfer in a single fracture. The technique is positron emission tomography (PET) and it offers the potential for visualising quantitatively the migration of dissolved tracers. Preliminary experiments have been undertaken involving the flow of Na-22 and F-18 labelled solutions through artificial fractures. The results demonstrate that PET is well suited to this application. (author)

  20. Quantum coherent π-electron rotations in a non-planar chiral molecule induced by using a linearly polarized UV laser pulse

    Science.gov (United States)

    Mineo, Hirobumi; Fujimura, Yuichi

    2015-06-01

    We propose an ultrafast quantum switching method of π-electron rotations, which are switched among four rotational patterns in a nonplanar chiral aromatic molecule (P)-2,2’- biphenol and perform the sequential switching among four rotational patterns which are performed by the overlapped pump-dump laser pulses. Coherent π-electron dynamics are generated by applying the linearly polarized UV pulse laser to create a pair of coherent quasidegenerated excited states. We also plot the time-dependent π-electron ring current, and discussed ring current transfer between two aromatic rings.

  1. Flexible and transparent silicon-on-polymer based sub-20 nm non-planar 3D FinFET for brain-architecture inspired computation

    KAUST Repository

    Sevilla, Galo T.

    2014-02-22

    An industry standard 8′′ silicon-on-insulator wafer based ultra-thin (1 μm), ultra-light-weight, fully flexible and remarkably transparent state-of-the-art non-planar three dimensional (3D) FinFET is shown. Introduced by Intel Corporation in 2011 as the most advanced transistor architecture, it reveals sub-20 nm features and the highest performance ever reported for a flexible transistor. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  2. Flexible and transparent silicon-on-polymer based sub-20 nm non-planar 3D FinFET for brain-architecture inspired computation

    KAUST Repository

    Sevilla, Galo T.; Rojas, Jhonathan Prieto; Fahad, Hossain M.; Hussain, Aftab M.; Ghanem, Rawan; Smith, Casey; Hussain, Muhammad Mustafa

    2014-01-01

    An industry standard 8′′ silicon-on-insulator wafer based ultra-thin (1 μm), ultra-light-weight, fully flexible and remarkably transparent state-of-the-art non-planar three dimensional (3D) FinFET is shown. Introduced by Intel Corporation in 2011 as the most advanced transistor architecture, it reveals sub-20 nm features and the highest performance ever reported for a flexible transistor. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  3. Functional integration over geometries

    International Nuclear Information System (INIS)

    Mottola, E.

    1995-01-01

    The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

  4. Kinematic geometry of gearing

    CERN Document Server

    Dooner, David B

    2012-01-01

    Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat

  5. From geometry to topology

    CERN Document Server

    Flegg, H Graham

    2001-01-01

    This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.

  6. Torsional heterotic geometries

    International Nuclear Information System (INIS)

    Becker, Katrin; Sethi, Savdeep

    2009-01-01

    We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.

  7. Geometrie verstehen: statisch - kinematisch

    Science.gov (United States)

    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.

  8. Elementary algebraic geometry

    CERN Document Server

    Kendig, Keith

    2015-01-01

    Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th

  9. Local analytic geometry

    CERN Document Server

    Abhyankar, Shreeram Shankar

    1964-01-01

    This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from

  10. Geometry of conics

    CERN Document Server

    Akopyan, A V

    2007-01-01

    The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca

  11. Geometry and trigonometry

    CERN Document Server

    2015-01-01

    This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent

  12. Geometry I essentials

    CERN Document Server

    REA, The Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric

  13. Graded geometry and Poisson reduction

    OpenAIRE

    Cattaneo, A S; Zambon, M

    2009-01-01

    The main result of [2] extends the Marsden-Ratiu reduction theorem [4] 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 in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics

  14. Hip fracture - discharge

    Science.gov (United States)

    ... neck fracture repair - discharge; Trochanteric fracture repair - discharge; Hip pinning surgery - discharge ... in the hospital for surgery to repair a hip fracture, a break in the upper part of ...

  15. Studies of Transport Properties of Fractures: Final Report

    Energy Technology Data Exchange (ETDEWEB)

    Stephen R. Brown

    2006-06-30

    We proposed to study several key factors controlling the character and evolution of fracture system permeability and transport processes. We suggest that due to surface roughness and the consequent channeling in single fractures and in fracture intersections, the tendency of a fracture system to plug up, remain permeable, or for permeability to increase due to chemical dissolution/precipitation conditions will depend strongly on the instantaneous flow channel geometry. This geometry will change as chemical interaction occurs, thus changing the permeability through time. To test this hypothesis and advance further understanding toward a predictive capability, we endeavored to physically model and analyze several configurations of flow and transport of inert and chemically active fluids through channels in single fractures and through fracture intersections. This was an integrated program utilizing quantitative observations of fractures and veins in drill core, quantitative and visual observations of flow and chemical dissolution and precipitation within replicas of real rough-walled fractures and fracture intersections, and numerical modeling via lattice Boltzmann methods.

  16. Self-potential observations during hydraulic fracturing

    Energy Technology Data Exchange (ETDEWEB)

    Moore, Jeffrey R.; Glaser, Steven D.

    2007-09-13

    The self-potential (SP) response during hydraulic fracturing of intact Sierra granite was investigated in the laboratory. Excellent correlation of pressure drop and SP suggests that the SP response is created primarily by electrokinetic coupling. For low pressures, the variation of SP with pressure drop is linear, indicating a constant coupling coefficient (Cc) of -200 mV/MPa. However for pressure drops >2 MPa, the magnitude of the Cc increases by 80% in an exponential trend. This increasing Cc is related to increasing permeability at high pore pressures caused by dilatancy of micro-cracks, and is explained by a decrease in the hydraulic tortuosity. Resistivity measurements reveal a decrease of 2% prior to hydraulic fracturing and a decrease of {approx}35% after fracturing. An asymmetric spatial SP response created by injectate diffusion into dilatant zones is observed prior to hydraulic fracturing, and in most cases this SP variation revealed the impending crack geometry seconds before failure. At rupture, injectate rushes into the new fracture area where the zeta potential is different than in the rock porosity, and an anomalous SP spike is observed. After fracturing, the spatial SP distribution reveals the direction of fracture propagation. Finally, during tensile cracking in a point load device with no water flow, a SP spike is observed that is caused by contact electrification. However, the time constant of this event is much less than that for transients observed during hydraulic fracturing, suggesting that SP created solely from material fracture does not contribute to the SP response during hydraulic fracturing.

  17. Proximal femoral fractures.

    Science.gov (United States)

    Webb, Lawrence X

    2002-01-01

    Fractures of the proximal femur include fractures of the head, neck, intertrochanteric, and subtrochanteric regions. Head fractures commonly accompany dislocations. Neck fractures and intertrochanteric fractures occur with greatest frequency in elderly patients with a low bone mineral density and are produced by low-energy mechanisms. Subtrochanteric fractures occur in a predominantly strong cortical osseous region which is exposed to large compressive stresses. Implants used to address these fractures must be able to accommodate significant loads while the fractures consolidate. Complications secondary to these injuries produce significant morbidity and include infection, nonunion, malunion, decubitus ulcers, fat emboli, deep venous thrombosis, pulmonary embolus, pneumonia, myocardial infarction, stroke, and death.

  18. On the theory of transport in fractured media for the safety analysis of a nuclear waste repository

    International Nuclear Information System (INIS)

    Mukhopadhyay, N.C.

    1982-10-01

    This report aims at developing a systematic theory of the role of fractures in the transport of radionuclides by groundwater, through fractured rocks from a deep-lying nuclear waste repository to the biosphere. Fractures are grouped into four 'irreducible' types: joints, nodes, shear zones and fracture zones, and the physical characteristics which influence radionuclide transport are expressed in mathematical terms. The question of radioactivity retention is then studied for various fracture types, using idealized geometries to model natural forms. Fundamental transport equations are derived for the fracture-pore complex, taking into consideration the special physical characteristics of fractures and the effects of sorption therein. (author)

  19. On the theory of transport of fluids in fractured media for the safety analysis of a nuclear waste repository

    International Nuclear Information System (INIS)

    Mukhopadhyay, N.C.

    1983-01-01

    A systematic theory is developed of the role of fractures in the transport of radionuclides by groundwater through fractured rocks from the nuclear waste repository to be built in deep geologic formations to the biosphere. Fractures are grouped into four ''irreducible'' types: joints, nodes, shear zones, and fracture zones, and their geometrical and sorption characteristics, having bearings on radionuclide transport, are expressed in mathematical terms. The question of radioactivity retention in various fracture types is then carefully studied using idealized geometries to mimic natural forms. Fundamental transport equations are derived for the fracture-pore complex, taking into consideration the special physical characteristics of fractures and the effects of sorption therein

  20. Studies Of Urea Geometry By Means Of Ab Initio Methods And Computer Simulations Of Liquids [estudo Da Geometria Da Uréia Por Métodos Ab Initio E Simulaição Computacional De Líquidos

    OpenAIRE

    Cirino J.J.V.; Bertran C.A.

    2002-01-01

    A study was carried out on the urea geometries using ab initio calculation and Monte Carlo computational simulation of liquids. The ab initio calculated results showed that urea has a non-planar conformation in the gas phase in which the hydrogen atoms are out of the plane formed by the heavy atoms. Free energies associated to the rotation of the amino groups of urea in water were obtained using the Monte Carlo method in which the thermodynamic perturbation theory is implemented. The magnitud...

  1. A multi-scale case study of natural fracture systems in outcrops and boreholes with applications to reservoir modelling

    NARCIS (Netherlands)

    Taal-van Koppen, J.K.J.

    2008-01-01

    Fractured reservoirs are notoriously difficult to characterize because the resolution of seismic data is too low to detect fractures whereas borehole data is detailed but sparse. Therefore, outcrops can be of great support in gaining knowledge of the three-dimensional geometry of fracture networks,

  2. Dissipative particle dynamics simulation of fluid motion through an unsaturated fracture and fracture junction

    International Nuclear Information System (INIS)

    Liu Moubin; Meakin, Paul; Huang Hai

    2007-01-01

    Multiphase fluid motion in unsaturated fractures and fracture networks involves complicated fluid dynamics, which is difficult to model using grid-based continuum methods. In this paper, the application of dissipative particle dynamics (DPD), a relatively new mesoscale method to simulate fluid motion in unsaturated fractures is described. Unlike the conventional DPD method that employs a purely repulsive conservative (non-dissipative) particle-particle interaction to simulate the behavior of gases, we used conservative particle-particle interactions that combine short-range repulsive and long-range attractive interactions. This new conservative particle-particle interaction allows the behavior of multiphase systems consisting of gases, liquids and solids to be simulated. Our simulation results demonstrate that, for a fracture with flat parallel walls, the DPD method with the new interaction potential function is able to reproduce the hydrodynamic behavior of fully saturated flow, and various unsaturated flow modes including thin film flow, wetting and non-wetting flow. During simulations of flow through a fracture junction, the fracture junction can be fully or partially saturated depending on the wetting property of the fluid, the injection rate and the geometry of the fracture junction. Flow mode switching from a fully saturated flow to a thin film flow can also be observed in the fracture junction

  3. A new method for evaluating the conformations and normal modes of macromolecule vibrations with a reduced force field. 2. Application to nonplanar distorted metal porphyrins

    Energy Technology Data Exchange (ETDEWEB)

    Unger, E.; Beck, M.; Lipski, R.J.; Dreybrodt, W.; Medforth, C.J.; Smith, K.M.; Schweitzer-Stenner, R.

    1999-11-11

    The authors have developed a novel method for molecular mechanics calculations and normal-mode analysis. It is based on symmetry of local units that constitutes the given molecule. Compared with general valence force field calculations, the number of free parameters is reduced by 40--80% in the procedure. It was found to reproduce very well the vibrational frequencies and mode compositions of aromatic compounds and porphyrins, as shown by comparison with DFT calculations. A slightly altered force field obtained from Ni(II) porphin was then used to calculate the structure and the normal modes of several meso-substituted Ni(II) porphyrins which are known to be subject to significant ruffling and/or saddling distortions. This method satisfactorily reproduces their nonplanar structure and Raman band frequencies in the natural abundance and isotopic derivative spectra. The polarization properties of bands from out-of-plane modes are in accordance with the predicted nonplanar distortions. Moreover, some of the modes below 800 cm{sup {minus}1} which appear intense in the Raman spectra contain considerable contributions from both in-plane and out-of-plane vibrations, so that the conventional mode assignments become questionable. The authors also demonstrate that the intensity and polarization of some low-frequency Raman bands can be used as a (quantitative) marker to elucidate type and magnitude of out-of-plane distortions. These were recently shown to affect heme groups of hemoglobin, myoglobin, and, in particular, of cytochrome c.

  4. Non-Planar Nano-Scale Fin Field Effect Transistors on Textile, Paper, Wood, Stone, and Vinyl via Soft Material-Enabled Double-Transfer Printing

    KAUST Repository

    Rojas, Jhonathan Prieto; Sevilla, Galo T.; Alfaraj, Nasir; Ghoneim, Mohamed T.; Kutbee, Arwa T.; Sridharan, Ashvitha; Hussain, Muhammad Mustafa

    2015-01-01

    The ability to incorporate rigid but high-performance nano-scale non-planar complementary metal-oxide semiconductor (CMOS) electronics with curvilinear, irregular, or asymmetric shapes and surfaces is an arduous but timely challenge in enabling the production of wearable electronics with an in-situ information-processing ability in the digital world. Therefore, we are demonstrating a soft-material enabled double-transfer-based process to integrate flexible, silicon-based, nano-scale, non-planar, fin-shaped field effect transistors (FinFETs) and planar metal-oxide-semiconductor field effect transistors (MOSFETs) on various asymmetric surfaces to study their compatibility and enhanced applicability in various emerging fields. FinFET devices feature sub-20 nm dimensions and state-of-the-art, high-κ/metal gate stack, showing no performance alteration after the transfer process. A further analysis of the transferred MOSFET devices, featuring 1 μm gate length exhibits ION ~70 μA/μm (VDS = 2 V, VGS = 2 V) and a low sub-threshold swing of around 90 mV/dec, proving that a soft interfacial material can act both as a strong adhesion/interposing layer between devices and final substrate as well as a means to reduce strain, which ultimately helps maintain the device’s performance with insignificant deterioration even at a high bending state.

  5. Nonplanar Nanoscale Fin Field Effect Transistors on Textile, Paper, Wood, Stone, and Vinyl via Soft Material-Enabled Double-Transfer Printing.

    Science.gov (United States)

    Rojas, Jhonathan P; Torres Sevilla, Galo A; Alfaraj, Nasir; Ghoneim, Mohamed T; Kutbee, Arwa T; Sridharan, Ashvitha; Hussain, Muhammad Mustafa

    2015-05-26

    The ability to incorporate rigid but high-performance nanoscale nonplanar complementary metal-oxide semiconductor (CMOS) electronics with curvilinear, irregular, or asymmetric shapes and surfaces is an arduous but timely challenge in enabling the production of wearable electronics with an in situ information-processing ability in the digital world. Therefore, we are demonstrating a soft-material enabled double-transfer-based process to integrate flexible, silicon-based, nanoscale, nonplanar, fin-shaped field effect transistors (FinFETs) and planar metal-oxide-semiconductor field effect transistors (MOSFETs) on various asymmetric surfaces to study their compatibility and enhanced applicability in various emerging fields. FinFET devices feature sub-20 nm dimensions and state-of-the-art, high-κ/metal gate stacks, showing no performance alteration after the transfer process. A further analysis of the transferred MOSFET devices, featuring 1 μm gate length, exhibits an ION value of nearly 70 μA/μm (VDS = 2 V, VGS = 2 V) and a low subthreshold swing of around 90 mV/dec, proving that a soft interfacial material can act both as a strong adhesion/interposing layer between devices and final substrate as well as a means to reduce strain, which ultimately helps maintain the device's performance with insignificant deterioration even at a high bending state.

  6. Non-Planar Nano-Scale Fin Field Effect Transistors on Textile, Paper, Wood, Stone, and Vinyl via Soft Material-Enabled Double-Transfer Printing

    KAUST Repository

    Rojas, Jhonathan Prieto

    2015-05-01

    The ability to incorporate rigid but high-performance nano-scale non-planar complementary metal-oxide semiconductor (CMOS) electronics with curvilinear, irregular, or asymmetric shapes and surfaces is an arduous but timely challenge in enabling the production of wearable electronics with an in-situ information-processing ability in the digital world. Therefore, we are demonstrating a soft-material enabled double-transfer-based process to integrate flexible, silicon-based, nano-scale, non-planar, fin-shaped field effect transistors (FinFETs) and planar metal-oxide-semiconductor field effect transistors (MOSFETs) on various asymmetric surfaces to study their compatibility and enhanced applicability in various emerging fields. FinFET devices feature sub-20 nm dimensions and state-of-the-art, high-κ/metal gate stack, showing no performance alteration after the transfer process. A further analysis of the transferred MOSFET devices, featuring 1 μm gate length exhibits ION ~70 μA/μm (VDS = 2 V, VGS = 2 V) and a low sub-threshold swing of around 90 mV/dec, proving that a soft interfacial material can act both as a strong adhesion/interposing layer between devices and final substrate as well as a means to reduce strain, which ultimately helps maintain the device’s performance with insignificant deterioration even at a high bending state.

  7. Growth of strained InGaAs/GaAs quantum wells and index guided injection lasers over nonplanar substrates by molecular beam epitaxy

    International Nuclear Information System (INIS)

    Arent, D.J.; Galeuchet, Y.D.; Nilsson, S.; Meier, H.P.

    1990-01-01

    Strained InGaAs/GaAs quantum wells were grown on nonplanar substrates by molecular beam epitaxy and studied by scanning electron microscopy and low temperature spatially and spectrally resolved cathodoluminescence spectroscopy. For (100) ridges and grooves formed with (311)A sidewalls, almost complete removal of In from the strained quantum wells on the (311)A facet is observed. Corresponding increases of In content in the quantum wells grown on the (100) facets indicate that most if not all of the In is displaced from the (311)A facet via interplanar adatom migration. Ga adatom migration is also observed under our growth conditions such that quantum wells grown nominally near the critical layer thickness on structures less than ≅2.5 μm wide are no longer pseudomorphically strained, as detected by luminescence linewidth analysis. We present the first results of strained InGaAs/GaAs index guided injection lasers grown by single-step molecular beam epitaxy over nonplanar substrates and show that differences greater than 50 meV in the effective band gap of a 70 A quantum well can be achieved between the gain region and the nonabsorbing waveguide without relaxing the strain. Room temperature threshold currents as low as 6 mA for 4 μmx750 μm uncoated devices lasing continuously at a wavelength of 1.01 μm have been achieved

  8. Sliding contact fracture of dental ceramics: Principles and validation

    Science.gov (United States)

    Ren, Linlin; Zhang, Yu

    2014-01-01

    Ceramic prostheses are subject to sliding contact under normal and tangential loads. Accurate prediction of the onset of fracture at two contacting surfaces holds the key to greater long-term performance of these prostheses. In this study, building on stress analysis of Hertzian contact and considering fracture criteria for linear elastic materials, a constitutive fracture mechanics relation was developed to incorporate the critical fracture load with the contact geometry, coefficient of friction and material fracture toughness. Critical loads necessary to cause fracture under a sliding indenter were calculated from the constitutive equation, and compared with the loads predicted from elastic stress analysis in conjunction with measured critical load for frictionless normal contact—a semi-empirical approach. The major predictions of the models were calibrated with experimentally determined critical loads of current and future dental ceramics after contact with a rigid spherical slider. Experimental results conform with the trends predicted by the models. PMID:24632538

  9. Real algebraic geometry

    CERN Document Server

    Bochnak, Jacek; Roy, Marie-Françoise

    1998-01-01

    This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

  10. Critique of information geometry

    International Nuclear Information System (INIS)

    Skilling, John

    2014-01-01

    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

  11. Geometry from Gauge Theory

    International Nuclear Information System (INIS)

    Correa, Diego H.; Silva, Guillermo A.

    2008-01-01

    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

  12. Emergent geometry of membranes

    Energy Technology Data Exchange (ETDEWEB)

    Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

    2015-11-13

    In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

  13. Geometry through history Euclidean, hyperbolic, and projective geometries

    CERN Document Server

    Dillon, Meighan I

    2018-01-01

    Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

  14. Hydraulic conductivity of rock fractures

    International Nuclear Information System (INIS)

    Zimmerman, R.W.; Bodvarsson, G.S.

    1994-10-01

    Yucca Mountain, Nevada contains numerous geological units that are highly fractured. A clear understanding of the hydraulic conductivity of fractures has been identified as an important scientific problem that must be addressed during the site characterization process. The problem of the flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of rigorous fluid mechanics. The derivation of the cubic law is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates, the only fracture geometry that is amenable to exact treatment. The various geometric and kinetic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is always less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area. 68 refs

  15. Effective Hydro-Mechanical Properties of Fluid-Saturated Fracture Networks

    Science.gov (United States)

    Pollmann, N.; Vinci, C.; Renner, J.; Steeb, H.

    2015-12-01

    Consideration of hydro-mechanical processes is essential for the characterization of liquid-resources as well as for many engineering applications. Furthermore, the modeling of seismic waves in fractured porous media finds application not only in geophysical exploration but also reservoir management. Fractures exhibit high-aspect-ratio geometries, i.e. they constitute thin and long hydraulic conduits. Motivated by this peculiar geometry, the investigation of the hydro-mechanically coupled processes is performed by means of a hybrid-dimensional modeling approach. The effective material behavior of domains including complex fracture patterns in a porous rock is assessed by investigating the fluid pressure and the solid displacement of the skeleton saturated by compressible fluids. Classical balance equations are combined with a Poiseuille-type flow in the dimensionally reduced fracture. In the porous surrounding rock, the classical Biot-theory is applied. For simple geometries, our findings show that two main fluid-flow processes occur, leak-off from fractures to the surrounding rock and fracture flow within and between the connected fractures. The separation of critical frequencies of the two flow processes is not straightforward, in particular for systems containing a large number of fractures. Our aim is to model three dimensional hydro-mechanically coupled processes within complex fracture patterns and in particular determine the frequency-dependent attenuation characteristics. Furthermore, the effect of asperities of the fracture surfaces on the fracture stiffness and on the hydraulic conductivity will be added to the approach.

  16. On organizing principles of discrete differential geometry. Geometry of spheres

    International Nuclear Information System (INIS)

    Bobenko, Alexander I; Suris, Yury B

    2007-01-01

    Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

  17. Higher geometry an introduction to advanced methods in analytic geometry

    CERN Document Server

    Woods, Frederick S

    2005-01-01

    For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

  18. Hydraulic Fracturing and Production Optimization in Eagle Ford Shale Using Coupled Geomechanics and Fluid Flow Model

    Science.gov (United States)

    Suppachoknirun, Theerapat; Tutuncu, Azra N.

    2017-12-01

    With increasing production from shale gas and tight oil reservoirs, horizontal drilling and multistage hydraulic fracturing processes have become a routine procedure in unconventional field development efforts. Natural fractures play a critical role in hydraulic fracture growth, subsequently affecting stimulated reservoir volume and the production efficiency. Moreover, the existing fractures can also contribute to the pressure-dependent fluid leak-off during the operations. Hence, a reliable identification of the discrete fracture network covering the zone of interest prior to the hydraulic fracturing design needs to be incorporated into the hydraulic fracturing and reservoir simulations for realistic representation of the in situ reservoir conditions. In this research study, an integrated 3-D fracture and fluid flow model have been developed using a new approach to simulate the fluid flow and deliver reliable production forecasting in naturally fractured and hydraulically stimulated tight reservoirs. The model was created with three key modules. A complex 3-D discrete fracture network model introduces realistic natural fracture geometry with the associated fractured reservoir characteristics. A hydraulic fracturing model is created utilizing the discrete fracture network for simulation of the hydraulic fracture and flow in the complex discrete fracture network. Finally, a reservoir model with the production grid system is used allowing the user to efficiently perform the fluid flow simulation in tight formations with complex fracture networks. The complex discrete natural fracture model, the integrated discrete fracture model for the hydraulic fracturing, the fluid flow model, and the input dataset have been validated against microseismic fracture mapping and commingled production data obtained from a well pad with three horizontal production wells located in the Eagle Ford oil window in south Texas. Two other fracturing geometries were also evaluated to optimize

  19. Traumatic thoracolumbar spine fractures

    NARCIS (Netherlands)

    J. Siebenga (Jan)

    2013-01-01

    textabstractTraumatic spinal fractures have the lowest functional outcomes and the lowest rates of return to work after injury of all major organ systems.1 This thesis will cover traumatic thoracolumbar spine fractures and not osteoporotic spine fractures because of the difference in fracture

  20. Fractures in multiple sclerosis

    DEFF Research Database (Denmark)

    Stenager, E; Jensen, K

    1991-01-01

    In a cross-sectional study of 299 MS patients 22 have had fractures and of these 17 after onset of MS. The fractures most frequently involved the femoral neck and trochanter (41%). Three patients had had more than one fracture. Only 1 patient had osteoporosis. The percentage of fractures increase...

  1. Failure analysis of fractured dental zirconia implants.

    Science.gov (United States)

    Gahlert, M; Burtscher, D; Grunert, I; Kniha, H; Steinhauser, E

    2012-03-01

    The purpose of the present study was the macroscopic and microscopic failure analysis of fractured zirconia dental implants. Thirteen fractured one-piece zirconia implants (Z-Look3) out of 170 inserted implants with an average in situ period of 36.75±5.34 months (range from 20 to 56 months, median 38 months) were prepared for macroscopic and microscopic (scanning electron microscopy [SEM]) failure analysis. These 170 implants were inserted in 79 patients. The patient histories were compared with fracture incidences to identify the reasons for the failure of the implants. Twelve of these fractured implants had a diameter of 3.25 mm and one implant had a diameter of 4 mm. All fractured implants were located in the anterior side of the maxilla and mandibula. The patient with the fracture of the 4 mm diameter implant was adversely affected by strong bruxism. By failure analysis (SEM), it could be demonstrated that in all cases, mechanical overloading caused the fracture of the implants. Inhomogeneities and internal defects of the ceramic material could be excluded, but notches and scratches due to sandblasting of the surface led to local stress concentrations that led to the mentioned mechanical overloading by bending loads. The present study identified a fracture rate of nearly 10% within a follow-up period of 36.75 months after prosthetic loading. Ninety-two per cent of the fractured implants were so-called diameter reduced implants (diameter 3.25 mm). These diameter reduced implants cannot be recommended for further clinical use. Improvement of the ceramic material and modification of the implant geometry has to be carried out to reduce the failure rate of small-sized ceramic implants. Nevertheless, due to the lack of appropriate laboratory testing, only clinical studies will demonstrate clearly whether and how far the failure rate can be reduced. © 2011 John Wiley & Sons A/S.

  2. Assessment of fracture risk

    International Nuclear Information System (INIS)

    Kanis, John A.; Johansson, Helena; Oden, Anders; McCloskey, Eugene V.

    2009-01-01

    Fractures are a common complication of osteoporosis. Although osteoporosis is defined by bone mineral density at the femoral neck, other sites and validated techniques can be used for fracture prediction. Several clinical risk factors contribute to fracture risk independently of BMD. These include age, prior fragility fracture, smoking, excess alcohol, family history of hip fracture, rheumatoid arthritis and the use of oral glucocorticoids. These risk factors in conjunction with BMD can be integrated to provide estimates of fracture probability using the FRAX tool. Fracture probability rather than BMD alone can be used to fashion strategies for the assessment and treatment of osteoporosis.

  3. An introduction to incidence geometry

    CERN Document Server

    De Bruyn, Bart

    2016-01-01

    This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end...

  4. Tracer dispersion in two-dimensional rough fractures.

    Science.gov (United States)

    Drazer, G; Koplik, J

    2001-05-01

    Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness are studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a boundary condition for tracer particles that improves the accuracy of the method. The reduction in the diffusive transport, due to the fractal geometry of the fracture surfaces, is analyzed for different fracture apertures. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for the irregular geometry of the fractures. Dispersion is studied when the two fracture surfaces are simply displaced normally to the mean fracture plane and when there is a lateral shift as well. Numerical results are analyzed using the Lambda parameter, related to convective transport within the fracture, and simple arguments based on lubrication approximation. At very low Péclet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces dispersion.

  5. Casimir forces and geometry

    International Nuclear Information System (INIS)

    Buescher, R.

    2005-01-01

    Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the

  6. Planetary Image Geometry Library

    Science.gov (United States)

    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

  7. Modeling earthquake sequences along the Manila subduction zone: Effects of three-dimensional fault geometry

    Science.gov (United States)

    Yu, Hongyu; Liu, Yajing; Yang, Hongfeng; Ning, Jieyuan

    2018-05-01

    To assess the potential of catastrophic megathrust earthquakes (MW > 8) along the Manila Trench, the eastern boundary of the South China Sea, we incorporate a 3D non-planar fault geometry in the framework of rate-state friction to simulate earthquake rupture sequences along the fault segment between 15°N-19°N of northern Luzon. Our simulation results demonstrate that the first-order fault geometry heterogeneity, the transitional-segment (possibly related to the subducting Scarborough seamount chain) connecting the steeper south segment and the flatter north segment, controls earthquake rupture behaviors. The strong along-strike curvature at the transitional-segment typically leads to partial ruptures of MW 8.3 and MW 7.8 along the southern and northern segments respectively. The entire fault occasionally ruptures in MW 8.8 events when the cumulative stress in the transitional-segment is sufficiently high to overcome the geometrical inhibition. Fault shear stress evolution, represented by the S-ratio, is clearly modulated by the width of seismogenic zone (W). At a constant plate convergence rate, a larger W indicates on average lower interseismic stress loading rate and longer rupture recurrence period, and could slow down or sometimes stop ruptures that initiated from a narrower portion. Moreover, the modeled interseismic slip rate before whole-fault rupture events is comparable with the coupling state that was inferred from the interplate seismicity distribution, suggesting the Manila trench could potentially rupture in a M8+ earthquake.

  8. Initiation to global Finslerian geometry

    CERN Document Server

    Akbar-Zadeh, Hassan

    2006-01-01

    After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p

  9. Ostrich eggs geometry

    Directory of Open Access Journals (Sweden)

    Šárka Nedomová

    2013-01-01

    Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.

  10. Nonperturbative quantum geometries

    International Nuclear Information System (INIS)

    Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara

    1988-01-01

    Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)

  11. Matrix Information Geometry

    CERN Document Server

    Bhatia, Rajendra

    2013-01-01

    This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR).  During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented  are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.  

  12. An Experimental Investigation of Hydraulic Fracturing in Shale Considering Anisotropy and Using Freshwater and Supercritical CO2

    Directory of Open Access Journals (Sweden)

    Jianming He

    2018-03-01

    Full Text Available The process of hydraulic fracturing makes use of a liquid to fracture reservoir rocks for the exploitation of unconventional resources. Hence, it is vital to understand the processes that produce the fracture networks that occur during hydraulic fracturing. A shale reservoir is one of the largest unconventional resources and it displays obvious anisotropic characteristics due to its inherent sedimentary structures. The viscosity and flow ability of the fracturing fluid plays an important role in this process. We conducted a series of hydraulic fracturing tests on shale cores (from the southern Sichuan Basin using freshwater and supercritical CO2 (SCO2 as fracturing fluids to investigate the different modes of fracture propagation. The pump pressure curves that we obtained during the fracturing experiment show how the shale responded to each of the fracturing fluids. We examined the influence of the anisotropic characteristics on the propagation of hydraulic fractures by conducting a series of hydraulic fracturing experiments on the shale cores using different bedding orientations. The bedding orientation of the shale had a profound influence on the fracture propagation when using either freshwater or a SCO2 fluid. The breakdown pressure of the shale core was affected not only by the bedding orientation but also by the fracturing fluid. A macroscopic observation of the fractures revealed different fracture geometries and propagation patterns. The results demonstrated that the anisotropic structures and the fracturing fluids could influence the path of the hydraulic fracture.

  13. Fracture size and transmissivity correlations: Implications for transport simulations in sparse three-dimensional discrete fracture networks following a truncated power law distribution of fracture size

    Science.gov (United States)

    Hyman, J.; Aldrich, G. A.; Viswanathan, H. S.; Makedonska, N.; Karra, S.

    2016-12-01

    We characterize how different fracture size-transmissivity relationships influence flow and transport simulations through sparse three-dimensional discrete fracture networks. Although it is generally accepted that there is a positive correlation between a fracture's size and its transmissivity/aperture, the functional form of that relationship remains a matter of debate. Relationships that assume perfect correlation, semi-correlation, and non-correlation between the two have been proposed. To study the impact that adopting one of these relationships has on transport properties, we generate multiple sparse fracture networks composed of circular fractures whose radii follow a truncated power law distribution. The distribution of transmissivities are selected so that the mean transmissivity of the fracture networks are the same and the distributions of aperture and transmissivity in models that include a stochastic term are also the same.We observe that adopting a correlation between a fracture size and its transmissivity leads to earlier breakthrough times and higher effective permeability when compared to networks where no correlation is used. While fracture network geometry plays the principal role in determining where transport occurs within the network, the relationship between size and transmissivity controls the flow speed. These observations indicate DFN modelers should be aware that breakthrough times and effective permeabilities can be strongly influenced by such a relationship in addition to fracture and network statistics.

  14. Hydraulic fracture diagnostic: recent advances and their impact; Analyses de la fracturation hydraulique: progres recents et leur impact

    Energy Technology Data Exchange (ETDEWEB)

    Wolhart, St.L. [GRI, United States (United States)

    2000-07-01

    The use of hydraulic fracturing has grown tremendously since its introduction over 50 years ago. Most wells in low permeability reservoirs are not economic without hydraulic fracture stimulation. Hydraulic fracturing is also seeing increasing use in high permeability applications. The success of this technology can be attributed to the great strides made in three areas: hydraulic fracture theory and modeling, improved surface and subsurface equipment and advanced fluid systems and proppers. However, industry still has limited capabilities when it comes to determining the geometry of the created hydraulic fracture. This limitation, in turn places limits on the continued improvement of hydraulic fracturing as a means to optimize productivity and recovery. GRI's Advanced Hydraulic Fracture Diagnostics Program has developed two new technologies, microseismic hydraulic fracture mapping and downhole tilt-meter hydraulic fracture mapping, to address this limitation. These two technologies have been utilized to improve field development and reduce hydraulic fracturing costs. This paper reviews these technologies and presents case histories of their use. (author)

  15. Paratrooper's ankle fracture: posterior malleolar fracture.

    Science.gov (United States)

    Young, Ki Won; Kim, Jin-su; Cho, Jae Ho; Kim, Hyung Seuk; Cho, Hun Ki; Lee, Kyung Tai

    2015-03-01

    We assessed the frequency and types of ankle fractures that frequently occur during parachute landings of special operation unit personnel and analyzed the causes. Fifty-six members of the special force brigade of the military who had sustained ankle fractures during parachute landings between January 2005 and April 2010 were retrospectively analyzed. The injury sites and fracture sites were identified and the fracture types were categorized by the Lauge-Hansen and Weber classifications. Follow-up surveys were performed with respect to the American Orthopedic Foot and Ankle Society ankle-hindfoot score, patient satisfaction, and return to preinjury activity. The patients were all males with a mean age of 23.6 years. There were 28 right and 28 left ankle fractures. Twenty-two patients had simple fractures and 34 patients had comminuted fractures. The average number of injury and fractures sites per person was 2.07 (116 injuries including a syndesmosis injury and a deltoid injury) and 1.75 (98 fracture sites), respectively. Twenty-three cases (41.07%) were accompanied by posterior malleolar fractures. Fifty-five patients underwent surgery; of these, 30 had plate internal fixations. Weber type A, B, and C fractures were found in 4, 38, and 14 cases, respectively. Based on the Lauge-Hansen classification, supination-external rotation injuries were found in 20 cases, supination-adduction injuries in 22 cases, pronation-external rotation injuries in 11 cases, tibiofibular fractures in 2 cases, and simple medial malleolar fractures in 2 cases. The mean follow-up period was 23.8 months, and the average follow-up American Orthopedic Foot and Ankle Society ankle-hindfoot score was 85.42. Forty-five patients (80.36%) reported excellent or good satisfaction with the outcome. Posterior malleolar fractures occurred in 41.07% of ankle fractures sustained in parachute landings. Because most of the ankle fractures in parachute injuries were compound fractures, most cases had to

  16. Analysis of fracture patterns and local stress field variations in fractured reservoirs

    Science.gov (United States)

    Deckert, Hagen; Drews, Michael; Fremgen, Dominik; Wellmann, J. Florian

    2010-05-01

    A meaningful qualitative evaluation of permeabilities in fractured reservoirs in geothermal or hydrocarbon industry requires the spatial description of the existing discontinuity pattern within the area of interest and an analysis how these fractures might behave under given stress fields. This combined information can then be used for better estimating preferred fluid pathway directions within the reservoir, which is of particular interest for defining potential drilling sites. A description of the spatial fracture pattern mainly includes the orientation of rock discontinuities, spacing relationships between single fractures and their lateral extent. We have examined and quantified fracture patterns in several outcrops of granite at the Costa Brava, Spain, and in the Black Forest, Germany, for describing reservoir characteristics. For our analysis of fracture patterns we have used photogrammetric methods to create high-resolution georeferenced digital 3D images of outcrop walls. The advantage of this approach, compared to conventional methods for fracture analysis, is that it provides a better 3D description of the fracture geometry as the entity of position, extent and orientation of single fractures with respect to their surrounding neighbors is conserved. Hence for instance, the method allows generating fracture density maps, which can be used for a better description of the spatial distribution of discontinuities in a given outcrop. Using photogrammetric techniques also has the advantage to acquire very large data sets providing statistically sound results. To assess whether the recorded discontinuities might act as fluid pathways information on the stress field is needed. A 3D model of the regional tectonic structure was created and the geometry of the faults was put into a mechanical 3D Boundary Element (BE) Model. The model takes into account the elastic material properties of the geological units and the orientation of single fault segments. The

  17. GPS: Geometry, Probability, and Statistics

    Science.gov (United States)

    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…

  18. Surrogate Modeling for Geometry Optimization

    DEFF Research Database (Denmark)

    Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie

    2009-01-01

    A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....

  19. Kaehler geometry and SUSY mechanics

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Nersessian, Armen

    2001-01-01

    We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed

  20. A prediction for bubbling geometries

    OpenAIRE

    Okuda, Takuya

    2007-01-01

    We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.

  1. Molecular motion in restricted geometries

    Indian Academy of Sciences (India)

    Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...

  2. Challenges in Continuum Modelling of Intergranular Fracture

    DEFF Research Database (Denmark)

    Coffman, Valerie; Sethna, James P.; Ingraffea, A. R.

    2011-01-01

    of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary......Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First...... properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation....

  3. Fracture toughness evaluation of circumferentially-cracked round bars

    International Nuclear Information System (INIS)

    Scibetta, M.

    1996-05-01

    The measure of the fracture toughness of a circumferentially-cracked round bar is generally performed through approximate formulae. Comparison of existing formulae to finite element results does not always show good agreement. Therefore an eta factor is introduced in order to improve the existing analytical formula. The axisymmetrical geometry is generally considered to be a high constrained geometry. Finite element calculations are performed to verify and quantify the constraint relative to the three point bending configuration (precracked Charpy)

  4. The application of positron emission tomography to the study of mass transfer in fractured rock

    International Nuclear Information System (INIS)

    Gilling, D.; Jefferies, N.L.; Fowles, P.; Hawkesworth, M.R.; Parker, D.J.

    1991-06-01

    In order to predict the transport of dissolved radioelements through a fractured rock it is necessary to determine both the geometry of the fracture network and the hydraulic properties of the individual fractures. This paper describes a technique for studying mass transfer in a single fracture. The technique is positron emission tomography (PET) and it offers the potential for visualising quantitatively the migration of dissolved tracers. Preliminary experiments have been undertaken involving the flow of Na-22 and F-18 labelled solutions through artificial fractures. The results demonstrate that PET is well suited to this application. (author)

  5. Basic algebraic geometry, v.2

    CERN Document Server

    Shafarevich, Igor Rostislavovich

    1994-01-01

    Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...

  6. Optical geometry across the horizon

    International Nuclear Information System (INIS)

    Jonsson, Rickard

    2006-01-01

    In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework

  7. Influence of fracture networks on radionuclide transport from solidified waste forms

    Energy Technology Data Exchange (ETDEWEB)

    Seetharam, S.C., E-mail: suresh.seetharam@sckcen.be [Performance Assessments Unit, Institute for Environment, Health and Safety, Belgian Nuclear Research Centre (SCK CEN), Boeretang 200, B-2400 Mol (Belgium); Perko, J.; Jacques, D. [Performance Assessments Unit, Institute for Environment, Health and Safety, Belgian Nuclear Research Centre (SCK CEN), Boeretang 200, B-2400 Mol (Belgium); Mallants, D. [CSIRO Land and Water, Waite Road – Gate 4, Glen Osmond, SA 5064 (Australia)

    2014-04-01

    Highlights: • Magnitude of peak radionuclide fluxes is less sensitive to the fracture network geometry. • Time of peak radionuclide fluxes is sensitive to the fracture networks. • Uniform flow model mimics a limiting case of a porous medium with large number of fine fractures. • Effect of fracture width on radionuclide flux depends on the ratio of fracture to matrix conductivity. • Effect of increased dispersivity in fractured media does not always result in a lower peak flux for specific fracture networks due to higher concentrations adjacent to the fracture plane. - Abstract: Analysis of the effect of fractures in porous media on fluid flow and mass transport is of great interest in many fields including geotechnical, petroleum, hydrogeology and waste management. This paper presents sensitivity analyses examining the effect of various hypothetical fracture networks on the performance of a planned near surface disposal facility in terms of radionuclide transport behaviour. As it is impossible to predict the initiation and evolution of fracture networks and their characteristics in concrete structures over time scales of interest, several fracture networks have been postulated to test the sensitivity of radionuclide release from a disposal facility. Fluid flow through concrete matrix and fracture networks are modelled via Darcy's law. A single species radionuclide transport equation is employed for both matrix and fracture networks, which include the processes advection, diffusion, dispersion, sorption/desorption and radioactive decay. The sensitivity study evaluates variations in fracture network configuration and fracture width together with different sorption/desorption characteristics of radionuclides in a cement matrix, radioactive decay constants and matrix dispersivity. The effect of the fractures is illustrated via radionuclide breakthrough curves, magnitude and time of peak mass flux, cumulative mass flux and concentration profiles. For the

  8. Influence of fracture networks on radionuclide transport from solidified waste forms

    International Nuclear Information System (INIS)

    Seetharam, S.C.; Perko, J.; Jacques, D.; Mallants, D.

    2014-01-01

    Highlights: • Magnitude of peak radionuclide fluxes is less sensitive to the fracture network geometry. • Time of peak radionuclide fluxes is sensitive to the fracture networks. • Uniform flow model mimics a limiting case of a porous medium with large number of fine fractures. • Effect of fracture width on radionuclide flux depends on the ratio of fracture to matrix conductivity. • Effect of increased dispersivity in fractured media does not always result in a lower peak flux for specific fracture networks due to higher concentrations adjacent to the fracture plane. - Abstract: Analysis of the effect of fractures in porous media on fluid flow and mass transport is of great interest in many fields including geotechnical, petroleum, hydrogeology and waste management. This paper presents sensitivity analyses examining the effect of various hypothetical fracture networks on the performance of a planned near surface disposal facility in terms of radionuclide transport behaviour. As it is impossible to predict the initiation and evolution of fracture networks and their characteristics in concrete structures over time scales of interest, several fracture networks have been postulated to test the sensitivity of radionuclide release from a disposal facility. Fluid flow through concrete matrix and fracture networks are modelled via Darcy's law. A single species radionuclide transport equation is employed for both matrix and fracture networks, which include the processes advection, diffusion, dispersion, sorption/desorption and radioactive decay. The sensitivity study evaluates variations in fracture network configuration and fracture width together with different sorption/desorption characteristics of radionuclides in a cement matrix, radioactive decay constants and matrix dispersivity. The effect of the fractures is illustrated via radionuclide breakthrough curves, magnitude and time of peak mass flux, cumulative mass flux and concentration profiles. For the

  9. Fracture mechanical materials characterisation

    International Nuclear Information System (INIS)

    Wallin, K.; Planman, T.; Nevalainen, M.

    1998-01-01

    The experimental fracture mechanics development has been focused on the determination of reliable lower-bound fracture toughness estimates from small and miniature specimens, in particular considering the statistical aspects and loading rate effects of fracture mechanical material properties. Additionally, materials aspects in fracture assessment of surface cracks, with emphasis on the transferability of fracture toughness data to structures with surface flaws have been investigated. Further a modified crack-arrest fracture toughness test method, to increase the effectiveness of testing, has been developed. (orig.)

  10. Ta2O5/ Al2O3/ SiO2 - antireflective coating for non-planar optical surfaces by atomic layer deposition

    Science.gov (United States)

    Pfeiffer, K.; Schulz, U.; Tünnermann, A.; Szeghalmi, A.

    2017-02-01

    Antireflective coatings are essential to improve transmittance of optical elements. Most research and development of AR coatings has been reported on a wide variety of plane optical surfaces; however, antireflection is also necessary on nonplanar optical surfaces. Physical vapor deposition (PVD), a common method for optical coatings, often results in thickness gradients on strongly curved surfaces, leading to a failure of the desired optical function. In this work, optical thin films of tantalum pentoxide, aluminum oxide and silicon dioxide were prepared by atomic layer deposition (ALD), which is based on self-limiting surface reactions. The results demonstrate that ALD optical layers can be deposited on both vertical and horizontal substrate surfaces with uniform thicknesses and the same optical properties. A Ta2O5/Al2O3/ SiO2 multilayer AR coating (400-700 nm) was successfully applied to a curved aspheric glass lens with a diameter of 50 mm and a center thickness of 25 mm.

  11. White emission from non-planar InGaN/GaN MQW LEDs grown on GaN template with truncated hexagonal pyramids.

    Science.gov (United States)

    Lee, Ming-Lun; Yeh, Yu-Hsiang; Tu, Shang-Ju; Chen, P C; Lai, Wei-Chih; Sheu, Jinn-Kong

    2015-04-06

    Non-planar InGaN/GaN multiple quantum well (MQW) structures are grown on a GaN template with truncated hexagonal pyramids (THPs) featuring c-plane and r-plane surfaces. The THP array is formed by the regrowth of the GaN layer on a selective-area Si-implanted GaN template. Transmission electron microscopy shows that the InGaN/GaN epitaxial layers regrown on the THPs exhibit different growth rates and indium compositions of the InGaN layer between the c-plane and r-plane surfaces. Consequently, InGaN/GaN MQW light-emitting diodes grown on the GaN THP array emit multiple wavelengths approaching near white light.

  12. Ipsilateral Traumatic Posterior Hip Dislocation, Posterior Wall and Transverse Acetabular Fracture with Trochanteric Fracture in an adult: Report of First Case

    Directory of Open Access Journals (Sweden)

    Skand Sinha

    2013-10-01

    Full Text Available Introduction: Posterior dislocation of the hip joint with associated acetabular and intertrochanteric fracture is a complex injury. Early recognition, prompt and stable reduction is needed of successful outcome. Case Report: 45 year old male patient presented with posterior dislocation of the hip with transverse fracture with posterior wall fracture of acetabulam and intertrochanteric fracture on the ipsilateral side. The complex fracture geometry was confirmed by CT scan. The patient was successfully managed by open reduction and internal fixation of intertrochanteric fracture was achieved with dynamic hip screw (DHS plate fixation followed by fixation of acetabular fracture with reconstruction plate. Conclusion: Hip dislocation combined with acetabular fracture is an uncommon injury; this article presents a unique case of posterior wall and transverse fractures of ipsilateral acetabulum with intertrochanteric fracture in a patient who sustained traumatic posterior hip dislocation. Early surgical intervention is important for satisfactory outcomes of such complex fracture-dislocation injuries. Keywords: Hip dislocation; acetabular fractures; intertrochanteric fracture; operative treatment.

  13. Fractures inside crystalline rocks. Effects of deformations on fluid circulations

    International Nuclear Information System (INIS)

    Gentier, S.

    2005-01-01

    The modeling of fluid flows inside granite massifs is an important task for the evaluation of the feasibility of radioactive waste storage inside such formations. This document makes a synthesis of the works carried out since about 15 years, in particular by the French bureau of geological and mining research (BRGM), about the hydro-mechanical behaviour of a fracture and about the hydrodynamical characterization of fracture networks inside crystalline rocks: 1 - introduction; 2 - hydro-mechanical behaviour under normal stress: experimental results (hydro-mechanical behaviour, flow regimes, mechanical behaviour, test protocol, complementary tests, influence of samples size), geometrical interpretation of experimental results (relation with walls geometry, relation with voids geometry, relation with contacts geometry), hydro-mechanical modeling (hydraulic modeling, mechanical modeling); 3 - from the hydro-mechanical behaviour under normal stress to the coupling with heat transfers and chemistry: experiment for the study of the chemo-thermo-hydro-mechanical coupling (experimental results, relation with walls morphology), thermo-hydro-mechanical experiments, thermo-hydro-chemical experiments with fractures, conclusions; 4 - hydro-mechanical behaviour during shear: experimental results, geometrical interpretation (relation with the geometry of damaged zones, relation with voids geometry, relation with walls geometry), hydro-mechanical modeling (mechanical modeling, hydro-mechanical modeling of the behaviour during shear). (J.S.)

  14. Approaching a universal scaling relationship between fracture stiffness and fluid flow

    Science.gov (United States)

    Pyrak-Nolte, Laura J.; Nolte, David D.

    2016-02-01

    A goal of subsurface geophysical monitoring is the detection and characterization of fracture alterations that affect the hydraulic integrity of a site. Achievement of this goal requires a link between the mechanical and hydraulic properties of a fracture. Here we present a scaling relationship between fluid flow and fracture-specific stiffness that approaches universality. Fracture-specific stiffness is a mechanical property dependent on fracture geometry that can be monitored remotely using seismic techniques. A Monte Carlo numerical approach demonstrates that a scaling relationship exists between flow and stiffness for fractures with strongly correlated aperture distributions, and continues to hold for fractures deformed by applied stress and by chemical erosion as well. This new scaling relationship provides a foundation for simulating changes in fracture behaviour as a function of stress or depth in the Earth and will aid risk assessment of the hydraulic integrity of subsurface sites.

  15. Hydromechanical modeling of clay rock including fracture damage

    Science.gov (United States)

    Asahina, D.; Houseworth, J. E.; Birkholzer, J. T.

    2012-12-01

    Argillaceous rock typically acts as a flow barrier, but under certain conditions significant and potentially conductive fractures may be present. Fracture formation is well-known to occur in the vicinity of underground excavations in a region known as the excavation disturbed zone. Such problems are of particular importance for low-permeability, mechanically weak rock such as clays and shales because fractures can be relatively transient as a result of fracture self-sealing processes. Perhaps not as well appreciated is the fact that natural fractures can form in argillaceous rock as a result of hydraulic overpressure caused by phenomena such as disequlibrium compaction, changes in tectonic stress, and mineral dehydration. Overpressure conditions can cause hydraulic fracturing if the fluid pressure leads to tensile effective stresses that exceed the tensile strength of the material. Quantitative modeling of this type of process requires coupling between hydrogeologic processes and geomechanical processes including fracture initiation and propagation. Here we present a computational method for three-dimensional, hydromechanical coupled processes including fracture damage. Fractures are represented as discrete features in a fracture network that interact with a porous rock matrix. Fracture configurations are mapped onto an unstructured, three-dimensonal, Voronoi grid, which is based on a random set of spatial points. Discrete fracture networks (DFN) are represented by the connections of the edges of a Voronoi cells. This methodology has the advantage that fractures can be more easily introduced in response to coupled hydro-mechanical processes and generally eliminates several potential issues associated with the geometry of DFN and numerical gridding. A geomechanical and fracture-damage model is developed here using the Rigid-Body-Spring-Network (RBSN) numerical method. The hydrogelogic and geomechanical models share the same geometrical information from a 3D Voronoi

  16. Complex analysis and CR geometry

    CERN Document Server

    Zampieri, Giuseppe

    2008-01-01

    Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...

  17. The geometry description markup language

    International Nuclear Information System (INIS)

    Chytracek, R.

    2001-01-01

    Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML

  18. Fractures (Broken Bones): First Aid

    Science.gov (United States)

    First aid Fractures (broken bones) Fractures (broken bones): First aid By Mayo Clinic Staff A fracture is a ... 10, 2018 Original article: http://www.mayoclinic.org/first-aid/first-aid-fractures/basics/ART-20056641 . Mayo Clinic ...

  19. Head First 2D Geometry

    CERN Document Server

    Fallow), Stray

    2009-01-01

    Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and

  20. A first course in geometry

    CERN Document Server

    Walsh, Edward T

    2014-01-01

    This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl

  1. Differential geometry curves, surfaces, manifolds

    CERN Document Server

    Kohnel, Wolfgang

    2002-01-01

    This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.

  2. Fracture toughness correlations

    International Nuclear Information System (INIS)

    Wallin, Kim

    1986-09-01

    In this study existing fracture parameter correlations are reviewed. Their applicability and reliability are discussed in detail. A new K IC -CVN-correlation, based on a theoretical brittle fracture model, is presented

  3. Rib fracture - aftercare

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/patientinstructions/000539.htm Rib fracture - aftercare To use the sharing features on this page, please enable JavaScript. A rib fracture is a crack or break in one or ...

  4. Sprains, Strains and Fractures

    Science.gov (United States)

    ... fractures. Many fractures and sprains occur during sports. Football players are particularly vulnerable to foot and ankle ... feet and ankles and take a complete medical history. He or she will also order tests, including ...

  5. Infant skull fracture (image)

    Science.gov (United States)

    Skull fractures may occur with head injuries. Although the skull is both tough and resilient and provides excellent ... or blow can result in fracture of the skull and may be accompanied by injury to the ...

  6. Ankle fracture - aftercare

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/patientinstructions/000548.htm Ankle fracture - aftercare To use the sharing features on this page, please enable JavaScript. An ankle fracture is a break in 1 or more ankle ...

  7. Monitoring hydraulic fractures: state estimation using an extended Kalman filter

    International Nuclear Information System (INIS)

    Rochinha, Fernando Alves; Peirce, Anthony

    2010-01-01

    There is considerable interest in using remote elastostatic deformations to identify the evolving geometry of underground fractures that are forced to propagate by the injection of high pressure viscous fluids. These so-called hydraulic fractures are used to increase the permeability in oil and gas reservoirs as well as to pre-fracture ore-bodies for enhanced mineral extraction. The undesirable intrusion of these hydraulic fractures into environmentally sensitive areas or into regions in mines which might pose safety hazards has stimulated the search for techniques to enable the evolving hydraulic fracture geometries to be monitored. Previous approaches to this problem have involved the inversion of the elastostatic data at isolated time steps in the time series provided by tiltmeter measurements of the displacement gradient field at selected points in the elastic medium. At each time step, parameters in simple static models of the fracture (e.g. a single displacement discontinuity) are identified. The approach adopted in this paper is not to regard the sequence of sampled elastostatic data as independent, but rather to treat the data as linked by the coupled elastic-lubrication equations that govern the propagation of the evolving hydraulic fracture. We combine the Extended Kalman Filter (EKF) with features of a recently developed implicit numerical scheme to solve the coupled free boundary problem in order to form a novel algorithm to identify the evolving fracture geometry. Numerical experiments demonstrate that, despite excluding significant physical processes in the forward numerical model, the EKF-numerical algorithm is able to compensate for the un-modeled dynamics by using the information fed back from tiltmeter data. Indeed the proposed algorithm is able to provide reasonably faithful estimates of the fracture geometry, which are shown to converge to the actual hydraulic fracture geometry as the number of tiltmeters is increased. Since the location of

  8. Atraumatic First Rib Fracture

    OpenAIRE

    Koray Aydogdu

    2014-01-01

    Rib fractures are usually seen after a trauma, while atraumatic spontaneous rib fractures are quite rare. A first rib fracture identified in our 17 years old female patient who had not a history of trauma except lifting a heavy weight was examined in details in terms of the potential complications and followed-up for a long time. We presented our experience on this case with atraumatic first rib fracture that has different views for the etiology in light of the literature.

  9. Metatarsal stress fractures - aftercare

    Science.gov (United States)

    ... Metatarsal stress fracture. In: Safran MR, Zachazewski J, Stone DA, eds. Instructions for Sports Medicine Patients . 2nd ed. Elsevier Saunders; 2012:648-652. Smith MS. Metatarsal fractures. In: Eiff PM, Hatch R, eds. Fracture Management for Primary Care . 3rd ed. ...

  10. Obesity and fracture risk

    OpenAIRE

    Gonnelli, Stefano; Caffarelli, Carla; Nuti, Ranuccio

    2014-01-01

    Obesity and osteoporosis are two common diseases with an increasing prevalence and a high impact on morbidity and mortality. Obese women have always been considered protected against osteoporosis and osteoporotic fractures. However, several recent studies have challenged the widespread belief that obesity is protective against fracture and have suggested that obesity is a risk factor for certain fractures.

  11. Imaging of insufficiency fractures

    Energy Technology Data Exchange (ETDEWEB)

    Krestan, Christian [Department of Radiology, Medical University of Vienna, Vienna General Hospital, Waehringerstr. 18-20, 1090 Vienna (Austria)], E-mail: christian.krestan@meduniwien.ac.at; Hojreh, Azadeh [Department of Radiology, Medical University of Vienna, Vienna General Hospital, Waehringerstr. 18-20, 1090 Vienna (Austria)

    2009-09-15

    This review focuses on the occurrence, imaging and differential diagnosis of insufficiency fractures. Prevalence, the most common sites of insufficiency fractures and their clinical implications are discussed. Insufficiency fractures occur with normal stress exerted on weakened bone. Postmenopausal osteoporosis is the most common cause of insufficiency fractures. Other conditions which affect bone turnover include osteomalacia, hyperparathyroidism, chronic renal failure and high-dose glucocorticoid therapy. It is a challenge for the radiologist to detect and diagnose insufficiency fractures, and to differentiate them from other bone lesions. Radiographs are still the most widely used imaging method for identification of insufficiency fractures, but sensitivity is limited, depending on the location of the fractures. Magnetic resonance imaging (MRI) is a very sensitive tool to visualize bone marrow abnormalities associated with insufficiency fractures. Thin section, multi-detector computed tomography (MDCT) depicts subtle fracture lines allowing direct visualization of cortical and trabecular bone. Bone scintigraphy still plays a role in detecting fractures, with good sensitivity but limited specificity. The most important differential diagnosis is underlying malignant disease leading to pathologic fractures. Bone densitometry and clinical history may also be helpful in confirming the diagnosis of insufficiency fractures.

  12. Advances in discrete differential geometry

    CERN Document Server

    2016-01-01

    This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

  13. Hyperbolic Metamaterials with Complex Geometry

    DEFF Research Database (Denmark)

    Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei

    2016-01-01

    We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...

  14. An introduction to differential geometry

    CERN Document Server

    Willmore, T J

    2012-01-01

    This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

  15. Symplectic geometry and Fourier analysis

    CERN Document Server

    Wallach, Nolan R

    2018-01-01

    Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.

  16. Topology and geometry for physicists

    CERN Document Server

    Nash, Charles

    1983-01-01

    Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr

  17. Fracture corridors as seal-bypass systems in siliciclastic reservoir-cap rock successions: Field-based insights from the Jurassic Entrada Formation (SE Utah, USA)

    NARCIS (Netherlands)

    Ogata, Kei; Senger, Kim; Braathen, Alvar; Tveranger, Jan

    2014-01-01

    Closely spaced, sub-parallel fracture networks contained within localized tabular zones that are fracture corridors may compromise top seal integrity and form pathways for vertical fluid flow between reservoirs at different stratigraphic levels. This geometry is exemplified by fracture corridors

  18. Spectral dimension of quantum geometries

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2014-01-01

    The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)

  19. Role of MRI in hip fractures, including stress fractures, occult fractures, avulsion fractures

    International Nuclear Information System (INIS)

    Nachtrab, O.; Cassar-Pullicino, V.N.; Lalam, R.; Tins, B.; Tyrrell, P.N.M.; Singh, J.

    2012-01-01

    MR imaging plays a vital role in the diagnosis and management of hip fractures in all age groups, in a large spectrum of patient groups spanning the elderly and sporting population. It allows a confident exclusion of fracture, differentiation of bony from soft tissue injury and an early confident detection of fractures. There is a spectrum of MR findings which in part is dictated by the type and cause of the fracture which the radiologist needs to be familiar with. Judicious but prompt utilisation of MR in patients with suspected hip fractures has a positive therapeutic impact with healthcare cost benefits as well as social care benefits.

  20. Dynamics and Scaling Properties of Fractures in clay-like Materials

    Energy Technology Data Exchange (ETDEWEB)

    Walmann, Thomas

    1998-12-31

    Computer models that can help oil companies predict realistic and physically correct fracture patterns are important. To verify such a model, experiments described in this thesis were undertaken, using wet clay and powder. The main focus was on extensional fractures, but other types of fractures were also studied. High resolution digital images of the fracture patterns were recorded and analyzed using statistical physics and fractal geometry. The characteristic shapes and size distributions of individual fractures and the overall fracture patterns obtained from laboratory model studies were compared to results from aerial photographs of a fracture pattern in a collapsed glacier that had undergone a similar deformation. A new scaling relation (a power-law) between the length of a fracture and the projected area is derived for fractures formed during clay model experiments. This scaling relation is found also in a field study of a fracture pattern in a glacier. The forms of the different distributions that characterizes fractures in clay experiments are discussed. Several characteristic lengths are associated with the laboratory experiments. They are related to the sample size and shape, the model material and the nature of the imposed deformation. The roughness of the fracture traces obtained from powder experiments was found to have a self-affine form. The roughness, or Hurst exponent, was found to have the value 0.73, plus or minus 0.09. A large number of interacting fractures were formed in the systems studied, and under such conditions the fluctuations about the direction perpendicular to the principle strain direction are influenced by neighbouring fractures. As expected, an upper cutoff for the scaling range was observed. But the length at which the crossover from a self-affine shape to a flat shape took place did not depend systematically on any of the experimental parameters or characteristic length scales. The total fracture trace patterns could not be

  1. Orbital fractures: a review

    Directory of Open Access Journals (Sweden)

    Jeffrey M Joseph

    2011-01-01

    Full Text Available Jeffrey M Joseph, Ioannis P GlavasDivision of Ophthalmic Plastic and Reconstructive Surgery, Department of Ophthalmology, School of Medicine, New York University, New York, NY, USA; Manhattan Eye, Ear, and Throat Hospital, New York, NY, USAAbstract: This review of orbital fractures has three goals: 1 to understand the clinically relevant orbital anatomy with regard to periorbital trauma and orbital fractures, 2 to explain how to assess and examine a patient after periorbital trauma, and 3 to understand the medical and surgical management of orbital fractures. The article aims to summarize the evaluation and management of commonly encountered orbital fractures from the ophthalmologic perspective and to provide an overview for all practicing ophthalmologists and ophthalmologists in training.Keywords: orbit, trauma, fracture, orbital floor, medial wall, zygomatic, zygomatic complex, zmc fracture, zygomaticomaxillary complex fractures 

  2. Mechanics of Hydraulic Fractures

    Science.gov (United States)

    Detournay, Emmanuel

    2016-01-01

    Hydraulic fractures represent a particular class of tensile fractures that propagate in solid media under pre-existing compressive stresses as a result of internal pressurization by an injected viscous fluid. The main application of engineered hydraulic fractures is the stimulation of oil and gas wells to increase production. Several physical processes affect the propagation of these fractures, including the flow of viscous fluid, creation of solid surfaces, and leak-off of fracturing fluid. The interplay and the competition between these processes lead to multiple length scales and timescales in the system, which reveal the shifting influence of the far-field stress, viscous dissipation, fracture energy, and leak-off as the fracture propagates.

  3. Fracture in Soft Materials

    DEFF Research Database (Denmark)

    Hassager, Ole

    Fracture is a phenomenon that is generally associated with solids. A key element in fracture theory is the so-called weakest link idea that fracture initiates from the largest pre-existing material imperfection. However, recent work has demonstrated that fracture can also happen in liquids, where...... surface tension will act to suppress such imperfections. Therefore, the weakest link idea does not seem immediately applicable to fracture in liquids. This presentation will review fracture in liquids and argue that fracture in soft liquids is a material property independent of pre-existing imperfections....... The following questions then emerge: What is the material description needed to predict crack initiation, crack speed and crack shape in soft materials and liquids....

  4. Determination of in-situ fracture apertures from digital borehole images

    International Nuclear Information System (INIS)

    Johansson, Maria C.; Stephansson, O.

    1998-01-01

    Imaging methods applied to borehole investigations have become common for mapping and characterisation of the rock mass. Today we have access to detailed information about the rock, but we lack some methods for analysis. In this study we develop a methodology for measurements of in-situ fracture geometry, from optical borehole images (BIP-system). We focus on the detailed information about fracture geometry, available thanks to the high image resolution. We have decided to perform the measurements using digital image processing, to avoid bias from the human analyst, and we present on-going work on the image processing methodology. Our method is based on iterative intensity thresholding. We work on grey-scale images, of open fractures that fully intersect the borehole. The fracture trace comes out as a dark sinusoidal in the borehole image. First, the darkest pixels in the image are extracted. Then the pixels, which are immediate neighbours to the first set, are included, under the condition that they are darker than a somewhat lower threshold. The including of neighbours is repeated until the fracture trace is filled. The resulting sinusoidal fracture trace is then used for finding an approximation of the fracture plane. The fracture plane orientation is used for determination of true aperture from the apparent aperture seen in the image. After this, fracture aperture statistics can be determined. The method works well for images of open fractures of simple geometry (sine wave). It needs to be improved to handle more complex geometry, e.g. crossing fracture traces. Today, some minor interaction from the analyst is needed, but slight modifications will minimise this

  5. The effect of specimen and flaw dimensions on fracture toughness

    Energy Technology Data Exchange (ETDEWEB)

    Nevalainen, M.J. [VTT Manufacturing Technology, Espoo (Finland)

    1997-06-01

    The effect of the specimen size and geometry on fracture toughness has been investigated both by experimental tests and computational analyses. The methods for constraint description, namely T-stress, Q-parameter and Small-Scale Yielding Correction (SSYC) have been compared and applied for various geometries. A statistical treatment for the specimen thickness effect on cleavage fracture toughness has been investigated. Elliptical surface cracks were compared with straight-thickness cracks and a method for crack shape correction was presented. Based on the results, the differences in apparent fracture toughness values obtained from various specimen configurations can be better understood and taken into account. 64 refs. The thesis includes also four previous publications by author.

  6. Concepts of flow in fractured rocks

    International Nuclear Information System (INIS)

    Black, J.H.

    1989-01-01

    The role of well testing is considered in the context of tracer tests in fractured rock. It is shown that the important information required by a tracer test includes not just the hydrogeological parameters (transmissivity and storage), but also the geometry of flow. This is usually implicit in well testing, perhaps because the tests are generally interpretationally insensitive to variations in flow geometry. It is also argued that both well and tracer tests change their flow geometry during their lifetime. They often start as pipe flow near a well and change to large scale, almost spherical, flow after long periods of time. The duration of a tracer test is compared with that of a well test and is found to reach an equivalent duration (of dimensionless time) that is at least 10 4 times longer. Care should be exercised in transposing flow geometries derived from mature well tests on to tracer tests which are not similar in dimensionless time. Finally, a 'sinusoidal flow test' is outlined which has prompted a new way of looking at well tests in terms of their flow geometry. The new analysis involves 'partial dimension' of flow and is probably highly appropriate to fissured rocks. Fissured rocks have, for too long, been seen as a regular system of planar, fully transmissive fissures. (author). 12 refs, 4 figs, 1 tab

  7. Modelling of ductile and cleavage fracture by local approach

    International Nuclear Information System (INIS)

    Samal, M.K.; Dutta, B.K.; Kushwaha, H.S.

    2000-08-01

    This report describes the modelling of ductile and cleavage fracture processes by local approach. It is now well known that the conventional fracture mechanics method based on single parameter criteria is not adequate to model the fracture processes. It is because of the existence of effect of size and geometry of flaw, loading type and rate on the fracture resistance behaviour of any structure. Hence, it is questionable to use same fracture resistance curves as determined from standard tests in the analysis of real life components because of existence of all the above effects. So, there is need to have a method in which the parameters used for the analysis will be true material properties, i.e. independent of geometry and size. One of the solutions to the above problem is the use of local approaches. These approaches have been extensively studied and applied to different materials (including SA33 Gr.6) in this report. Each method has been studied and reported in a separate section. This report has been divided into five sections. Section-I gives a brief review of the fundamentals of fracture process. Section-II deals with modelling of ductile fracture by locally uncoupled type of models. In this section, the critical cavity growth parameters of the different models have been determined for the primary heat transport (PHT) piping material of Indian pressurised heavy water reactor (PHWR). A comparative study has been done among different models. The dependency of the critical parameters on stress triaxiality factor has also been studied. It is observed that Rice and Tracey's model is the most suitable one. But, its parameters are not fully independent of triaxiality factor. For this purpose, a modification to Rice and Tracery's model is suggested in Section-III. Section-IV deals with modelling of ductile fracture process by locally coupled type of models. Section-V deals with the modelling of cleavage fracture process by Beremins model, which is based on Weibulls

  8. Energy based methods for determining elastic plastic fracture

    International Nuclear Information System (INIS)

    Witt, F.J.

    1979-01-01

    Several methods are currently in use or under study for calculating various conditions of fracturing for varying degrees of plasticity. Among these are innovations on the J-integral concept, crack opening displacement or angle, the two parameter concept and the equivalent energy method. Methods involving crack arrest and ductile tearing also fall in this category. Each of these methods have many salient points and some efforts are underway to establish the underlying relationship between them. In this paper, the current research directions of J-integral and equivalent energy methodologies are reviewed with a broader discussion presented for the equivalent energy methodology. The fundamental basis of equivalent energy methodology rests with the volumetric energy ratio. For fractures governed by linear elastic fracture mechanics, the volumetric energy ratio is independent of flaw size and geometry and depends only on the scale factor between model and prototype and temperature. The behavioral aspects of the volumetric energy ratios have been investigated throughout the temperature range from brittle fracture to fully ductile fracture. For five different specimen and structural configurations it has been shown experimentally that the volumetric energy ratio retains its basic properties. That is, the volumetric energy ratio while changing in actual value, maintains its independence of geometry and flaw size while retaining a unique dependence on scale factor and temperature. This property interpreted in terms of fracture mechanics leads to the equivalent energy method. (orig.)

  9. Ballistic fractures: indirect fracture to bone.

    Science.gov (United States)

    Dougherty, Paul J; Sherman, Don; Dau, Nathan; Bir, Cynthia

    2011-11-01

    Two mechanisms of injury, the temporary cavity and the sonic wave, have been proposed to produce indirect fractures as a projectile passes nearby in tissue. The purpose of this study is to evaluate the temporal relationship of pressure waves using strain gauge technology and high-speed video to elucidate whether the sonic wave, the temporary cavity, or both are responsible for the formation of indirect fractures. Twenty-eight fresh frozen cadaveric diaphyseal tibia (2) and femurs (26) were implanted into ordnance gelatin blocks. Shots were fired using 9- and 5.56-mm bullets traversing through the gelatin only, passing close to the edge of the bone, but not touching, to produce an indirect fracture. High-speed video of the impact event was collected at 20,000 frames/s. Acquisition of the strain data were synchronized with the video at 20,000 Hz. The exact time of fracture was determined by analyzing and comparing the strain gauge output and video. Twenty-eight shots were fired, 2 with 9-mm bullets and 26 with 5.56-mm bullets. Eight indirect fractures that occurred were of a simple (oblique or wedge) pattern. Comparison of the average distance of the projectile from the bone was 9.68 mm (range, 3-20 mm) for fractured specimens and 15.15 mm (range, 7-28 mm) for nonfractured specimens (Student's t test, p = 0.036). In this study, indirect fractures were produced after passage of the projectile. Thus, the temporary cavity, not the sonic wave, was responsible for the indirect fractures.

  10. Modeling interfacial fracture in Sierra.

    Energy Technology Data Exchange (ETDEWEB)

    Brown, Arthur A.; Ohashi, Yuki; Lu, Wei-Yang; Nelson, Stacy A. C.; Foulk, James W.,; Reedy, Earl David,; Austin, Kevin N.; Margolis, Stephen B.

    2013-09-01

    This report summarizes computational efforts to model interfacial fracture using cohesive zone models in the SIERRA/SolidMechanics (SIERRA/SM) finite element code. Cohesive surface elements were used to model crack initiation and propagation along predefined paths. Mesh convergence was observed with SIERRA/SM for numerous geometries. As the funding for this project came from the Advanced Simulation and Computing Verification and Validation (ASC V&V) focus area, considerable effort was spent performing verification and validation. Code verification was performed to compare code predictions to analytical solutions for simple three-element simulations as well as a higher-fidelity simulation of a double-cantilever beam. Parameter identification was conducted with Dakota using experimental results on asymmetric double-cantilever beam (ADCB) and end-notched-flexure (ENF) experiments conducted under Campaign-6 funding. Discretization convergence studies were also performed with respect to mesh size and time step and an optimization study was completed for mode II delamination using the ENF geometry. Throughout this verification process, numerous SIERRA/SM bugs were found and reported, all of which have been fixed, leading to over a 10-fold increase in convergence rates. Finally, mixed-mode flexure experiments were performed for validation. One of the unexplained issues encountered was material property variability for ostensibly the same composite material. Since the variability is not fully understood, it is difficult to accurately assess uncertainty when performing predictions.

  11. Variable geometry Darrieus wind machine

    Science.gov (United States)

    Pytlinski, J. T.; Serrano, D.

    1983-08-01

    A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.

  12. Flux compactifications and generalized geometries

    International Nuclear Information System (INIS)

    Grana, Mariana

    2006-01-01

    Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry

  13. Flux compactifications and generalized geometries

    Energy Technology Data Exchange (ETDEWEB)

    Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)

    2006-11-07

    Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.

  14. Euclidean geometry and its subgeometries

    CERN Document Server

    Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

    2015-01-01

    In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

  15. Guide to Computational Geometry Processing

    DEFF Research Database (Denmark)

    Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

    be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

  16. Electrodynamics and Spacetime Geometry: Foundations

    Science.gov (United States)

    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.

  17. Dayside merging and cusp geometry

    International Nuclear Information System (INIS)

    Crooker, N.U.

    1979-01-01

    Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle

  18. DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS

    International Nuclear Information System (INIS)

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

    2001-01-01

    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

  19. Geometric Transformations in Engineering Geometry

    Directory of Open Access Journals (Sweden)

    I. F. Borovikov

    2015-01-01

    Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

  20. Prediction of fracture initiation in square cup drawing of DP980 using an anisotropic ductile fracture criterion

    Science.gov (United States)

    Park, N.; Huh, H.; Yoon, J. W.

    2017-09-01

    This paper deals with the prediction of fracture initiation in square cup drawing of DP980 steel sheet with the thickness of 1.2 mm. In an attempt to consider the influence of material anisotropy on the fracture initiation, an uncoupled anisotropic ductile fracture criterion is developed based on the Lou—Huh ductile fracture criterion. Tensile tests are carried out at different loading directions of 0°, 45°, and 90° to the rolling direction of the sheet using various specimen geometries including pure shear, dog-bone, and flat grooved specimens so as to calibrate the parameters of the proposed fracture criterion. Equivalent plastic strain distribution on the specimen surface is computed using Digital Image Correlation (DIC) method until surface crack initiates. The proposed fracture criterion is implemented into the commercial finite element code ABAQUS/Explicit by developing the Vectorized User-defined MATerial (VUMAT) subroutine which features the non-associated flow rule. Simulation results of the square cup drawing test clearly show that the proposed fracture criterion is capable of predicting the fracture initiation with sufficient accuracy considering the material anisotropy.

  1. KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

    Directory of Open Access Journals (Sweden)

    Irkham Ulil Albab

    2014-10-01

    Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

  2. Discrete fracture modelling of the Finnsjoen rock mass: Phase 2

    International Nuclear Information System (INIS)

    Geier, J.E.; Axelsson, C.L.; Haessler, L.; Benabderrahmane, A.

    1992-04-01

    A discrete fracture network (DFN) model of the Finnsjoen site was derived from field data, and used to predict block-scale flow and transport properties. The DFN model was based on a compound Poisson process, with stochastic fracture zones, and individual fracture concentrated around the fracture zones. This formulation was used to represent the multitude of fracture zones at the site which could be observed on lineament maps and in boreholes, but were not the focus of detailed characterization efforts. Due to a shortage of data for fracture geometry at depth, distributions of fracture orientation and size were assumed to be uniform throughout the site. Transmissivity within individual fracture planes was assumed to vary according to a fractal model. Constant-head packer tests were simulated with the model, and the observed transient responses were compared with actual tests in terms of distributions of interpreted transmissivity and flow dimension, to partially validate the model. Both simulated and actual tests showed a range of flow dimension from sublinear to spherical, indicating local variations in the connectivity of the fracture population. A methodology was developed for estimation of an effective stochastic continuum from the DFN model, but this was only partly demonstrated. Directional conductivities for 40 m block were estimated using the DFN model. These show extremely poor correlation with results of multiple packer tests in the same blocks, indicating possible limitation of small-scale packer tests for predicting block-scale properties. Estimates are given of effective flow porosity and flow wetted surface, based on the block-scale flow fields calculated by the DFN model, and probabilistic models for the relationships among local fracture transmissivity, void space, and specific surface. The database for constructing these models is extremely limited. A review is given of the existing database for single fracture hydrologic properties. (127 refs

  3. Fracture flow due to hydrothermally induced quartz growth

    Science.gov (United States)

    Kling, Tobias; Schwarz, Jens-Oliver; Wendler, Frank; Enzmann, Frieder; Blum, Philipp

    2017-09-01

    Mineral precipitations are a common feature and limitation of initially open, permeable rock fractures by forming sealing structures or secondary roughness in open voids. Hence, the objective of this numerical study is the evaluation of hydraulic properties of fractures sealed by hydrothermally induced needle and compact quartz growth. Phase-field models of progressive syntaxial and idiomorphic quartz growth are implemented into a fluid flow simulation solving the Navier-Stokes equation. Flow simulations for both quartz types indicate an obvious correlation between changes in permeability, fracture properties (e.g. aperture, relative roughness and porosity) and crystal growth behavior, which also forms distinct flow paths. Thus, at lower sealing stages initial fracture permeability significantly drops down for the 'needle fracture' forming highly tortuous flow paths, while the 'compact fracture' records a considerably smaller loss. Fluid flow in both sealing fractures most widely is governed by a ;parallel plate;-like cubic law behavior. However, the 'needle fracture' also reveals flow characteristics of a porous media. A semi-theoretical equation is introduced that links geometrical (am) with hydraulically effective apertures (ah) and the relative fracture roughness. For this purpose, a geometry factor α is introduced being α = 2.5 for needle quartz and α = 1.0 for compact quartz growth. In contrast to most common ah-am-relationships this novel formulation not only reveals more precise predictions for the needle (RMSE = 1.5) and the compact fractures (RMSE = 3.2), but also exhibit a larger range of validity concerning the roughness of the 'needle' (σ/am = 0-2.4) and the 'compact fractures' (σ/am = 0-1.8).

  4. Graphical debugging of combinational geometry

    International Nuclear Information System (INIS)

    Burns, T.J.; Smith, M.S.

    1992-01-01

    A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development

  5. Lectures on Algebraic Geometry I

    CERN Document Server

    Harder, Gunter

    2012-01-01

    This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho

  6. Combinatorial geometry in the plane

    CERN Document Server

    Hadwiger, Hugo; Klee, Victor

    2014-01-01

    Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa

  7. Modern differential geometry for physicists

    CERN Document Server

    Isham, C J

    1989-01-01

    These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields

  8. Comparison theorems in Riemannian geometry

    CERN Document Server

    Cheeger, Jeff

    2008-01-01

    The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

  9. Geometry, topology, and string theory

    Energy Technology Data Exchange (ETDEWEB)

    Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)

    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.

  10. Spatial geometry and special relativity

    DEFF Research Database (Denmark)

    Kneubil, Fabiana Botelho

    2016-01-01

    In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...

  11. Stochastic geometry and its applications

    CERN Document Server

    Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph

    2013-01-01

    An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a

  12. Introduction to topology and geometry

    CERN Document Server

    Stahl, Saul

    2014-01-01

    An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele

  13. Algebraic geometry and theta functions

    CERN Document Server

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  14. Geometry, topology, and string theory

    International Nuclear Information System (INIS)

    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

  15. Origin of Permeability and Structure of Flows in Fractured Media

    Science.gov (United States)

    De Dreuzy, J.; Darcel, C.; Davy, P.; Erhel, J.; Le Goc, R.; Maillot, J.; Meheust, Y.; Pichot, G.; Poirriez, B.

    2013-12-01

    After more than three decades of research, flows in fractured media have been shown to result from multi-scale geological structures. Flows result non-exclusively from the damage zone of the large faults, from the percolation within denser networks of smaller fractures, from the aperture heterogeneity within the fracture planes and from some remaining permeability within the matrix. While the effect of each of these causes has been studied independently, global assessments of the main determinisms is still needed. We propose a general approach to determine the geological structures responsible for flows, their permeability and their organization based on field data and numerical modeling [de Dreuzy et al., 2012b]. Multi-scale synthetic networks are reconstructed from field data and simplified mechanical modeling [Davy et al., 2010]. High-performance numerical methods are developed to comply with the specificities of the geometry and physical properties of the fractured media [Pichot et al., 2010; Pichot et al., 2012]. And, based on a large Monte-Carlo sampling, we determine the key determinisms of fractured permeability and flows (Figure). We illustrate our approach on the respective influence of fracture apertures and fracture correlation patterns at large scale. We show the potential role of fracture intersections, so far overlooked between the fracture and the network scales. We also demonstrate how fracture correlations reduce the bulk fracture permeability. Using this analysis, we highlight the need for more specific in-situ characterization of fracture flow structures. Fracture modeling and characterization are necessary to meet the new requirements of a growing number of applications where fractures appear both as potential advantages to enhance permeability and drawbacks for safety, e.g. in energy storage, stimulated geothermal energy and non-conventional gas productions. References Davy, P., et al. (2010), A likely universal model of fracture scaling and

  16. A Generic analytical solution for modelling pumping tests in wells intersecting fractures

    Science.gov (United States)

    Dewandel, Benoît; Lanini, Sandra; Lachassagne, Patrick; Maréchal, Jean-Christophe

    2018-04-01

    The behaviour of transient flow due to pumping in fractured rocks has been studied for at least the past 80 years. Analytical solutions were proposed for solving the issue of a well intersecting and pumping from one vertical, horizontal or inclined fracture in homogeneous aquifers, but their domain of application-even if covering various fracture geometries-was restricted to isotropic or anisotropic aquifers, whose potential boundaries had to be parallel or orthogonal to the fracture direction. The issue thus remains unsolved for many field cases. For example, a well intersecting and pumping a fracture in a multilayer or a dual-porosity aquifer, where intersected fractures are not necessarily parallel or orthogonal to aquifer boundaries, where several fractures with various orientations intersect the well, or the effect of pumping not only in fractures, but also in the aquifer through the screened interval of the well. Using a mathematical demonstration, we show that integrating the well-known Theis analytical solution (Theis, 1935) along the fracture axis is identical to the equally well-known analytical solution of Gringarten et al. (1974) for a uniform-flux fracture fully penetrating a homogeneous aquifer. This result implies that any existing line- or point-source solution can be used for implementing one or more discrete fractures that are intersected by the well. Several theoretical examples are presented and discussed: a single vertical fracture in a dual-porosity aquifer or in a multi-layer system (with a partially intersecting fracture); one and two inclined fractures in a leaky-aquifer system with pumping either only from the fracture(s), or also from the aquifer between fracture(s) in the screened interval of the well. For the cases with several pumping sources, analytical solutions of flowrate contribution from each individual source (fractures and well) are presented, and the drawdown behaviour according to the length of the pumped screened interval of

  17. Simulation of a multistage fractured horizontal well in a water-bearing tight fractured gas reservoir under non-Darcy flow

    Science.gov (United States)

    Zhang, Rui-Han; Zhang, Lie-Hui; Wang, Rui-He; Zhao, Yu-Long; Huang, Rui

    2018-06-01

    Reservoir development for unconventional resources such as tight gas reservoirs is in increasing demand due to the rapid decline of production in conventional reserves. Compared with conventional reservoirs, fluid flow in water-bearing tight gas reservoirs is subject to more nonlinear multiphase flow and gas slippage in nano/micro matrix pores because of the strong collisions between rock and gas molecules. Economic gas production from tight gas reservoirs depends on extensive application of water-based hydraulic fracturing of horizontal wells, associated with non-Darcy flow at a high flow rate, geomechanical stress sensitivity of un-propped natural fractures, complex flow geometry and multiscale heterogeneity. How to efficiently and accurately predict the production performance of a multistage fractured horizontal well (MFHW) is challenging. In this paper, a novel multicontinuum, multimechanism, two-phase simulator is established based on unstructured meshes and the control volume finite element method to analyze the production performance of MFHWs. The multiple interacting continua model and discrete fracture model are coupled to integrate the unstimulated fractured reservoir, induced fracture networks (stimulated reservoir volumes, SRVs) and irregular discrete hydraulic fractures. Several simulations and sensitivity analyses are performed with the developed simulator for determining the key factors affecting the production performance of MFHWs. Two widely applied fracturing models, classic hydraulic fracturing which generates long double-wing fractures and the volumetric fracturing aimed at creating large SRVs, are compared to identify which of them can make better use of tight gas reserves.

  18. Bifurcating Particle Swarms in Smooth-Walled Fractures

    Science.gov (United States)

    Pyrak-Nolte, L. J.; Sun, H.

    2010-12-01

    Particle swarms can occur naturally or from industrial processes where small liquid drops containing thousands to millions of micron-size to colloidal-size particles are released over time from seepage or leaks into fractured rock. The behavior of these particle swarms as they fall under gravity are affected by particle interactions as well as interactions with the walls of the fractures. In this paper, we present experimental results on the effect of fractures on the cohesiveness of the swarm and the formation of bifurcation structures as they fall under gravity and interact with the fracture walls. A transparent cubic sample (100 mm x 100 mm x 100 mm) containing a synthetic fracture with uniform aperture distributions was optically imaged to quantify the effect of confinement within fractures on particle swarm formation, swarm velocity, and swarm geometry. A fracture with a uniform aperture distribution was fabricated from two polished rectangular prisms of acrylic. A series of experiments were performed to determine how swarm movement and geometry are affected as the walls of the fracture are brought closer together from 50 mm to 1 mm. During the experiments, the fracture was fully saturated with water. We created the swarms using two different particle sizes in dilute suspension (~ 1.0% by mass). The particles were 3 micron diameter fluorescent polymer beads and 25 micron diameter soda-lime glass beads. Experiments were performed using swarms that ranged in size from 5 µl to 60 µl. The swarm behavior was imaged using an optical fluorescent imaging system composed of a CCD camera illuminated by a 100 mW diode-pumped doubled YAG laser. As a swarm falls in an open-tank of water, it forms a torroidal shape that is stable as long as no ambient or background currents exist in the water tank. When a swarm is released into a fracture with an aperture less than 5 mm, the swarm forms the torroidal shape but it is distorted because of the presence of the walls. The

  19. A new equi-dimensional fracture model using polyhedral cells for microseismic data sets

    KAUST Repository

    Al-Hinai, Omar

    2017-04-09

    We present a method for modeling flow in porous media in the presence of complex fracture networks. The approach utilizes the Mimetic Finite Difference (MFD) method. We employ a novel equi-dimensional approach for meshing fractures. By using polyhedral cells we avoid the common challenge in equi-dimensional fracture modeling of creating small cells at the intersection point. We also demonstrate how polyhedra can mesh complex fractures without introducing a large number of cells. We use polyhedra and the MFD method a second time for embedding fracture boundaries in the matrix domain using a “cut-cell” paradigm. The embedding approach has the advantage of being simple and localizes irregular cells to the area around the fractures. It also circumvents the need for conventional mesh generation, which can be challenging when applied to complex fracture geometries. We present numerical results confirming the validity of our approach for complex fracture networks and for different flow models. In our first example, we compare our method to the popular dual-porosity technique. Our second example compares our method with directly meshed fractures (single-porosity) for two-phase flow. The third example demonstrates two-phase flow for the case of intersecting ellipsoid fractures in three-dimensions, which are typical in microseismic analysis of fractures. Finally, we demonstrate our method on a two-dimensional fracture network produced from microseismic field data.

  20. Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

    KAUST Repository

    Nick, H. M.

    2011-11-04

    A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density. © 2011 American Physical Society.

  1. Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

    KAUST Repository

    Nick, H. M.; Paluszny, A.; Blunt, M. J.; Matthai, S. K.

    2011-01-01

    A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density. © 2011 American Physical Society.

  2. 2D Geoelectric Imaging of the Uneme-Nekhua Fracture Zone

    Directory of Open Access Journals (Sweden)

    Muslim B. Aminu

    2014-01-01

    Full Text Available We have employed 2D geoelectric imaging to reveal the geometry and nature of a fracture zone in Uneme-Nekhua, southwestern Nigeria. The fracture zone is discernable from an outcropping rock scarp and appears to define the course of a seasonal stream. Data were acquired using the dipole-dipole survey array configuration with electrode separation of 6 m and a maximum dipole length of 60 m. Three traverses with lengths varying between 72 m and 120 m were laid orthogonal to the course of the seasonal stream. 2D geoelectric images of the subsurface along the profiles imaged a north-south trending fracture zone. This fracture zone appears to consist of two vertical fractures with more intense definition downstream. The eastern fracture is buried by recent sediment, while the western fracture appears to have experienced more recent tectonic activity as it appears to penetrate through the near surface. Perhaps at some point, deformation ceased on the eastern fracture and further strain was transferred to the western fracture. The fracture zone generally defines the course of the north-south seasonal stream with the exception of the downstream end where the fracture appears to have died out entirely. Two associated basement trenches lying parallel to and east of the fracture zone are also imaged.

  3. Non-linear hydrotectonic phenomena: Part I - fluid flow in open fractures under dynamical stress loading

    International Nuclear Information System (INIS)

    Archambeau, C.B.

    1994-01-01

    A fractured solid under stress loading (or unloading) can be viewed as behaving macroscopically as a medium with internal, hidden, degrees of freedom, wherein changes in fracture geometry (i.e. opening, closing and extension) and flow of fluid and gas within fractures will produce major changes in stresses and strains within the solid. Likewise, the flow process within fractures will be strongly coupled to deformation within the solid through boundary conditions on the fracture surfaces. The effects in the solid can, in part, be phenomenologically represented as inelastic or plastic processes in the macroscopic view. However, there are clearly phenomena associated with fracture growth and open fracture fluid flows that produce effects that can not be described using ordinary inelastic phenomenology. This is evident from the fact that a variety of energy release phenomena can occur, including seismic emissions of previously stored strain energy due to fracture growth, release of disolved gas from fluids in the fractures resulting in enhanced buoyancy and subsequent energetic flows of gas and fluids through the fracture system which can produce raid extension of old fractures and the creation of new ones. Additionally, the flows will be modulated by the opening and closing of fractures due to deformation in the solid, so that the flow process is strongly coupled to dynamical processes in the surrounding solid matrix, some of which are induced by the flow itself

  4. A new equi-dimensional fracture model using polyhedral cells for microseismic data sets

    KAUST Repository

    Al-Hinai, Omar; Dong, Rencheng; Srinivasan, Sanjay; Wheeler, Mary F.

    2017-01-01

    We present a method for modeling flow in porous media in the presence of complex fracture networks. The approach utilizes the Mimetic Finite Difference (MFD) method. We employ a novel equi-dimensional approach for meshing fractures. By using polyhedral cells we avoid the common challenge in equi-dimensional fracture modeling of creating small cells at the intersection point. We also demonstrate how polyhedra can mesh complex fractures without introducing a large number of cells. We use polyhedra and the MFD method a second time for embedding fracture boundaries in the matrix domain using a “cut-cell” paradigm. The embedding approach has the advantage of being simple and localizes irregular cells to the area around the fractures. It also circumvents the need for conventional mesh generation, which can be challenging when applied to complex fracture geometries. We present numerical results confirming the validity of our approach for complex fracture networks and for different flow models. In our first example, we compare our method to the popular dual-porosity technique. Our second example compares our method with directly meshed fractures (single-porosity) for two-phase flow. The third example demonstrates two-phase flow for the case of intersecting ellipsoid fractures in three-dimensions, which are typical in microseismic analysis of fractures. Finally, we demonstrate our method on a two-dimensional fracture network produced from microseismic field data.

  5. The Idea of Order at Geometry Class.

    Science.gov (United States)

    Rishel, Thomas

    The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…

  6. Teaching Spatial Geometry in a Virtual World

    DEFF Research Database (Denmark)

    Förster, Klaus-Tycho

    2017-01-01

    Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...

  7. Atraumatic First Rib Fracture

    Directory of Open Access Journals (Sweden)

    Koray Aydogdu

    2014-12-01

    Full Text Available Rib fractures are usually seen after a trauma, while atraumatic spontaneous rib fractures are quite rare. A first rib fracture identified in our 17 years old female patient who had not a history of trauma except lifting a heavy weight was examined in details in terms of the potential complications and followed-up for a long time. We presented our experience on this case with atraumatic first rib fracture that has different views for the etiology in light of the literature.

  8. Fracture mechanics safety approaches

    International Nuclear Information System (INIS)

    Roos, E.; Schuler, X.; Eisele, U.

    2004-01-01

    Component integrity assessments require the knowledge of reliable fracture toughness parameters characterising the initiation of the failure process in the whole relevant temperature range. From a large number of fracture mechanics tests a statistically based procedure was derived allowing to quantify the initiation of fracture toughness as a function of temperature as a closed function as well as the temperature dependence of the cleavage instability parameters. Alternatively to the direct experimental determination one also can use a correlation between fracture toughness and notch impact energy. (orig.)

  9. Scaphoid fractures in children

    Directory of Open Access Journals (Sweden)

    Gajdobranski Đorđe

    2014-01-01

    Full Text Available Introduction. Scaphoid fractures are rare in childhood. Diagnosis is very difficult to establish because carpal bones are not fully ossified. In suspected cases comparative or delayed radiography is used, as well as computerized tomography, magnetic resonance imaging, ultrasound and bone scintigraphy. Majority of scaphoid fractures are treated conservatively with good results. In case of delayed fracture healing various types of treatment are available. Objective. To determine the mechanism of injury, clinical healing process, types and outcome of treatment of scaphoid fractures in children. Methods. We retrospectively analyzed patients with traumatic closed fracture of the scaphoid bone over a ten-year period (2002-2011. The outcome of the treatment of “acute” scaphoid fracture was evaluated using the Mayo Wrist Score. Results. There were in total 34 patients, of mean age 13.8 years, with traumatic closed fracture of the scaphoid bone, whose bone growth was not finished yet. Most common injury mechanism was fall on outstretched arm - 76% of patients. During the examined period 31 children with “acute” fracture underwent conservative treatment, with average immobilization period of 51 days. Six patients were lost to follow-up. In the remaining 25 patients, after completed rehabilitation, functional results determined by the Mayo Wrist Score were excellent. Conclusion. Conservative therapy of “acute” scaphoid fractures is an acceptable treatment option for pediatric patients with excellent functional results.

  10. Pathological fractures in children

    Science.gov (United States)

    De Mattos, C. B. R.; Binitie, O.; Dormans, J. P.

    2012-01-01

    Pathological fractures in children can occur as a result of a variety of conditions, ranging from metabolic diseases and infection to tumours. Fractures through benign and malignant bone tumours should be recognised and managed appropriately by the treating orthopaedic surgeon. The most common benign bone tumours that cause pathological fractures in children are unicameral bone cysts, aneurysmal bone cysts, non-ossifying fibromas and fibrous dysplasia. Although pathological fractures through a primary bone malignancy are rare, these should be recognised quickly in order to achieve better outcomes. A thorough history, physical examination and review of plain radiographs are crucial to determine the cause and guide treatment. In most benign cases the fracture will heal and the lesion can be addressed at the time of the fracture, or after the fracture is healed. A step-wise and multidisciplinary approach is necessary in caring for paediatric patients with malignancies. Pathological fractures do not have to be treated by amputation; these fractures can heal and limb salvage can be performed when indicated. PMID:23610658

  11. Analogical Reasoning in Geometry Education

    Science.gov (United States)

    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…

  12. Normal forms in Poisson geometry

    NARCIS (Netherlands)

    Marcut, I.T.

    2013-01-01

    The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric

  13. Exploring Bundling Theory with Geometry

    Science.gov (United States)

    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…

  14. Stochastic Modelling of River Geometry

    DEFF Research Database (Denmark)

    Sørensen, John Dalsgaard; Schaarup-Jensen, K.

    1996-01-01

    Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

  15. Matter in toy dynamical geometries

    NARCIS (Netherlands)

    Konopka, T.J.

    2009-01-01

    One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect

  16. Let??s teach geometry

    OpenAIRE

    Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a

    2010-01-01

    In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.

  17. Granular flows in constrained geometries

    Science.gov (United States)

    Murthy, Tejas; Viswanathan, Koushik

    Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.

  18. General Relativity: Geometry Meets Physics

    Science.gov (United States)

    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…

  19. Learners engaging with transformation geometry

    African Journals Online (AJOL)

    participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...

  20. Multivariable calculus and differential geometry

    CERN Document Server

    Walschap, Gerard

    2015-01-01

    This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.

  1. College geometry a unified development

    CERN Document Server

    Kay, David C

    2011-01-01

    ""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273

  2. The elasto plastic fracture mechanics in ductile metal sheets

    International Nuclear Information System (INIS)

    Khan, M.A.; Malik, M.N.; Naeem, A.; Haq, A.U.; Atkins, A.G.

    1999-01-01

    The crack initiation of propagation in ductile metal sheets are caused by various micro and macro changes taking place due to material properties, applied loads, shape of the indenter (tool geometry) and the environmental conditions. These microstructural failures are directly related to the atomic bonding, crystal lattices, grain boundary status, material flaws in matrix, inhomogeneities and anisotropy in the metal sheets. The Elasto-Plastic related energy based equations are applied to these Rigid Plastic materials to determine the onset of fracture in metal forming. The combined stress and strain criterion of a critical plastic work per unit volume is no more considered as a universal ductile fracture criterion, rather a critical plastic work per unit volume dependence on all sort of stresses (hydrostatic) are the required features for the sheet metal failure (fracture). In this present study, crack initiation and propagation are related empirically with fracture toughness and the application of the theory in industry to save energy. (author)

  3. Geometry.

    Science.gov (United States)

    Mahaffey, Michael L.

    One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…

  4. Geometri

    DEFF Research Database (Denmark)

    Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...

  5. Borehole imaging tool detects well bore fractures

    International Nuclear Information System (INIS)

    Ma, T.A.; Bigelow, E.L.

    1993-01-01

    This paper reports on borehole imaging data which can provide high quality geological and petrophysical information to improve fracture identification, dip computations, and lithology determinations in a well bore. The ability to visually quantify the area of a borehole wall occupied by fractures and vugs enhances reservoir characterization and well completion operations. The circumferential borehole imaging log (CBIL) instrument is an acoustic logging device designed to produce a map of the entire borehole wall. The visual images can confirm computed dips and the geological features related to dip. Borehole geometry, including breakout, are accurately described by complete circumferential caliper measurements, which is important information for drilling and completion engineers. In may reservoirs, the images can identify porosity type, bedding characteristics, and petrophysical parameters

  6. Fracture of the styloid process associated with the mandible fracture

    Directory of Open Access Journals (Sweden)

    K N Dubey

    2013-01-01

    Full Text Available Fracture of the styloid process (SP of temporal bone is an uncommon injuries. Fracture of the SP can be associated with the facial injuries including mandible fracture. However, injury to the SP may be concealed and missed diagnosis may lead to the improper or various unnecessary treatments. A rare case of SP fracture associated with the ipsilateral mandibular fracture and also the diagnostic and management considerations of the SP fracture are discussed.

  7. Discrete differential geometry. Consistency as integrability

    OpenAIRE

    Bobenko, Alexander I.; Suris, Yuri B.

    2005-01-01

    A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

  8. Modelling tracer transport in fractured rock at Stripa

    International Nuclear Information System (INIS)

    Herbert, A.

    1992-01-01

    We present the results of a modelling study, making predictions for tracer transport experiments carried out within the H-zone feature in the Stripa mine. We use a direct fracture network approach to represent the system of interconnected flow-conducting fractures comprising this zone. It is a highly fractured granite, and our fracture-network models include up to 60000 fractures. We have had to develop efficient algorithms to calculate the flow and transport through these networks; these techniques are described and justified. The first stage of modelling addressed two saline injection experiments. The results of these were known to us and so in addition to 'predicting' the results of these experiments, we used them to calibrate a flow model of the experimental site. This model was then used to make true 'blind' predictions for a set of tracer experiments carried out in the natural head-field, caused by an open drift. Where our flow model was good, our predictions were found to be very accurate, explaining the dispersion in the tracer breakthrough in terms of the fracture network geometry. Discrepancies for experiments in less well characterised regions of the H-zone are presented, and we suggest that the errors in these predictions are a consequence of the inaccuracies of the flow-field. We have demonstrated the use of large-scale fracture network modelling. It has proved very successful, and made very accurate predictions of field experiments carried out at the Stripa mine. The measured dispersion of tracers can be accounted for by the geometry of the fracture network flow system. (14 refs.) (au)

  9. Numerically robust geometry engine for compound solid geometries

    International Nuclear Information System (INIS)

    Vlachoudis, V.; Sinuela-Pastor, D.

    2013-01-01

    Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)

  10. The Process of Hydraulic Fracturing

    Science.gov (United States)

    Hydraulic fracturing, know as fracking or hydrofracking, produces fractures in a rock formation by pumping fluids (water, proppant, and chemical additives) at high pressure down a wellbore. These fractures stimulate the flow of natural gas or oil.

  11. Fracture network topology and characterization of structural permeability

    Science.gov (United States)

    Hansberry, Rowan; King, Rosalind; Holford, Simon

    2017-04-01

    other permeability indicators such as drilling fluid losses, and pore pressure measurements. Initial work with these techniques has led to new developments in our ability to image subsurface faults and fractures at a variety of scales from independent datasets. We establish a strong relationship between features identified using seismic attribute analysis and interpreted natural fractures. However, care must be taken to use these methods in a case-by-case basis, as controls on fracture distribution and orientation can vary significantly with both regional and local influences. These results outline and effective method by which structural permeability can be assessed with existing petroleum datasets. However, unlike the broad stress field, mapping fracture orientation and characteristics within the Australian Continent is complicated as the distribution, geometry, areal extent and connectivity of fracture networks can vary significantly.

  12. Evaluation of fracture mechanics analyses used in RPV integrity assessment regarding brittle fracture

    International Nuclear Information System (INIS)

    Moinereau, D.; Faidy, C.; Valeta, M.P.; Bhandari, S.; Guichard, D.

    1997-01-01

    Electricite de France has conducted during these last years some experimental and numerical research programmes in order to evaluate fracture mechanics analyses used in nuclear reactor pressure vessels structural integrity assessment, regarding the risk of brittle fracture. These programmes included cleavage fracture tests on large scale cladded specimens containing subclad flaws with their interpretations by 2D and 3D numerical computations, and validation of finite element codes for pressurized thermal shocks analyses. Four cladded specimens made of ferritic steel A508 C13 with stainless steel cladding, and containing shallow subclad flaws, have been tested in four point bending at very low temperature in order to obtain cleavage failure. The specimen failure was obtained in each case in base metal by cleavage fracture. These tests have been interpreted by two-dimensional and three-dimensional finite element computations using different fracture mechanics approaches (elastic analysis with specific plasticity corrections, elastic-plastic analysis, local approach to cleavage fracture). The failure of specimens are conservatively predicted by different analyses. The comparison between the elastic analyses and elastic-plastic analyses shows the conservatism of specific plasticity corrections used in French RPV elastic analyses. Numerous finite element calculations have also been performed between EDF, CEA and Framatome in order to compare and validate several fracture mechanics post processors implemented in finite element programmes used in pressurized thermal shock analyses. This work includes two-dimensional numerical computations on specimens with different geometries and loadings. The comparisons show a rather good agreement on main results, allowing to validate the finite element codes and their post-processors. (author). 11 refs, 24 figs, 3 tabs

  13. Evaluation of fracture mechanics analyses used in RPV integrity assessment regarding brittle fracture

    Energy Technology Data Exchange (ETDEWEB)

    Moinereau, D [Electricite de France, Dept. MTC, Moret-sur-Loing (France); Faidy, C [Electricite de France, SEPTEN, Villeurbanne (France); Valeta, M P [Commisariat a l` Energie Atomique, Dept. DMT, Gif-sur-Yvette (France); Bhandari, S; Guichard, D [Societe Franco-Americaine de Constructions Atomiques (FRAMATOME), 92 - Paris-La-Defense (France)

    1997-09-01

    Electricite de France has conducted during these last years some experimental and numerical research programmes in order to evaluate fracture mechanics analyses used in nuclear reactor pressure vessels structural integrity assessment, regarding the risk of brittle fracture. These programmes included cleavage fracture tests on large scale cladded specimens containing subclad flaws with their interpretations by 2D and 3D numerical computations, and validation of finite element codes for pressurized thermal shocks analyses. Four cladded specimens made of ferritic steel A508 C13 with stainless steel cladding, and containing shallow subclad flaws, have been tested in four point bending at very low temperature in order to obtain cleavage failure. The specimen failure was obtained in each case in base metal by cleavage fracture. These tests have been interpreted by two-dimensional and three-dimensional finite element computations using different fracture mechanics approaches (elastic analysis with specific plasticity corrections, elastic-plastic analysis, local approach to cleavage fracture). The failure of specimens are conservatively predicted by different analyses. The comparison between the elastic analyses and elastic-plastic analyses shows the conservatism of specific plasticity corrections used in French RPV elastic analyses. Numerous finite element calculations have also been performed between EDF, CEA and Framatome in order to compare and validate several fracture mechanics post processors implemented in finite element programmes used in pressurized thermal shock analyses. This work includes two-dimensional numerical computations on specimens with different geometries and loadings. The comparisons show a rather good agreement on main results, allowing to validate the finite element codes and their post-processors. (author). 11 refs, 24 figs, 3 tabs.

  14. NDE and fracture mechanics evaluation of bottom-head weld indications in a BWR reactor pressure vessel

    Energy Technology Data Exchange (ETDEWEB)

    Brickstad, B [Swedish Plant Inspectorate, Stockholm (Sweden)

    1988-12-31

    This document deals with the Non Destructive Examination (NDE) and the fracture mechanics evaluation of bottom head welds in a BWR. The NDE equipment is presented, together with the geometry of evaluated flaw regions. After the fracture mechanics evaluation, it appeared that the plant results fulfilled the usual conditions, and the plant was allowed to operate one more year. (TEC).

  15. [Trochanteric femoral fractures].

    Science.gov (United States)

    Douša, P; Čech, O; Weissinger, M; Džupa, V

    2013-01-01

    At the present time proximal femoral fractures account for 30% of all fractures referred to hospitals for treatment. Our population is ageing, the proportion of patients with post-menopausal or senile osteoporosis is increasing and therefore the number of proximal femoral fractures requiring urgent treatment is growing too. In the age category of 50 years and older, the incidence of these fractures has increased exponentially. Our department serves as a trauma centre for half of Prague and part of the Central Bohemia Region with a population of 1 150 000. Prague in particular has a high number of elderly citizens. Our experience is based on extensive clinical data obtained from the Register of Proximal Femoral Fractures established in 1997. During 14 years, 4280 patients, 3112 women and 1168 men, were admitted to our department for treatment of proximal femoral fractures. All patients were followed up until healing or development of complications. In the group under study, 82% were patients older than 70 years; 72% of those requiring surgery were in their seventies and eighties. Men were significantly younger than women (pfractures were 2.3-times more frequent in women than in men. In the category under 60 years, men significantly outnumbered women (pfractures were, on the average, eight years older than the patients with intertrochanteric fractures, which is a significant difference (pTrochanteric fractures accounted for 54.7% and femoral neck fractures for 45.3% of all fractures. The inter-annual increase was 5.9%, with more trochanteric than femoral neck fractures. There was a non-significant decrease in intertrochanteric (AO 31-A3) fractures. On the other hand, the number of pertrochanteric (AO 31-A1+2) fractures increased significantly (pfractures were treated with a proximal femoral nail; a short nail was used in 1260 and a long nail in 134 of them. A dynamic hip screw (DHS) was employed to treat 947 fractures. Distinguishing between pertrochanteric (21-A1

  16. Fracture toughness of dentin/resin-composite adhesive interfaces.

    Science.gov (United States)

    Tam, L E; Pilliar, R M

    1993-05-01

    The reliability and validity of tensile and shear bond strength determinations of dentin-bonded interfaces have been questioned. The fracture toughness value (KIC) reflects the ability of a material to resist crack initiation and unstable propagation. When applied to an adhesive interface, it should account for both interfacial bond strength and inherent defects at or near the interface, and should therefore be more appropriate for characterization of interface fracture resistance. This study introduced a fracture toughness test for the assessment of dentin/resin-composite bonded interfaces. The miniature short-rod specimen geometry was used for fracture toughness testing. Each specimen contained a tooth slice, sectioned from a bovine incisor, to form the bonded interface. The fracture toughness of an enamel-bonded interface was assessed in addition to the dentin-bonded interfaces. Tensile bond strength specimens were also prepared from the dentin surfaces of the cut bovine incisors. A minimum of ten specimens was fabricated for each group of materials tested. After the specimens were aged for 24 h in distilled water at 37 degrees C, the specimens were loaded to failure in an Instron universal testing machine. There were significant differences (p adhesives tested. Generally, both the fracture toughness and tensile bond strength measurements were highest for AllBond 2, intermediate for 3M MultiPurpose, and lowest for Scotchbond 2. Scanning electron microscopy of the fractured specimen halves confirmed that crack propagation occurred along the bond interface during the fracture toughness test. It was therefore concluded that the mini-short-rod fracture toughness test provided a valid method for characterization of the fracture resistance of the dentin-resin composite interface.

  17. Effect of tool geometry on friction stir spot welding of polypropylene sheets

    Directory of Open Access Journals (Sweden)

    M. K. Bilici

    2012-10-01

    Full Text Available The effects of tool geometry and properties on friction stir spot welding properties of polypropylene sheets were studied. Four different tool pin geometries, with varying pin angles, pin lengths, shoulder diameters and shoulder angles were used for friction stir spot welding. All the welding operations were done at the room temperature. Lap-shear tensile tests were carried out to find the weld static strength. Weld cross section appearance observations were also done. From the experiments the effect of tool geometry on friction stir spot weld formation and weld strength were determined. The optimum tool geometry for 4 mm thick polypropylene sheets were determined. The tapered cylindrical pin gave the biggest and the straight cylindrical pin gave the lowest lap-shear fracture load.

  18. Hand fracture - aftercare

    Science.gov (United States)

    ... an orthopedic surgeon if: Your metacarpal bones are broken and shifted out of place Your fingers do not line up correctly Your fracture nearly went through the skin Your fracture went through the skin Your pain is severe or becoming worse Self-care at Home You may have pain and swelling for 1 ...

  19. TIBIAL SHAFT FRACTURES.

    Science.gov (United States)

    Kojima, Kodi Edson; Ferreira, Ramon Venzon

    2011-01-01

    The long-bone fractures occur most frequently in the tibial shaft. Adequate treatment of such fractures avoids consolidation failure, skewed consolidation and reoperation. To classify these fractures, the AO/OTA classification method is still used, but it is worthwhile getting to know the Ellis classification method, which also includes assessment of soft-tissue injuries. There is often an association with compartmental syndrome, and early diagnosis can be achieved through evaluating clinical parameters and constant clinical monitoring. Once the diagnosis has been made, fasciotomy should be performed. It is always difficult to assess consolidation, but the RUST method may help in this. Radiography is assessed in two projections, and points are scored for the presence of the fracture line and a visible bone callus. Today, the dogma of six hours for cleaning the exposed fracture is under discussion. It is considered that an early start to intravenous antibiotic therapy and the lesion severity are very important. The question of early or late closure of the lesion in an exposed fracture has gone through several phases: sometimes early closure has been indicated and sometimes late closure. Currently, whenever possible, early closure of the lesion is recommended, since this diminishes the risk of infection. Milling of the canal when the intramedullary nail is introduced is still a controversial subject. Despite strong personal positions in favor of milling, studies have shown that there may be some advantage in relation to closed fractures, but not in exposed fractures.

  20. Physeal Fractures in Foals.

    Science.gov (United States)

    Levine, David G; Aitken, Maia R

    2017-08-01

    Physeal fractures are common musculoskeletal injuries in foals and should be included as a differential diagnosis for the lame or nonweightbearing foal. Careful evaluation of the patient, including precise radiographic assessment, is paramount in determining the options for treatment. Prognosis mostly depends on the patient's age, weight, and fracture location and configuration. Copyright © 2017 Elsevier Inc. All rights reserved.

  1. Scale dependency of fractional flow dimension in a fractured formation

    Directory of Open Access Journals (Sweden)

    Y.-C. Chang

    2011-07-01

    Full Text Available The flow dimensions of fractured media were usually predefined before the determination of the hydraulic parameters from the analysis of field data in the past. However, it would be improper to make assumption about the flow geometry of fractured media before site characterization because the hydraulic structures and flow paths are complex in the fractured media. An appropriate way to investigate the hydrodynamic behavior of a fracture system is to determine the flow dimension and aquifer parameters simultaneously. The objective of this study is to analyze a set of field data obtained from four observation wells during an 11-day hydraulic test at Chingshui geothermal field (CGF in Taiwan in determining the hydrogeologic properties of the fractured formation. Based on the generalized radial flow (GRF model and the optimization scheme, simulated annealing, an approach is therefore developed for the data analyses. The GRF model allows the flow dimension to be integer or fractional. We found that the fractional flow dimension of CGF increases near linearly with the distance between the pumping well and observation well, i.e. the flow dimension of CGF exhibits scale-dependent phenomenon. This study provides insights into interpretation of fracture flow at CGF and gives a reference for characterizing the hydrogeologic properties of fractured media.

  2. Bone stress in runners with tibial stress fracture.

    Science.gov (United States)

    Meardon, Stacey A; Willson, John D; Gries, Samantha R; Kernozek, Thomas W; Derrick, Timothy R

    2015-11-01

    Combinations of smaller bone geometry and greater applied loads may contribute to tibial stress fracture. We examined tibial bone stress, accounting for geometry and applied loads, in runners with stress fracture. 23 runners with a history of tibial stress fracture & 23 matched controls ran over a force platform while 3-D kinematic and kinetic data were collected. An elliptical model of the distal 1/3 tibia cross section was used to estimate stress at 4 locations (anterior, posterior, medial and lateral). Inner and outer radii for the model were obtained from 2 planar x-ray images. Bone stress differences were assessed using two-factor ANOVA (α=0.05). Key contributors to observed stress differences between groups were examined using stepwise regression. Runners with tibial stress fracture experienced greater anterior tension and posterior compression at the distal tibia. Location, but not group, differences in shear stress were observed. Stepwise regression revealed that anterior-posterior outer diameter of the tibia and the sagittal plane bending moment explained >80% of the variance in anterior and posterior bone stress. Runners with tibial stress fracture displayed greater stress anteriorly and posteriorly at the distal tibia. Elevated tibial stress was associated with smaller bone geometry and greater bending moments about the medial-lateral axis of the tibia. Future research needs to identify key running mechanics associated with the sagittal plane bending moment at the distal tibia as well as to identify ways to improve bone geometry in runners in order to better guide preventative and rehabilitative efforts. Copyright © 2015 Elsevier Ltd. All rights reserved.

  3. Treatment of midfacial fractures

    International Nuclear Information System (INIS)

    Schubert, J.

    2007-01-01

    Fractures of the midface constitute half of all traumas involving facial bones. Computed tomography is very useful in primary diagnosis. Isolated fractures of the nasal bone and lateral midfacial structures may be diagnosed sufficiently by conventional X-rays. An exact description of the fracture lines along the midfacial buttresses is essential for treatment planning. For good aesthetics and function these have to be reconstructed accurately, which can be checked with X-rays. The treatment of midfacial fractures has been revolutionized over the last two decades. A stable three-dimensional reconstruction of the facial shape is now possible and the duration of treatment has shortened remarkably. The frequently occurring isolated fractures in the lateral part of the midface may be treated easily and effectively by semisurgical methods such as the Gillies procedure or hook-repositioning. (orig.)

  4. Dating fractures in infants

    Energy Technology Data Exchange (ETDEWEB)

    Halliday, K.E., E-mail: kath.halliday@nuh.nhs.uk [Department of Radiology, Nottingham University Hospitals, Queen' s Medical Centre, Nottingham (United Kingdom); Broderick, N J; Somers, J M [Department of Radiology, Nottingham University Hospitals, Queen' s Medical Centre, Nottingham (United Kingdom); Hawkes, R [Department of Radiology, Paul O' Gorman Building, Bristol (United Kingdom)

    2011-11-15

    Aim: To document the timing of the appearance of the radiological features of fracture healing in a group of infants in which the date of injury was known and to assess the degree of interobserver agreement. Materials and methods: Three paediatric radiologists independently assessed 161 images of 37 long bone fractures in 31 patients aged 0-44 months. The following features were assessed: soft-tissue swelling, subperiosteal new bone formation (SPNBF), definition of fracture line, presence or absence of callus, whether callus was well or ill defined, and the presence of endosteal callus. Results: Agreement between observers was only moderate for all discriminators except SPNBF. SPNBF was invariably seen after 11 days but was uncommon before this time even in the very young. In one case SPNBF was seen at 4 days. Conclusion: With the exception of SPNBF, the criteria relied on to date fractures are either not reproducible or are poor discriminators of fracture age.

  5. Dating fractures in infants

    International Nuclear Information System (INIS)

    Halliday, K.E.; Broderick, N.J.; Somers, J.M.; Hawkes, R.

    2011-01-01

    Aim: To document the timing of the appearance of the radiological features of fracture healing in a group of infants in which the date of injury was known and to assess the degree of interobserver agreement. Materials and methods: Three paediatric radiologists independently assessed 161 images of 37 long bone fractures in 31 patients aged 0-44 months. The following features were assessed: soft-tissue swelling, subperiosteal new bone formation (SPNBF), definition of fracture line, presence or absence of callus, whether callus was well or ill defined, and the presence of endosteal callus. Results: Agreement between observers was only moderate for all discriminators except SPNBF. SPNBF was invariably seen after 11 days but was uncommon before this time even in the very young. In one case SPNBF was seen at 4 days. Conclusion: With the exception of SPNBF, the criteria relied on to date fractures are either not reproducible or are poor discriminators of fracture age.

  6. Tibial Plateau Fractures

    DEFF Research Database (Denmark)

    Elsøe, Rasmus

    This PhD thesis reported an incidence of tibial plateau fractures of 10.3/100,000/year in a complete Danish regional population. The results reported that patients treated for a lateral tibial plateau fracture with bone tamp reduction and percutaneous screw fixation achieved a satisfactory level...... with only the subgroup Sport significantly below the age matched reference population. The thesis reports a level of health related quality of life (Eq5d) and disability (KOOS) significantly below established reference populations for patients with bicondylar tibial plateau fracture treated with a ring...... fixator, both during treatment and at 19 months following injury. In general, the thesis demonstrates that the treatment of tibial plateau fractures are challenging and that some disabilities following these fractures must be expected. Moreover, the need for further research in the area, both with regard...

  7. Fracturing formations in wells

    Energy Technology Data Exchange (ETDEWEB)

    Daroza, R A

    1964-05-15

    This well stimulation method comprises introducing through the well bore a low-penetrating, dilatant fluid, and subjecting the fluid to sufficient pressure to produce fractures in the formation. The fluid is permitted to remain in contact with the formation so as to become diluted by the formation fluids, and thereby lose its properties of dilatancy. Also, a penetrating fluid, containing a propping agent suspended therein, in introduced into contact with the fractures at a pressure substantially reduced with respect to that pressure which would have been required, prior to the fracturing operation performed using the low-penetrating dilatant fluid. The propping agent is deposited within the fractures, and thereafter, fluid production is resumed from the fractured formation. (2 claims)

  8. Kinematics of tectonic fracture development during regional folding in sandstones of the Kamlial Formation, Khushalgarh, northern Pakistan

    International Nuclear Information System (INIS)

    Sayab, M.

    2005-01-01

    Systematic relationships between the fracture orientation and fold geometry in sedimentary rocks have been used to explain the development of synfolding fractures. Based on field observations at the Khushalgarh syncline, located east of the Kohat Plateau, we proposed that the orientation of fractures was influenced dominantly by two tectonic fracture sets, that is, the NE-SW and NW-SE. The NE-SW fracture set dominantly formed as mode 1 (tensile), where as, the NW-SE fracture set developed as mode 11 (shear) conjugate fractures. The NE-SW trending fractures follow the axis of the syncline, whereas, the NW-SE fracture about crosscuts the fold axis. Most of the NE-SW fractures abut against the NW-SW fracture set. Based on the orientation and crosscutting relationship, their modes in response to stress, we conclude that the NE-SW trending fractures formed early than those of NW-SE fracture set. Though, both the fracture sets are formed during the folding, we suggest that they were not formed at the same time. Their crosscutting relationship suggests that they developed sequentially rather than synchronously. Our interpretations support the laboratory-based models where only one fracture orientation (or set of fractures with one orientation) form in response to single stress. However, as the stress distribution in folded strata changes over time new fractures of distinct orientations can form during or late in the folding history. We conclude that the sandstone units underwent bedding-parallel extension during folding, where bedding is stretched to accommodate extension. Parallel to the fold axis orientation. Bending of the limbs is a likely mechanism for the development of observed NE-SW trending fractures during folding, whereas the NW-SE fractures developed late in the folded history. (author)

  9. Code subspaces for LLM geometries

    Science.gov (United States)

    Berenstein, David; Miller, Alexandra

    2018-03-01

    We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

  10. Euclidean distance geometry an introduction

    CERN Document Server

    Liberti, Leo

    2017-01-01

    This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

  11. Fractal geometry and computer graphics

    CERN Document Server

    Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

    1992-01-01

    Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

  12. The geometry of celestial mechanics

    CERN Document Server

    Geiges, Hansjörg

    2016-01-01

    Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.

  13. Differential geometry and mathematical physics

    CERN Document Server

    Rudolph, Gerd

    Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...

  14. Grassmannian geometry of scattering amplitudes

    CERN Document Server

    Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav

    2016-01-01

    Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...

  15. Foliation theory in algebraic geometry

    CERN Document Server

    McKernan, James; Pereira, Jorge

    2016-01-01

    Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013.  Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...

  16. Groups and Geometries : Siena Conference

    CERN Document Server

    Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria

    1998-01-01

    On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi­ tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...

  17. Needle decompositions in Riemannian geometry

    CERN Document Server

    Klartag, Bo'az

    2017-01-01

    The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

  18. Systematics of IIB spinorial geometry

    OpenAIRE

    Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.

    2005-01-01

    We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...

  19. Geometry Dependence of Stellarator Turbulence

    International Nuclear Information System (INIS)

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

    2009-01-01

    Using the nonlinear gyrokinetic code package GENE/GIST, 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 2D 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 Schrodinger-like equation governing linear drift modes

  20. Superbanana orbits in stellarator geometries

    International Nuclear Information System (INIS)

    Derr, J.A.; Shohet, J.L.

    1979-04-01

    The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron

  1. Turtle geometry the Python way

    OpenAIRE

    Battle, S.

    2014-01-01

    An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.

  2. Topics in modern differential geometry

    CERN Document Server

    Verstraelen, Leopold

    2017-01-01

    A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

  3. Computational geometry for reactor applications

    International Nuclear Information System (INIS)

    Brown, F.B.; Bischoff, F.G.

    1988-01-01

    Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications

  4. Number theory III Diophantine geometry

    CERN Document Server

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  5. Riemannian geometry and geometric analysis

    CERN Document Server

    Jost, Jürgen

    2017-01-01

    This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.  The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...

  6. Donaldson invariants in algebraic geometry

    International Nuclear Information System (INIS)

    Goettsche, L.

    2000-01-01

    In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

  7. Aspects of differential geometry II

    CERN Document Server

    Gilkey, Peter

    2015-01-01

    Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...

  8. Experimental Analysis of Hydraulic Fracture Growth and Acoustic Emission Response in a Layered Formation

    Science.gov (United States)

    Ning, Li; Shicheng, Zhang; Yushi, Zou; Xinfang, Ma; Shan, Wu; Yinuo, Zhang

    2018-04-01

    Microseismic/acoustic emission (AE) monitoring is an essential technology for understanding hydraulic fracture (HF) geometry and stimulated reservoir volume (SRV) during hydraulic fracturing in unconventional reservoirs. To investigate HF growth mechanisms and features of induced microseismic/AE events in a layered formation, laboratory fracturing experiments were performed on shale specimens (30 cm × 30 cm × 30 cm) with multiple bedding planes (BPs) under triaxial stresses. AE monitoring was used to reveal the spatial distribution and hypocenter mechanisms of AE events induced by rock failure. Computerized tomography scanning was used to observe the internal fracture geometry. Experimental results showed that the various HF geometries could be obviously distinguished based on injection pressure curves and AE responses. Fracture complexity was notably increased when vertically growing HFs connected with and opened more BPs. The formation of a complex fracture network was generally indicated by frequent fluctuations in injection pressure curves, intense AE activity, and three-dimensionally distributed AE events. Investigations of the hypocenter mechanisms revealed that shear failure/event dominated in shale specimens. Shear and tensile events were induced in hydraulically connected regions, and shear events also occurred around BPs that were not hydraulically connected. This led to an overestimation of HF height and SRV in layered formations based on the AE location results. The results also showed that variable injection rate and using plugging agent were conducive in promoting HF to penetrate through the weak and high-permeability BPs, thereby increasing the fracture height.

  9. Interpreting Gas Production Decline Curves By Combining Geometry and Topology

    Science.gov (United States)

    Ewing, R. P.; Hu, Q.

    2014-12-01

    Shale gas production forms an increasing fraction of domestic US energy supplies, but individual gas production wells show steep production declines. Better understanding of this production decline would allow better economic forecasting; better understanding of the reasons behind the decline would allow better production management. Yet despite these incentives, production declines curves remain poorly understood, and current analyses range from Arps' purely empirical equation to new sophisticated approaches requiring multiple unavailable parameters. Models often fail to capture salient features: for example, in log-log space many wells decline with an exponent markedly different from the -0.5 expected from diffusion, and often show a transition from one decline mode to another. We propose a new approach based on the assumption that the rate-limiting step is gas movement from the matrix to the induced fracture network. The matrix is represented as an assemblage of equivalent spheres (geometry), with low matrix pore connectivity (topology) that results in a distance-dependent accessible porosity profile given by percolation theory. The basic theory has just 2 parameters: the sphere size distribution (geometry), and the crossover distance (topology) that characterizes the porosity distribution. The theory is readily extended to include e.g. alternative geometries and bi-modal size distributions. Comparisons with historical data are promising.

  10. Algebraic Geometry and Number Theory Summer School

    CERN Document Server

    Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

    2017-01-01

    This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

  11. Geometry success in 20 minutes a day

    CERN Document Server

    LLC, LearningExpress

    2014-01-01

    Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr

  12. Computed tomograms of blowout fracture

    International Nuclear Information System (INIS)

    Ito, Haruhide; Hayashi, Minoru; Shoin, Katsuo; Hwang, Wen-Zern; Yamamoto, Shinjiro; Yonemura, Taizo.

    1985-01-01

    We studied 18 cases of orbital fractures, excluding optic canal fracture. There were 11 cases of pure blowout fracture and 3 of the impure type. The other 4 cases were orbital fractures without blowout fracture. The cardinal syndromes were diplopia, enophthalmos, and sensory disturbances of the trigeminal nerve in the pure type of blowout fracture. Many cases of the impure type of blowout fracture or of orbital fracture showed black eyes or a swelling of the eyelids which masked enophthalmos. Axial and coronal CT scans demonstrated: 1) the orbital fracture, 2) the degree of enophthalmos, 3) intraorbital soft tissue, such as incarcerated or prolapsed ocular muscles, 4) intraorbital hemorrhage, 5) the anatomical relation of the orbital fracture to the lacrimal canal, the trochlea, and the trigeminal nerve, and 6) the lesions of the paranasal sinus and the intracranial cavity. CT scans play an important role in determining what surgical procedures might best be employed. Pure blowout fractures were classified by CT scans into these four types: 1) incarcerating linear fracture, 2) trapdoor fracture, 3) punched-out fracture, and 4) broad fracture. Cases with severe head injury should be examined to see whether or not blowout fracture is present. If the patients are to hope to return to society, a blowout fracture should be treated as soon as possible. (author)

  13. Computed tomograms of blowout fracture

    Energy Technology Data Exchange (ETDEWEB)

    Ito, Haruhide; Hayashi, Minoru; Shoin, Katsuo; Hwang, Wen-Zern; Yamamoto, Shinjiro; Yonemura, Taizo

    1985-02-01

    We studied 18 cases of orbital fractures, excluding optic canal fracture. There were 11 cases of pure blowout fracture and 3 of the impure type. The other 4 cases were orbital fractures without blowout fracture. The cardinal syndromes were diplopia, enophthalmos, and sensory disturbances of the trigeminal nerve in the pure type of blowout fracture. Many cases of the impure type of blowout fracture or of orbital fracture showed black eyes or a swelling of the eyelids which masked enophthalmos. Axial and coronal CT scans demonstrated: 1) the orbital fracture, 2) the degree of enophthalmos, 3) intraorbital soft tissue, such as incarcerated or prolapsed ocular muscles, 4) intraorbital hemorrhage, 5) the anatomical relation of the orbital fracture to the lacrimal canal, the trochlea, and the trigeminal nerve, and 6) the lesions of the paranasal sinus and the intracranial cavity. CT scans play an important role in determining what surgical procedures might best be employed. Pure blowout fractures were classified by CT scans into these four types: 1) incarcerating linear fracture, 2) trapdoor fracture, 3) punched-out fracture, and 4) broad fracture. Cases with severe head injury should be examined to see whether or not blowout fracture is present. If the patients are to hope to return to society, a blowout fracture should be treated as soon as possible. (author).

  14. Investigation of Mechanical Properties and Fracture Simulation of Solution-Treated AA 5754

    Science.gov (United States)

    Kumar, Pankaj; Singh, Akhilendra

    2017-10-01

    In this work, mechanical properties and fracture toughness of as-received and solution-treated aluminum alloy 5754 (AA 5754) are experimentally evaluated. Solution heat treatment of the alloy is performed at 530 °C for 2 h, and then, quenching is done in water. Yield strength, ultimate tensile strength, impact toughness, hardness, fatigue life, brittle fracture toughness (K_{Ic} ) and ductile fracture toughness (J_{Ic} ) are evaluated for as-received and solution-treated alloy. Extended finite element method has been used for the simulation of tensile and fracture behavior of material. Heaviside function and asymptotic crack tip enrichment functions are used for modelling of the crack in the geometry. Ramberg-Osgood material model coupled with fracture energy is used to simulate the crack propagation. Fracture surfaces obtained from various mechanical tests are characterized by scanning electron microscopy.

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

    Science.gov (United States)

    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

  16. Radiological diagnosis of fractures

    International Nuclear Information System (INIS)

    Finlay, D.B.L.; Allen, M.J.

    1984-01-01

    This book is about radiology of fractures. While it contains sections of clinical features it is not intended that readers should rely entirely upon these for the diagnosis and management of the injured patient. As in the diagnosis and treatment of all medical problems, fracture management must be carried out in a logical step-by-step fashion - namely, history, examination, investigation, differential diagnosis, diagnosis and then treatment. Each section deals with a specific anatomical area and begins with line drawings of the normal radiographs demonstrating the anatomy. Accessory views that may be requested, and the indications for these, are included. Any radiological pitfalls for the area in general are then described. The fractures in adults are then examined in turn, their radiological features described, and any pitfalls in their diagnosis discussed. A brief note of important clinical findings is included. A brief mention is made of pediatric fractures which are of significance and their differences to the adult pattern indicated. Although fractures can be classified into types with different characteristics, in life every fracture is individual. Fractures by and large follow common patterns, but many have variations

  17. Spontaneous rib fractures.

    Science.gov (United States)

    Katrancioglu, Ozgur; Akkas, Yucel; Arslan, Sulhattin; Sahin, Ekber

    2015-07-01

    Other than trauma, rib fracture can occur spontaneously due to a severe cough or sneeze. In this study, patients with spontaneous rib fractures were analyzed according to age, sex, underlying pathology, treatment, and complications. Twelve patients who presented between February 2009 and February 2011 with spontaneous rib fracture were reviewed retrospectively. The patients' data were evaluated according to anamnesis, physical examination, and chest radiographs. The ages of the patients ranged from 34 to 77 years (mean 55.91 ± 12.20 years), and 7 (58.4%) were male. All patients had severe cough and chest pain. The fractures were most frequently between 4th and 9th ribs; multiple rib fractures were detected in 5 (41.7%) patients. Eight (66.7%) patients had chronic obstructive pulmonary disease, 2 (16.7%) had bronchial asthma, and 2 (16.7%) had osteoporosis. Bone densitometry revealed a high risk of bone fracture in all patients. Patients with chronic obstructive pulmonary disease or bronchial asthma had been treated with high-dose steroids for over a year. Spontaneous rib fracture due to severe cough may occur in patients with osteoporosis, chronic obstructive pulmonary disease, or bronchial asthma, receiving long-term steroid therapy. If these patients have severe chest pain, chest radiography should be performed to check for bone lesions. © The Author(s) 2015.

  18. Why ductile fracture mechanics

    International Nuclear Information System (INIS)

    Ritchie, R.O.

    1983-01-01

    Until recently, the engineering application of fracture mechanics has been specific to a description of macroscopic fracture behavior in components and structural parts which remain nominally elastic under loading. While this approach, termed linear elastic fracture mechanics, has been found to be invaluable for the continuum analysis of crack growth in brittle and high strength materials, it is clearly inappropriate for characterizing failure in lower strength ductile alloys where extensive inelastic deformation precedes and accompanies crack initiation and subsequent propagation. Accordingly, much effort has been devoted in recent years toward the development of nonlinear or ductile fracture mechanics methodology to characterize fracture behavior under elastic/plastic conditions; an effort which has been principally motivated by problems in nuclear industry. In this paper, the concepts of ductile (elastic/plastic) fracture mechanics are introduced and applied to the problem of both stationary and nonstationary cracks. Specifically, the limitations inherent in this approach are defined, together with a description of the microstructural considerations and applications relevant to the failure of ductile materials by fracture, fatigue, and creep

  19. Orbital wall fractures

    International Nuclear Information System (INIS)

    Iinuma, Toshitaka; Ishio, Ken-ichirou; Yoshinami, Hiroyoshi; Kuriyama, Jun-ichi; Hirota, Yoshiharu.

    1993-01-01

    A total of 59 cases of mild facial fractures (simple orbital wall fractures, 34 cases, other facial fractures, 25 cases) with the clinical suspects of orbital wall fractures were evaluated both by conventional views (Waters' and Caldwell views) and coronal CT scans. Conventional views were obtained, as an average, after 4 days and CT after 7 days of injuries. Both the medial wall and the floor were evaluated at two sites, i.e., anterior and posterior. The ethmoid-maxillary plate was also included in the study. The degree of fractures was classified as, no fractures, fractures of discontinuity, dislocation and fragmentation. The coronal CT images in bone window condition was used as reference and the findings were compared between conventional views and CT. The correct diagnosis was obtained as follows: orbital floor (anterior, 78%, posterior, 73%), medial orbital wall (anterior, 72%, posterior, 72%) and ethmoid-maxillary plate (64%). The false positive diagnosis was as follows: orbital floor (anterior only, 13%), medial orbital wall (anterior only, 7%) and ethmoid-maxillary plate (11%). The false negative diagnosis was as follows: orbital floor (anterior, 9%, posterior, 10%), medial orbital wall (anterior, 21%, posterior, 28%) and ethmoid-maxillary plate (21%). The results were compared with those of others in the past. (author)

  20. Chance Fracture Secondary to a Healed Kyphotic Compression Osteoporotic Fracture

    Directory of Open Access Journals (Sweden)

    Teh KK

    2009-11-01

    Full Text Available Chance fracture is an unstable vertebral fracture, which usually results from a high velocity injury. An elderly lady with a previously healed osteoporotic fracture of the T12 and L1 vertebra which resulted in a severe kyphotic deformity subsequently sustained a Chance fracture of the adjacent L2 vertebrae after a minor fall. The previously fracture left her with a deformity which resulted in significant sagittal imbalance therefore predisposing her to this fracture. This case highlights the importance of aggressive treatment of osteoporotic fractures in order to prevent significant sagittal imbalance from resultant (i.e. kyphotic deformity.