Discrete differential geometry: the nonplanar quadrilateral mesh.
Twining, Carole J; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.
A New Physics-Based Modeling of Multiple Non-Planar Hydraulic Fractures Propagation
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [University of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind [University of Utah; Jiang, Shu [Energy & Geoscience Institute
2015-10-01
Because of the low permeability in shale plays, closely spaced hydraulic fractures and multilateral horizontal wells are generally required to improve production. Therefore, understanding the potential fracture interaction and stress evolution is critical in optimizing fracture/well design and completion strategy in multi-stage horizontal wells. In this paper, a novel fully coupled reservoir flow and geomechanics model based on the dual-lattice system is developed to simulate multiple non-planar fractures propagation. The numerical model from Discrete Element Method (DEM) is used to simulate the mechanics of fracture propagations and interactions, while a conjugate irregular lattice network is generated to represent fluid flow in both fractures and formation. The fluid flow in the formation is controlled by Darcy’s law, but within fractures it is simulated by using cubic law for laminar flow through parallel plates. 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. We investigate the fracture propagation path in both homogeneous and heterogeneous reservoirs using the simulator developed. Stress shadow caused by the transverse fracture will change the orientation of principal stress in the fracture neighborhood, which may inhibit or alter the growth direction of nearby fracture clusters. However, the initial in-situ stress anisotropy often helps overcome this phenomenon. Under large in-situ stress anisotropy, the hydraulic fractures are more likely to propagate in a direction that is perpendicular to the minimum horizontal stress. Under small in-situ stress anisotropy, there is a greater chance for fractures from nearby clusters to merge with each other. Then, we examine the differences in fracture geometry caused by fracturing in cemented or uncemented wellbore. Moreover, the impact of
Mali, Kunal S; Zöphel, Lukas; Ivasenko, Oleksandr; Müllen, Klaus; De Feyter, Steven
2013-10-01
In this work, we provide evidence for multiple non-planar adsorption geometries of a novel pyrenocyanine derivative at the liquid-solid interface under ambient conditions. When adsorbed at the organic liquid-solid interface, lead pyrenocyanine forms well-ordered monolayers that exhibit peculiar non-periodic contrast variation. The different contrast of the adsorbed molecules is attributed to dissimilar adsorption geometries which arise from the non-planar conformation of the molecules. The non-planarity of the molecular backbone in turn arises due to a combination of the angularly extended pyrene subunits and the presence of the large lead ion, which is too big to fit inside the central cavity and thus is located out of the aromatic plane. The two possible locations of the lead atom, namely below and above the aromatic plane, could be identified as depression and protrusion in the central cavity, respectively. The manifestation of such multiple adsorption geometries on the structure of the resultant monolayer is discussed in detail. The packing density of these 2D arrays of molecules could be tuned by heating of the sample wherein the molecular packing changes from a low-density, pseudo six-fold symmetric to a high-density, two-fold symmetric arrangement. Finally, a well-ordered two-component system could be constructed by incorporating C60 molecules in the adlayer of lead pyrenocyanine at the liquid-solid interface.
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran [College of Textile Technology, Berhampore 742101, Murshidabad, West Bengal (India)]. E-mail: sran_g@yahoo.com
2005-04-11
It has been found that the dust ion acoustic solitary wave (DIASW) is governed by a modified form of Korteweg-de Vries (KdV) equation modified by the effects of ionization, particle collisions and bounded nonplanar geometry. Approximate analytical time evolution solution and also the numerical solution of modified form of KdV equation reveal that the wave amplitude grows exponentially with time due to ionization, whereas the bounded nonplanar geometry and collision reduce the instability growth rate.
Effect of superthermal electrons on dust-acoustic Gardner solitons in nonplanar geometry
Indian Academy of Sciences (India)
Deb Kumar Ghosh; Yday Narayan Ghosh; Prasanta Chatterjee; C S Wong
2013-04-01
The properties of nonplanar (cylindrical and spherical) dust-acoustic solitary waves (DASWs) in an unmagnetized, collisionless three-component dusty plasma, whose constituents are negatively charged cold dust fluid, superthermal/non-Maxwellian electrons (represented by kappa distribution) and Boltzmann distributed ions, are investigated by deriving the modified Gardner (MG) equation. The well-known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar DA Gardner solitons (GSs) are discussed. It is seen that the properties of nonplanar DAGSs (positive and negative) significantly differ as the value of spectral index changes.
Indian Academy of Sciences (India)
Uday Narayan Ghosh; Prasantha Chatterjee; Deb Kumar Ghosh
2013-10-01
Interaction of nonplanar ion-acoustic solitary waves is an important source of information for studying the nature and characteristics of ion-acoustic solitary waves (IASWs). The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising of nonthermal distributed electrons and warm ions is investigated using the extended version of Poincaré–Lighthill–Kuo (PLK) perturbation method. How the interactions are taking place in cylindrical and spherical geometries are shown numerically. Analytical phase shifts are derived for nonplanar geometry. The effects of the ion to electron temperature parameter and the nonthermal electrons parameter on the phase shift are studied. It is shown that the properties of the interaction of IASWs in different geometries are very different.
Vertebral Geometry Parameters Can Predict Fractures
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P Tofighi
2007-08-01
Full Text Available Background: The aim of this study was to investigate vertebral geometry changes and determine cutoff value of vertebral height to predict fractures. Methods: In a cross-sectional study, 280 postmenopausal women recruited .In all subjects bone mineral density and radiog¬raphy of the lumbar spine performed. Lateral radiographs were evaluated for identification of vertebral fractures, using a validated semiquantitative method. T-score of vertebral height was calculated based on data extracted from Iranian Multi¬center Osteoporosis Study. ROC curve used to determine cut off value of vertebral height T-score to predict fractures. Results: The mean of age and BMI were 55.34±8.7 years and 27.73±5 kg/m2, respectively. Among osteoporotic women, 59.8% had one or more vertebral fractures and 23.8% had at least 2 fractures. In fracture group the T-score of spine and femur BMD was lower than the others. The mean of vertebral height in women without fractures was 12.94±0.6 cm, and in the patient with 4 or more fractures was12.3, thus every fracture accompany with 1.2% decreases in the height of vertebrae. The prevalence of vertebral fracture in osteoporotic patients was 71.4% and in healthy cases 39.5%. Better estimation of vertebral height T score in ROC curve was less than -0.7.The sensitivity and specificity of the cut off value were 81.3% and 52.9%, respectively. Conclusion: Vertebral fractures are common fractures in postmenopausal women. There was a correlation between verte¬bral height and fractures. Vertebral geometric parameters especially height T score can be used for fracture screening.
Vertebral Geometry Parameters Can Predict Fractures
Directory of Open Access Journals (Sweden)
P Tofighi
2007-01-01
Conclusion: Vertebral fractures are common fractures in postmenopausal women. There was a correlation between verte¬bral height and fractures. Vertebral geometric parameters especially height T score can be used for fracture screening.
Indian Academy of Sciences (India)
M EGHBALI; B FAROKHI; M ESLAMIFAR
2017-01-01
The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational instability (MI) of DIA waves governed by the NLS equation is also presented. The effects of different ranges of the non-extensive parameter $q$ on the MI are studied. The growth rate of the MI is also given for different values of $q$. It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the netdust-charge number density and non-planar geometry.
Eghbali, M.; Farokhi, B.; Eslamifar, M.
2017-01-01
The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational instability (MI) of DIA waves governed by the NLS equation is also presented. The effects of different ranges of the non-extensive parameter q on the MI are studied. The growth rate of the MI is also given for different values of q. It is found that the basic features of the DIA waves are significantly modified by non-extensive electron distribution, polarity of the net dust-charge number density and non-planar geometry.
Brankovič, Jana; Jovanovski, Sašo; Jevnikar, Peter; Hofmeister, Alexander; Reininger-Gutmann, Birgit; Jan, Janja; Grošelj, Maja; Osredkar, Joško; Uršič, Matjaž; Fazarinc, Gregor; Pogačnik, Azra; Vrecl, Milka
2017-04-01
Exposure to widespread lipophilic and bioaccumulative polychlorinated biphenyls (PCBs) induces diverse biochemical and toxicological responses in various organs, including the bone. The aim of this study was to evaluate the changes in growth rate, geometry, serum, and bone biochemical parameters and biomechanics of juvenile rat femur induced by lactational exposure to nonplanar PCB-155 and planar PCB-169 individually and in combination. Fifteen lactating Wistar rats were divided into four groups (PCB-169, PCB-155, PCB-155+169, and control), and PCBs were administered intraperitoneally at different time points after delivery. Femurs from 22-day-old offspring were analyzed by microCT, three-point bending test and inductively coupled plasma-mass spectrometry (ICP-MS) to obtain data on bone geometry, biomechanics and mineral composition. The serum levels of calcium, phosphate and alkaline phosphatase were also determined. Lactational exposure to planar PCB-169 resulted in shorter and thinner femurs, reduced endosteal and periosteal perimeters, smaller total cross-sectional and medullary areas, and lowered serum bone marker levels and calcium levels in the bone, while femur mechanical properties were not significantly altered. The changes observed in the combination exposure (PCB-155+169) group were similar to those observed in the PCB-169 group but were less pronounced. In summary, our results demonstrate that alterations in lactationally exposed offspring were primarily induced by planar PCB-169. The milder outcome in the combined group suggested that the PCB-169-mediated toxic effects on the bone might be reduced by a nonplanar PCB-155 congener. © 2016 Wiley Periodicals, Inc. Environ Toxicol 32: 1135-1146, 2017.
Comment on a spurious prediction of a non-planar geometry for benzene at the MP2 level of theory
Samala, Nagaprasad Reddy; Jordan, Kenneth D.
2017-02-01
MP2 calculations with the full aug-cc-pVTZ basis set give a non-planar structure for benzene. Although this non-physical result can be avoided by using the smaller aug-cc-pVDZ basis set or by scaling or deleting selected functions from the aug-cc-pVTZ basis set, such changes to the basis set can result in calculated values of the frequencies of the b2g out-of-plane vibrations that are considerably underestimated. The origin of this behavior is traced to linear dependency problems with the aug-cc-pVDZ and aug-cc-pVTZ basis sets when used for benzene.
Proximal femoral bone geometry in osteoporotic hip fractures in Thailand.
2015-01-01
A number of different bone geometries have been reported to be correlated with osteoporosis, bone mineral density and fractures. Those correlations are used for diagnosis, treatment and prediction of fracture risk in osteoporosis cases. However there have been no studies of significant bone parameters predicting osteoporosis and hip fracture in Thailand To evaluate the correlation between geometric parameters of the proximal femur and both the Singh index and bone mineral density as well as to investigate the relationship between those two metrics and osteoporotic hip fracture in the Thai population. Forty-four Thai patients with osteoporotic hip fractures andforty-five healthy Thai people matched for age and gender were included in the present study. Bone mineral density and bone geometry from plain hip radiographs of non-fracture sites in the fracture group and proximal femur radiographs of the same site in the healthy group were measured That data were analyzed to determine levels of correlation. Bone geometries were also analyzed to determine hip fracture predictive capacity. Correlation between the Singh index and bone mineral density was significant (p hip fracture (p = 0.014 and p = 0.035, respectively). Each 1 mm reduction in the width of the femoral medial neck cortex increased the osteoporotic hip fracture risk by a factor of 2.7 (OR = 0.37, 95% CI = 0.15-0.93). In the Thai population, bone geometry from plain radiographs can help predict the risk of osteoporotic hip fracture. Osteoporosis is correlated with a low Singh index value. The width of the femoral medial neck cortex is a reliable predictor of hip fracture risk.
Haggard, Hal M; Kamiński, Wojciech; Riello, Aldo
2014-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains at the leading order an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged ...
Haggard, Hal M.; Han, Muxin; Kamiński, Wojciech; Riello, Aldo
2015-11-01
We study the expectation value of a nonplanar Wilson graph operator in SL (2, C) Chern-Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. This can be understood as arising from the relation between Chern-Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL (2, C) Chern-Simons theory in 3 dimensions with knotted graph defects.
Directory of Open Access Journals (Sweden)
Hal M. Haggard
2015-11-01
Full Text Available We study the expectation value of a nonplanar Wilson graph operator in SL(2,C Chern–Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C Chern–Simons theory in 3 dimensions with knotted graph defects.
Effects of Hip Geometry on Fracture Patterns of Proximal Femur
Directory of Open Access Journals (Sweden)
Seyyed Morteza Kazemi
2016-07-01
Full Text Available Background: Some studies have previously shown that geometry of proximal femur can affect the probability of fracture and type of fracture. It happens since the geometry of the proximal femur determines how a force is applied to its different parts. In this study, we have compared proximal femur’s geometric characteristics in femoral neck (FNF, intertrochanteric (ITF and Subtrochanteric (STF fractures. Methods: In this study, 60 patients who had hip fractures were studied as case studies. They were divided into FNF, ITF and STF groups based on their fracture types (20 patients in each group. Patients were studied with x-ray radiography and CT scans. Radiological parameters including femoral neck length from lateral cortex to center of femoral head (FNL, diameter of femoral head (FHD, diameter of femoral neck (FND, femoral head neck offset (FHNO, neck-shaft angle (alpha, femoral neck anteversion (beta were measured and compared in all three groups. Results: Amount of FNL was significantly higher in STF group compared to FNF (0.011 while ITF and STF as well as FNT and ITF did not show a significant different. Also, FND in FNF group was significantly lower than the other two groups, i.e. ITF and STF. In other cases there were no instances of significant statistical difference. Conclusion: Hip geometry can be used to identify individuals who are at the risk of fracture with special pattern. Also, it is important to have more studies in different populations and more in men.
Effects of Hip Geometry on Fracture Patterns of Proximal Femur
Kazemi, Seyyed Morteza; Qoreishy, Mohamad; Keipourfard, Ali; Sajjadi, Mohammadreza Minator; Shokraneh, Shahram
2016-01-01
Background: Some studies have previously shown that geometry of proximal femur can affect the probability of fracture and type of fracture. It happens since the geometry of the proximal femur determines how a force is applied to its different parts. In this study, we have compared proximal femur’s geometric characteristics in femoral neck (FNF), intertrochanteric (ITF) and Subtrochanteric (STF) fractures. Methods: In this study, 60 patients who had hip fractures were studied as case studies. They were divided into FNF, ITF and STF groups based on their fracture types (20 patients in each group). Patients were studied with x-ray radiography and CT scans. Radiological parameters including femoral neck length from lateral cortex to center of femoral head (FNL), diameter of femoral head (FHD), diameter of femoral neck (FND), femoral head neck offset (FHNO), neck-shaft angle (alpha), femoral neck anteversion (beta) were measured and compared in all three groups. Results: Amount of FNL was significantly higher in STF group compared to FNF (0.011) while ITF and STF as well as FNT and ITF did not show a significant different. Also, FND in FNF group was significantly lower than the other two groups, i.e. ITF and STF. In other cases there were no instances of significant statistical difference. Conclusion: Hip geometry can be used to identify individuals who are at the risk of fracture with special pattern. Also, it is important to have more studies in different populations and more in men. PMID:27517071
Measurement of Fracture Geometry for Accurate Computation of Hydraulic Conductivity
Chae, B.; Ichikawa, Y.; Kim, Y.
2003-12-01
Fluid flow in rock mass is controlled by geometry of fractures which is mainly characterized by roughness, aperture and orientation. Fracture roughness and aperture was observed by a new confocal laser scanning microscope (CLSM; Olympus OLS1100). The wavelength of laser is 488nm, and the laser scanning is managed by a light polarization method using two galvano-meter scanner mirrors. The system improves resolution in the light axis (namely z) direction because of the confocal optics. The sampling is managed in a spacing 2.5 μ m along x and y directions. The highest measurement resolution of z direction is 0.05 μ m, which is the more accurate than other methods. For the roughness measurements, core specimens of coarse and fine grained granites were provided. Measurements were performed along three scan lines on each fracture surface. The measured data were represented as 2-D and 3-D digital images showing detailed features of roughness. Spectral analyses by the fast Fourier transform (FFT) were performed to characterize on the roughness data quantitatively and to identify influential frequency of roughness. The FFT results showed that components of low frequencies were dominant in the fracture roughness. This study also verifies that spectral analysis is a good approach to understand complicate characteristics of fracture roughness. For the aperture measurements, digital images of the aperture were acquired under applying five stages of uniaxial normal stresses. This method can characterize the response of aperture directly using the same specimen. Results of measurements show that reduction values of aperture are different at each part due to rough geometry of fracture walls. Laboratory permeability tests were also conducted to evaluate changes of hydraulic conductivities related to aperture variation due to different stress levels. The results showed non-uniform reduction of hydraulic conductivity under increase of the normal stress and different values of
A cubic matrix-fracture geometry model for radial tracer flow in naturally fractured reservoirs
Energy Technology Data Exchange (ETDEWEB)
Jetzabeth Ramirez-Sabag; Fernando Samaniego V.
1992-01-01
This study presents a general solution for the radial flow of tracers in naturally fractured reservoirs, with cubic blocks matrix-fracture geometry. Continuous and finite step injection of chemical and radioactive tracers are considered. The reservoir is treated as being composed of two regions: a mobile where dispersion and convection take place and a stagnant where only diffusion and adsorption are allowed. Radioactive decay is considered in both regions. The model of this study is thoroughly compared under proper simplified conditions to those previously presented in the literature. The coupled matrix to fracture solution in the Laplace space is numerically inverted by means of the Crump algorithm. A detailed validation of the model with respect to solutions previously presented and/or simplified physical conditions solutions (i.e., homogeneous case) or limit solutions (i.e., naturally fractured nearly homogeneous) was carried out. The influence of the three of the main dimensionless parameters that enter into the solution was carefully investigated. A comparison of results for three different naturally fractured systems, vertical fractures (linear flow), horizontal fractures (radial flow) and the cubic geometry model of this study, is presented.
Hydromechanical Normal Deformation Experiments and Coupling to Fracture Surface Geometry
Thörn, J.; Fransson, A. M.
2015-12-01
Civil engineering structures founded in fractured crystalline rock, such as the Fennoscandian Shield (Norway-Sweden-Finland) requires allowance for both stability and/or deformations of the rock mass and groundwater ingress and groundwater pressure changes. Coupling these issues could be the key to solving the challenges that arise from construction of e.g. hydropower dams, road and railroad tunnels, and most certainly the construction of nuclear waste repositories within fractured crystalline rock, all of which are currently planned in Sweden. Excavation related deformation in fractures may cause groundwater leakage even from the most elaborate pre-excavation grouting works. A better understanding on hydraulically (or grouting) induced deformations in the near-field of tunnels, where the stress field is re-distributed due to the opening may both provide a basis for more accurate numerical modelling and grouting or excavation procedures that minimize the damage on the completed grouting fans. Subjects of this study were experiments conducted as measurement of deformations in boreholes close to tunnels due to stepwise injection tests, and laboratory hydromechanical experiments conducted as flow and normal deformation measurements in a permeameter during cycles of up to 2.5 MPa confining pressure, and subsequent surface scanning of the samples for coupling of HM-results to geometric appearance, aperture and contact geometry. When expressed in terms of hydraulic aperture (b) and fracture normal stiffness (kn) the results of both in situ and lab experiments support a previously suggested relationship based on field data where kn is inversely proportional to roughly b2. The relationship was assumed to be valid for low compressive stress across fractures with limited previous deformation. One important data set used to establish the relationship was transmissivity and storage coefficients from hydraulic interference tests previously performed at Äspö Hard Rock
van de Ketterij, R.G.
2001-01-01
Hydraulic fracturing is a technique frequently used to stimulate the production of an oil or gas well by creating a fracture in the porous rock around the wellbore. The success of a hydraulic fracture treatment depends heavily on the created fracture geometry. The optimum situation arises when a sin
Haggard, Hal M.; Muxin Han; Wojciech Kamiński; Aldo Riello
2015-01-01
We study the expectation value of a nonplanar Wilson graph operator in SL(2,C) Chern-Simons theory on $S^3$. In particular we analyze its asymptotic behaviour in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat co...
Influence of bone mineral density and hip geometry on the different types of hip fracture.
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.
Simulation Study of CO2-EOR in Tight Oil Reservoirs with Complex Fracture Geometries.
Zuloaga-Molero, Pavel; Yu, Wei; Xu, Yifei; Sepehrnoori, Kamy; Li, Baozhen
2016-09-15
The recent development of tight oil reservoirs has led to an increase in oil production in the past several years due to the progress in horizontal drilling and hydraulic fracturing. However, the expected oil recovery factor from these reservoirs is still very low. CO2-based enhanced oil recovery is a suitable solution to improve the recovery. One challenge of the estimation of the recovery is to properly model complex hydraulic fracture geometries which are often assumed to be planar due to the limitation of local grid refinement approach. More flexible methods like the use of unstructured grids can significantly increase the computational demand. In this study, we introduce an efficient methodology of the embedded discrete fracture model to explicitly model complex fracture geometries. We build a compositional reservoir model to investigate the effects of complex fracture geometries on performance of CO2 Huff-n-Puff and CO2 continuous injection. The results confirm that the appropriate modelling of the fracture geometry plays a critical role in the estimation of the incremental oil recovery. This study also provides new insights into the understanding of the impacts of CO2 molecular diffusion, reservoir permeability, and natural fractures on the performance of CO2-EOR processes in tight oil reservoirs.
Simulation Study of CO2-EOR in Tight Oil Reservoirs with Complex Fracture Geometries
Zuloaga-Molero, Pavel; Yu, Wei; Xu, Yifei; Sepehrnoori, Kamy; Li, Baozhen
2016-09-01
The recent development of tight oil reservoirs has led to an increase in oil production in the past several years due to the progress in horizontal drilling and hydraulic fracturing. However, the expected oil recovery factor from these reservoirs is still very low. CO2-based enhanced oil recovery is a suitable solution to improve the recovery. One challenge of the estimation of the recovery is to properly model complex hydraulic fracture geometries which are often assumed to be planar due to the limitation of local grid refinement approach. More flexible methods like the use of unstructured grids can significantly increase the computational demand. In this study, we introduce an efficient methodology of the embedded discrete fracture model to explicitly model complex fracture geometries. We build a compositional reservoir model to investigate the effects of complex fracture geometries on performance of CO2 Huff-n-Puff and CO2 continuous injection. The results confirm that the appropriate modelling of the fracture geometry plays a critical role in the estimation of the incremental oil recovery. This study also provides new insights into the understanding of the impacts of CO2 molecular diffusion, reservoir permeability, and natural fractures on the performance of CO2-EOR processes in tight oil reservoirs.
Eigenpolarization theory of monolithic nonplanar ring oscillators
Nilsson, Alan C.; Gustafson, Eric K.; Byer, Robert L.
1989-01-01
Diode-laser-pumped monolithic nonplanar ring oscillators (NPROs) in an applied magnetic field can operate as unidirectional traveling-wave lasers. The diode laser pumping, monolithic construction, and unidirectional oscillation lead to narrow linewidth radiation. Here, a comprehensive theory of the eigenpolarizations of a monolithic NPRO is presented. It is shown how the properties of the integral optical diode that forces unidirectional operation depend on the choice of the gain medium, the applied magnetic field, the output coupler, and the geometry of the nonplanar ring light path. Using optical equivalence theorems to gain insight into the polarization characteristics of the NPRO, a strategy for designing NPROs with low thresholds and large loss nonreciprocities is given. An analysis of the eigenpolarizations for one such NPRO is presented, alternative optimization approaches are considered, and the prospects for further reducing the linewidths of these lasers are briefly discussed.
Indian Academy of Sciences (India)
Bishnu P Panda; Smita Mohanty; S K Nayak
2014-08-01
In this study, organically modified Na-MMT clay was used for the preparation of blend nanocomposites containing different ratios of polypropylene (PP) and ethylene propylene diene monomer (EPDM) elastomer in a twin screw extruder. Maleic-grafted PP (MAPP) was used as compatibilizer for making PP hydrophilic. Surface modification of Na–MMT was made by using amino propyl trimethoxy silane (APS) and trimethyl amine as coupling agent with surface grafting catalyst, respectively. A fracture mechanics approach has been adopted by mode I test and the effects of specimen geometry have been investigated. Increase in interlaminar fracture energy value, c, was observed as the crack propagated through the composite, i.e. a rising ‘R-curve’ for both blend and nanocomposites. Deep fracture studies were carried out at different temperatures (–60 °C to 60 °C) using Izod impact and SENT tests. Fracture energy, fracture stress and brittle ductile transition were determined from crack initiation and propagation process, which showed significant improvement in impact and fracture energy at positive temperature. The wide-angle X-ray diffraction (XRD) patterns showed increased -spacing of clay layers, indicating enhanced compatibility between PP and clay with the addition of maleated polypropylene (MAPP). Morphology/impact property relationships and an explanation of the toughening mechanisms were made by comparing the impact properties with scanning electron micrographs (SEMs) of fracture surfaces. The transmission electron microscopy (TEM) photomicrographs illustrated the intercalated and partially exfoliated structures of the hybrids with clay, MAPP and elastomer.
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
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.
Numerical and Experimental Studies of Particle Settling in Real Fracture Geometries
Roy, Pratanu; Du Frane, Wyatt L.; Kanarska, Yuliya; Walsh, Stuart D. C.
2016-11-01
Proppant is a vital component of hydraulic stimulation operations, improving conductivity by maintaining fracture aperture. While correct placement is a necessary part of ensuring that proppant performs efficiently, the transport behavior of proppant in natural rock fractures is poorly understood. In particular, as companies pursue new propping strategies involving new types of proppant, more accurate models of proppant behavior are needed to help guide their deployment. A major difficulty with simulating reservoir-scale proppant behavior is that continuum models traditionally used to represent large-scale slurry behavior loose applicability in fracture geometries. Particle transport models are often based on representative volumes that are at the same scale or larger than fractures found in hydraulic fracturing operations, making them inappropriate for modeling these types of flows. In the absence of a first-principles approach, empirical closure relations are needed. However, even such empirical closure relationships are difficult to derive without an accurate understanding of proppant behavior on the particle level. Thus, there is a need for experiments and simulations capable of probing phenomena at the sub-fracture scale. In this paper, we present results from experimental and numerical studies investigating proppant behavior at the sub-fracture level, in particular, the role of particle dispersion during proppant settling. In the experimental study, three-dimensional printing techniques are used to accurately reproduce the topology of a fractured Marcellus shale sample inside a particle-flow cell. By recreating the surface in clear plastic resin, proppant movement within the fracture can be tracked directly in real time without the need for X-ray imaging. Particle tracking is further enhanced through the use of mixtures of transparent and opaque proppant analogues. The accompanying numerical studies employ a high-fidelity three-dimensional particle-flow model
Evidence for a Nonplanar Amplituhedron
Bern, Zvi; Litsey, Sean; Stankowicz, James; Trnka, Jaroslav
2015-01-01
The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of the integrand that incorporates these structures. This geometric construction further implies the amplitude is fully specified by constraining it to vanish on spurious residues. By writing the amplitude in a dlog basis, we provide nontrivial evidence that these analytic properties and "zero conditions" carry over into the nonplanar sector. This suggests that the concept of the amplituhedron can be extended to the the nonplanar sector of N = 4 super-Yang-Mills theory.
Evidence for a nonplanar amplituhedron
Bern, Zvi; Herrmann, Enrico; Litsey, Sean; Stankowicz, James; Trnka, Jaroslav
2016-06-01
The scattering amplitudes of planar mathcal{N} = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of the integrand that incorporates these structures. This geometric construction further implies the amplitude is fully specified by constraining it to vanish on spurious residues. By writing the amplitude in a dlog basis, we provide nontrivial evidence that these analytic properties and "zero conditions" carry over into the nonplanar sector. This suggests that the concept of the amplituhedron can be extended to the nonplanar sector of mathcal{N} = 4 super-Yang-Mills theory.
Murach, Michelle M; Kang, Yun-Seok; Goldman, Samuel D; Schafman, Michelle A; Schlecht, Stephen H; Moorhouse, Kevin; Bolte, John H; Agnew, Amanda M
2017-05-25
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 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.
Bachmann, Katherine Neubecker; Fazeli, Pouneh K; Lawson, Elizabeth A; Russell, Brian M; Riccio, Ariana D; Meenaghan, Erinne; Gerweck, Anu V; Eddy, Kamryn; Holmes, Tara; Goldstein, Mark; Weigel, Thomas; Ebrahimi, Seda; Mickley, Diane; Gleysteen, Suzanne; Bredella, Miriam A; Klibanski, Anne; Miller, Karen K
2014-12-01
Data suggest that anorexia nervosa (AN) and obesity are complicated by elevated fracture risk, but skeletal site-specific data are lacking. Traditional bone mineral density (BMD) measurements are unsatisfactory at both weight extremes. Hip structural analysis (HSA) uses dual-energy X-ray absorptiometry data to estimate hip geometry and femoral strength. Factor of risk (φ) is the ratio of force applied to the hip from a fall with respect to femoral strength; higher values indicate higher hip fracture risk. The objective of the study was to investigate hip fracture risk in AN and overweight/obese women. This was a cross-sectional study. The study was conducted at a Clinical Research Center. PATIENTS included 368 women (aged 19-45 y): 246 AN, 53 overweight/obese, and 69 lean controls. HSA-derived femoral geometry, peak factor of risk for hip fracture, and factor of risk for hip fracture attenuated by trochanteric soft tissue (φ(attenuated)) were measured. Most HSA-derived parameters were impaired in AN and superior in obese/overweight women vs controls at the narrow neck, intertrochanteric, and femoral shaft (P ≤ .03). The φ(attenuated) was highest in AN and lowest in overweight/obese women (P fractures. Femoral geometry by HSA, hip BMD, and factor of risk for hip fracture attenuated by soft tissue are impaired in AN and superior in obesity, suggesting higher and lower hip fracture risk, respectively. Only attenuated factor of risk was associated with fragility fracture prevalence, suggesting that variability in soft tissue padding may help explain site-specific fracture risk not captured by BMD.
Indian Academy of Sciences (India)
Shailendra Kumar; S V Barai
2012-02-01
This paper presents numerical investigation of the inﬂuence of the specimen geometry, loading condition, size-effect and softening function of concrete on double- fracture parameters. The input data needed for computation of the double- fracture parameters are obtained from the well-known version of Fictitious Crack Model (FCM). FCM is developed for three standard specimens: three-point bend test, compact tension specimen and four-point bend test of size range 100–600 mm at relative size of initial crack length 0.3. The analysis of numerical results shows some interesting behaviour of double- fracture parameters.
Nonplanar ion-acoustic shocks in electron–positron–ion plasmas: Effect of superthermal electrons
Indian Academy of Sciences (India)
Deb Kumar Ghosh; Prasantha Chatterjee; Pankaj Kumar Mandal; Biswajit Sahu
2013-09-01
Ion-acoustic shock waves (IASWs) in a homogeneous unmagnetized plasma, comprising superthermal electrons, positrons, and singly charged adiabatically hot positive ions are investigated via two-dimensional nonplanar Kadomstev–Petviashvili–Burgers (KPB) equation. It is found that the profiles of the nonlinear shock structures depend on the superthermality of electrons. The influence of other plasma parameters such as, ion kinematic viscosity and ion temperature, is discussed in the presence of superthermal electrons in nonplanar geometry. It is also seen that the IASWs propagating in cylindrical/spherical geometry with transverse perturbation will be deformed as time goes on.
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
Change of manufacturing technique for the W7-X nonplanar coil cases
Energy Technology Data Exchange (ETDEWEB)
Gehring, M. E-mail: michael_gehring@bb-power.de; Schaefer, P.; Herrmann, K.D.; Scheller, H
2001-11-01
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.
T. Muka (Taulant); K. Trajanoska (Katerina); J.C. Kiefte-de Jong (Jessica); L. Oei (Ling); A.G. Uitterlinden (André); A. Hofman (Albert); A. Dehghan (Abbas); M.C. Zillikens (Carola); O.H. Franco (Oscar); F. Rivadeneira Ramirez (Fernando)
2015-01-01
textabstractThe association between metabolic syndrome (MS) and bone health remains unclear. We aimed to study the association between MS and hip bone geometry (HBG), femoral neck bone mineral density (FN-BMD), and the risk of osteoporosis and incident fractures. Data of 2040 women and 1510 men part
T. Muka (Taulant); K. Trajanoska (Katerina); J.C. Kiefte-de Jong (Jessica); L. Oei (Ling); A.G. Uitterlinden (André); A. Hofman (Albert); A. Dehghan (Abbas); M.C. Zillikens (Carola); O.H. Franco (Oscar); F. Rivadeneira Ramirez (Fernando)
2015-01-01
textabstractThe association between metabolic syndrome (MS) and bone health remains unclear. We aimed to study the association between MS and hip bone geometry (HBG), femoral neck bone mineral density (FN-BMD), and the risk of osteoporosis and incident fractures. Data of 2040 women and 1510 men part
Directory of Open Access Journals (Sweden)
N.Natarajan
2010-10-01
Full Text Available Modeling of solute transport through fractured rock is an important component of in many disciplines especially groundwater contamination and nuclear waste disposal. Several studies have been conducted on single rock fracture using parallel plate model and recently solute and thermal transport has been numerically modeled in the sinusoidal fracture matrix coupled system. The effect of linear sorption has been studied on the same. Results suggest the high matrix porosity and matrix diffusion coefficient enhance the sorption process and reduce the matrix diffusion of solutes. The velocity of the fluid reduces with increment in fracture aperture.
Nonplanar Ion-Acoustic Solitons in Electron-Positron-Ion Quantum Plasmas
Institute of Scientific and Technical Information of China (English)
S. A. Khan; S. Mahmood; Arshad M. Mirza
2009-01-01
@@ The propagation of nonplanar quantum ion-acoustic solitary waves in a dense, unmagnetized electron-positron-ion (e-p-i) plasma are studied by using the Korteweg-de Vries (KdV) model The quantum hydrodynamic (QHD) equations are used taking into account the quantum diffraction and quantum statistics corrections. The analytical and numerical solutions of KdV equation reveal that the nonplanar ion-acoustic solitons are modified significantly with quantum corrections and positron concentration, and behave differently in different geometries.
Energy Technology Data Exchange (ETDEWEB)
Faybishenko, Boris [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Doughty, Christine [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Steiger, Michael [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Long, Jane C.S. [Univ. of Nevada, Reno, NV (US). Mackay School of Mines; Wood, Tom [Parsons Engineering, Inc., Idaho Falls, ID (United States); Jacobsen, Janet [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lore, Jason [Stanford Univ., CA (United States); Zawislanski, Peter T. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
1999-03-01
A conceptual model of the geometry and physics of water flow in a fractured basalt vadose zone was developed based on the results of lithological studies and a series of ponded infiltration tests conducted at the Box Canyon site near the Idaho National Engineering and Environmental Laboratory (INEEL) in Idaho. The infiltration tests included one two-week test in 1996, three two-day tests in 1997, and one four-day test in 1997. For the various tests, initial infiltration rates ranged from 4.1 cm/day to 17.7 cm/day and then decreased with time, presumably due to mechanical or microbiological clogging of fractures and vesicularbasalt in the near-surface zone, as well as the effect of entrapped air. The subsurface moisture redistribution was monitored with tensiometers, neutron logging, time domain reflectrometry and ground penetrating radar. A conservative tracer, potassium bromide, was added to the pond water at a concentration of 3 g/L to monitor water flow with electrical resistivity probes and water sampling. Analysis of the data showed evidence of preferential flow rather than the propagation of a uniform wetting front. We propose a conceptual model describing the saturation-desaturation behavior of the basalt, in which rapid preferential flow through vertical column-bounding fractures occurs from the surface to the base of the basalt flow. After the rapid wetting of column-bounding fractures, a gradual wetting of other fractures and the basalt matrix occurs. Fractures that are saturated early in the tests may become desaturated thereafter, which we attribute to the redistribution of water between fractures and matrix. Lateral movement of water was also observed within a horizontal central fracture zone and rubble zone, which could have important implications for contaminant accumulation at contaminated sites.
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.
Azzola, Jérôme; Valley, Benoît; Schmittbuhl, Jean; Genter, Albert; Hehn, Régis
2017-04-01
In the Upper Rhine Graben, several deep geothermal projects based on the Enhanced Geothermal System (EGS) exploit local geothermal reservoirs. The principle underlying this technology consists of increasing the hydraulic performances of the reservoir by stimulating natural fractures using different methods, in order to extract hot water with commercially flow rates. In this domain, the knowledge of the in-situ stress state is of central importance to predict the response of the rock mass to stimulations. Here we characterized the stress tensor from Ultrasonic Borehole Imager (UBI) in the open hole section of the EGS doublet located in Rittershoffen, France (in the Upper Rhine Graben). Interestingly extensive logging programs were leaded at different key moments of the development of the injection well using hydraulic, thermal and chemical stimulation (Baujard et al., 2017)1. The time lapse UBI dataset consists of images of the injection well before, shortly and lastly after the stimulation. The geometry of the induced fractures in compression (breakouts) picked on the UBI images are used to determine the orientation of the in-situ stress tensor. The magnitude of the principal stresses is deduced from the drilling data. The magnitude of the maximum horizontal principal stress is evaluated using an inversion method with three failure criteria (Mohr-Coulomb, Mogi-Coulomb and modified Hoek-Brown criterion) and under the assumption of a vertical or a deviated well. Moreover, the characteristic of the dataset enables the analysis of the evolution of the borehole fracturing, as the deepening or widening of the induced fractures. The correlation of the UBI image allows firstly to determine the tool trajectory and to adapt the post and pre-stimulation images. It secondly leads to the estimation of a complete displacement field which characterizes the deformation induced by the stimulations. Even if the variable image quality deeply conditions the comparison, the considered
El-Tantawy, S. A.; Aboelenen, Tarek
2017-05-01
Planar and nonplanar (cylindrical and spherical) ion-acoustic super rogue waves in an unmagnetized electronegative plasma are investigated, both analytically (for planar geometry) and numerically (for planar and nonplanar geometries). Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonplanar/modified nonlinear Schrödinger equation (NLSE), which describes a slow modulation of the nonlinear wave amplitude. The local modulational instability of the ion-acoustic structures governed by the planar and nonplanar NLSE is reported. Furthermore, the existence region of rogue waves is strictly defined. The parameters used in our calculations are from the lab observation data. The local discontinuous Galerkin (LDG) method is used to find rogue wave solutions of the planar and nonplanar NLSE and to prove L2 stability of this method. Also, it is found that the numerical simulations and the exact (analytical) solutions of the planar NLSE match remarkably well and numerical examples show that the convergence orders of the proposed LDG method are N + 1 when polynomials of degree N are used. Moreover, it is noted that the spherical rogue waves travel faster than their cylindrical counterpart. Also, the numerical solution showed that the spherical and cylindrical amplitudes of the localized pulses decrease with the increase in the time | τ |.
Indian Academy of Sciences (India)
M AMINA; S A EMA; A A MAMUN
2017-06-01
A rigorous theoretical investigation has been carried out on the propagation of nonplanar (cylindrical and spherical) dust-acoustic shock waves (DASHWs) in a collisionless four-component unmagnetized dusty plasmasystem containing massive, micron-sized, positively and negatively charged inertial dust grains along with $q$ (nonextensive) distributed electrons and ions. The well-known reductive perturbation technique has been used to derive the modified Burgers equation (which describes the shock wave properties) and its numerical solution. It has been observed that the effects of charged dust grains of opposite polarity, nonextensivity of electrons and ions, and different dusty plasma parameters have significantly modified the fundamental properties (viz., polarity, amplitude, width, etc.) of the shock waves. The properties of DASHWs in nonplanar geometry are found tobe significantly different from those in one-dimensional planar geometry. The findings of our results from this theoretical investigation may be useful in understanding the nonlinear features of localized electrostatic disturbancesin both space and laboratory dusty plasmas.
Pourahmadian, Fatemeh; Haddar, Houssem
2016-01-01
A non-iterative waveform sensing approach is proposed toward (i) geometric reconstruction of penetrable fractures, and (ii) quantitative identification of their heterogeneous contact condition by seismic i.e. elastic waves. To this end, the fracture support $\\Gamma$ (which may be non-planar and unconnected) is first recovered without prior knowledge of the interfacial condition by way of the recently established approaches to non-iterative waveform tomography of heterogeneous fractures, e.g. the methods of generalized linear sampling and topological sensitivity. Given suitable approximation $\\breve\\Gamma$ of the fracture geometry, the jump in the displacement field across $\\breve\\Gamma$ i.e. the fracture opening displacement (FOD) profile is computed from remote sensory data via a regularized inversion of the boundary integral representation mapping the FOD to remote observations of the scattered field. Thus obtained FOD is then used as input for solving the traction boundary integral equation on $\\breve\\Gamm...
Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry
Vasoya, Manish; Rycroft, Chris H.; Bouchbinder, Eran
2016-08-01
Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass, and the notch radius ρ . Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation time scale τ0pl and an effective loading time scale τext(K˙ I,ρ ) , where K˙ I is the tensile stress-intensity-factor rate. The toughness is predicted to scale with √{ρ } independently of ξ ≡τext/τ0pl for ξ ≪1 , to scale as T √{ρ }log (ξ ) for ξ ≫1 (related to thermal activation, where T is the temperature), and to feature a nonmonotonic behavior in the crossover region ξ ˜O (1 ) (related to plastic yielding dynamics). These predictions are verified using 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of time-scale competition and far-from-steady-state elasto-viscoplastic dynamics for understanding the toughness and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented, and possible implications for applications are discussed.
Structural mechanisms of nonplanar hemes in proteins
Energy Technology Data Exchange (ETDEWEB)
Shelnutt, J.A.
1997-05-01
The objective is to assess the occurrence of nonplanar distortions of hemes and other tetrapyrroles in proteins and to determine the biological function of these distortions. Recently, these distortions were found by us to be conserved among proteins belonging to a functional class. Conservation of the conformation of the heme indicates a possible functional role. Researchers have suggested possible mechanisms by which heme distortions might influence biological properties; however, no heme distortion has yet been shown conclusively to participate in a structural mechanism of hemoprotein function. The specific aims of the proposed work are: (1) to characterize and quantify the distortions of the hemes in all of the more than 300 hemoprotein X-ray crystal structures in terms of displacements along the lowest-frequency normal coordinates, (2) to determine the structural features of the protein component that generate and control these nonplanar distortions by using spectroscopic studies and molecular-mechanics calculations for the native proteins, their mutants and heme-peptide fragments, and model porphyrins, (3) to determine spectroscopic markers for the various types of distortion, and, finally, (4) to discover the functional significance of the nonplanar distortions by correlating function with porphyrin conformation for proteins and model porphyrins.
NUMERICAL ANALYSIS OF THE NON-NEWTONIAN BLOOD FLOW IN THE NON-PLANAR ARTERY WITH BIFURCATION
Institute of Scientific and Technical Information of China (English)
CHEN Jie; LU Xi-yun; ZHUANG Li-xian; WANG Wen
2004-01-01
A numerical analysis of non-Newtonian fluid flow in non-planar artery with bifurcation was performed by using a finite element method to solve the three-dimensional Navier-Stokes equations coupled with the non-Newtonian constitutive models, including Carreau,Cross and Bingham models. The objective of this study is to investigate the effects of the non-Newtonian properties of blood as well as curvature and out-of-plane geometry in the non-planar daughter vessels on the velocity distribution and wall shear stress. The results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are of important in hemodynamics and play a significant role in vascular biology and pathophysiology.
Cinque, Russell; Komagata, Tadashi; Kiuchi, Taiichi; Browning, Clyde; Schiavone, Patrick; Petroni, Paolo; Martin, Luc; Quaglio, Thomas
2013-09-01
VSB mask writers, which create patterns using a combination of rectangles and 45 degree triangles, are ill-suited to non- Manhattan geometries. This issue is particularly acute for layouts which contain a large fraction of curvilinear "offangle" patterns such as photonic or DRAM designs. Unable to faithfully reproduce the "off-angle" structures, traditional VSB mask writers approximate the desired design using abutted rectangular shots or small shapes to smooth out line edge roughness. Fidelity to the original pattern comes at a cost of increased shot count and reduced throughput. Aselta has developed a novel fracture algorithm to dramatically reduce the shot count of such designs. Using a traditional VSB pattern generator, the new algorithm provides significant shot count reduction. When combined with a modified JBX-3200MV VSB, the shot count is reduced while maintaining the same level of fidelity. The data preparation software tool has also the capability of trading off a more accurate level of fidelity with an even more reduced shot count. The paper will first describe the basic principles of the fracturing algorithm and e-beam writer hardware configuration then demonstrate the advantage of the method on a variety of patterns.
Directory of Open Access Journals (Sweden)
Taulant Muka
Full Text Available The association between metabolic syndrome (MS and bone health remains unclear. We aimed to study the association between MS and hip bone geometry (HBG, femoral neck bone mineral density (FN-BMD, and the risk of osteoporosis and incident fractures. Data of 2040 women and 1510 men participants in the third visit (1997-1999 of the Rotterdam Study (RSI-3, a prospective population based cohort, were available (mean follow-up 6.7 years. MS was defined according to the recent harmonized definition. HBG parameters were measured at the third round visit whereas FN-BMD was assessed at the third round and 5 years later. Incident fractures were identified from medical registry data. After correcting for age, body mass index (BMI, lifestyle factors and medication use, individuals with MS had lower bone width (β = -0.054, P = 0.003, lower cortical buckling ratio (β = -0.81, P = 0.003 and lower odds of having osteoporosis (odds ratio =0.56, P = 0.007 in women but not in men. Similarly, MS was associated with higher FN-BMD only in women (β = 0.028, P=0.001. In the analyses of MS components, the glucose component (unrelated to diabetes status was positively associated with FN-BMD in both genders (β = 0.016, P = 0.01 for women and β = 0.022, P = 0.004 for men. In men, waist circumference was inversely associated with FN-BMD (β = -0.03, P = 0.004. No association was observed with fracture risk in either sex. In conclusion, women with MS had higher FN-BMD independent of BMI. The glucose component of MS was associated with high FN-BMD in both genders, highlighting the need to preserve glycemic control to prevent skeletal complications.
Muka, Taulant; Trajanoska, Katerina; Kiefte-de Jong, Jessica C.; Oei, Ling; Uitterlinden, André G; Hofman, Albert; Dehghan, Abbas; Zillikens, M. Carola; Franco, Oscar H.; Rivadeneira, Fernando
2015-01-01
The association between metabolic syndrome (MS) and bone health remains unclear. We aimed to study the association between MS and hip bone geometry (HBG), femoral neck bone mineral density (FN-BMD), and the risk of osteoporosis and incident fractures. Data of 2040 women and 1510 men participants in the third visit (1997–1999) of the Rotterdam Study (RSI-3), a prospective population based cohort, were available (mean follow-up 6.7 years). MS was defined according to the recent harmonized definition. HBG parameters were measured at the third round visit whereas FN-BMD was assessed at the third round and 5 years later. Incident fractures were identified from medical registry data. After correcting for age, body mass index (BMI), lifestyle factors and medication use, individuals with MS had lower bone width (β = -0.054, P = 0.003), lower cortical buckling ratio (β = -0.81, P = 0.003) and lower odds of having osteoporosis (odds ratio =0.56, P = 0.007) in women but not in men. Similarly, MS was associated with higher FN-BMD only in women (β = 0.028, P=0.001). In the analyses of MS components, the glucose component (unrelated to diabetes status) was positively associated with FN-BMD in both genders (β = 0.016, P = 0.01 for women and β = 0.022, P = 0.004 for men). In men, waist circumference was inversely associated with FN-BMD (β = -0.03, P = 0.004). No association was observed with fracture risk in either sex. In conclusion, women with MS had higher FN-BMD independent of BMI. The glucose component of MS was associated with high FN-BMD in both genders, highlighting the need to preserve glycemic control to prevent skeletal complications. PMID:26066649
Kavanagh, J. L.; Rogers, B. D.; Boutelier, D.; Cruden, A. R.
2017-02-01
Analogue experiments using gelatine were carried out to investigate the role of the mechanical properties of rock layers and their bonded interfaces on the formation and propagation of magma-filled fractures in the crust. Water was injected at controlled flux through the base of a clear-Perspex tank into superposed and variably bonded layers of solidified gelatine. Experimental dykes and sills were formed, as well as dyke-sill hybrid structures where the ascending dyke crosses the interface between layers but also intrudes it to form a sill. Stress evolution in the gelatine was visualised using polarised light as the intrusions grew, and its evolving strain was measured using digital image correlation (DIC). During the formation of dyke-sill hybrids there are notable decreases in stress and strain near the dyke as sills form, which is attributed to a pressure decrease within the intrusive network. Additional fluid is extracted from the open dykes to help grow the sills, causing the dyke protrusion in the overlying layer to be almost completely drained. Scaling laws and the geometry of the propagating sill suggest sill growth into the interface was toughness-dominated rather than viscosity-dominated. We define KIc* as the fracture toughness of the interface between layers relative to the lower gelatine layer KIcInt / KIcG. Our results show that KIc* influences the type of intrusion formed (dyke, sill or hybrid), and the magnitude of KIcInt impacted the growth rate of the sills. KIcInt was determined during setup of the experiment by controlling the temperature of the upper layer Tm when it was poured into place, with Tm < 24 °C resulting in an interface with relatively low fracture toughness that is favourable for sill or dyke-sill hybrid formation. The experiments help to explain the dominance of dykes and sills in the rock record, compared to intermediate hybrid structures.
Elementary framework for cold field emission from quantum-confined, non-planar emitters
Energy Technology Data Exchange (ETDEWEB)
Patterson, A. A., E-mail: apatters@mit.edu; Akinwande, A. I. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA and Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-05-07
For suitably small field emitters, the effects of quantum confinement at the emitter tip may have a significant impact on the emitter performance and total emitted current density (ECD). Since the geometry of a quantum system uniquely determines the magnitude and distribution of its energy levels, a framework for deriving ECD equations from cold field electron emitters of arbitrary geometry and dimensionality is developed. In the interest of obtaining semi-analytical ECD equations, the framework is recast in terms of plane wave solutions to the Schrödinger equation via the use of the Jeffreys-Wentzel-Kramers-Brillouin approximation. To demonstrate the framework's consistency with our previous work and its capabilities in treating emitters with non-planar geometries, ECD equations were derived for the normally unconfined cylindrical nanowire (CNW) and normally confined (NC) CNW emitter geometries. As a function of the emitter radius, the NC CNW emitter ECD profile displayed a strong dependence on the Fermi energy and had an average ECD that exceeded the Fowler-Nordheim equation for typical values of the Fermi energy due to closely spaced, singly degenerate energy levels (excluding electron spin), comparatively large electron supply values, and the lack of a transverse, zero-point energy. Such characteristics suggest that emitters with non-planar geometries may be ideal for emission from both an electron supply and electrostatics perspective.
Aggelis, D. G.; Blom, J.; El Kadi, M.; Wastiels, J.
2014-03-01
In this work the flexural behavior of textile reinforced cement (TRC) laminate is examined using acoustic emission (AE). The TRC composite is a combination of inorganic phosphate cement (IPC) with randomly distributed glass fibres. IPC has been developed at the "Vrije Universiteit Brussel" and shows a neutral pH meaning that glass fibers are hardly attacked. During bending, stresses lead to the activation of damage mechanisms like matrix cracking, delaminations and fiber pull-out being in succession or overlapping in time. AE records the responses of the damage propagation events and allows the monitoring of the fracture behavior from the onset to the final stage. The effect of the span in three-point bending tests, which is varied to create different stress fields, is targeted. Parameters like duration and frequency reveal information about the mode of the damage sources in relation to the span. Results show that as the span decreases, the dominant damage mode shifts away from bending and acquires more shear characteristics by increasing the interlaminar shearing events.
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...
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamidreza M.
2016-10-01
Aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs. This uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical and diagenetic processes that control aperture. In the absence of cement bridges and high pore pressure, fractures in the subsurface are generally considered to be closed. However, experimental work, outcrop analyses and subsurface data show that some fractures remain open, and that aperture varies even along a single fracture. However, most fracture flow models consider constant apertures for fractures. We create a stress-dependent heterogeneous aperture by combining Finite Element modeling of discrete fracture networks with an empirical aperture model. Using a modeling approach that considers fractures 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 σ1 has a controlling impact on aperture and permeability, where hydraulic opening is maximum for an angle of 15°. At this angle, the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress. Averaging the heterogeneous aperture to scale up permeability probably results in an underestimation of flow, indicating the need to incorporate full aperture distributions rather than simplified aperture models in reservoir-scale flow models.
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
Non-planar microfabricated gas chromatography column
Lewis, Patrick R.; Wheeler, David R.
2007-09-25
A non-planar microfabricated gas chromatography column comprises a planar substrate having a plurality of through holes, a top lid and a bottom lid bonded to opposite surfaces of the planar substrate, and inlet and outlet ports for injection of a sample gas and elution of separated analytes. A plurality of such planar substrates can be aligned and stacked to provide a longer column length having a small footprint. Furthermore, two or more separate channels can enable multi-channel or multi-dimensional gas chromatography. The through holes preferably have a circular cross section and can be coated with a stationary phase material or packed with a porous packing material. Importantly, uniform stationary phase coatings can be obtained and band broadening can be minimized with the circular channels. A heating or cooling element can be disposed on at least one of the lids to enable temperature programming of the column.
Higher Loop Nonplanar Anomalous Dimensions from Symmetry
Koch, Robert de Mello; Messamah, Ilies
2013-01-01
In this article we study the action of the one loop dilatation operator on operators with a classical dimension of order N. These operators belong to the su(2) sector and are constructed using two complex fields Y and Z. For these operators non-planar diagrams contribute already at the leading order in N and the planar and large N limits are distinct. The action of the one loop and the two loop dilatation operator reduces to a set of decoupled oscillators and factorizes into an action on the Z fields and an action on the Y fields. Direct computation has shown that the action on the Y fields is the same at one and two loops. In this article, using the su(2) symmetry algebra as well as structural features of field theory, we give compelling evidence that the factor in the dilatation operator that acts on the Ys is given by the one loop expression, at any loop order.
Energy Technology Data Exchange (ETDEWEB)
Sokolov, Mikhail A. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Nanstad, Randy K. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2016-09-01
Small specimens are playing the key role in evaluating properties of irradiated materials. The use of small specimens provides several advantages. Typically, only a small volume of material can be irradiated in a reactor at desirable conditions in terms of temperature, neutron flux, and neutron dose. A small volume of irradiated material may also allow for easier handling of specimens. Smaller specimens reduce the amount of radioactive material, minimizing personnel exposures and waste disposal. However, use of small specimens imposes a variety of challenges as well. These challenges are associated with proper accounting for size effects and transferability of small specimen data to the real structures of interest. Any fracture toughness specimen that can be made out of the broken halves of standard Charpy specimens may have exceptional utility for evaluation of reactor pressure vessels (RPVs) since it would allow one to determine and monitor directly actual fracture toughness instead of requiring indirect predictions using correlations established with impact data. The Charpy V-notch specimen is the most commonly used specimen geometry in surveillance programs. Assessment and validation of mini-CT specimen geometry has been performed on previously well characterized HSST Plate 13B, an A533B class 1 steel. It was shown that the fracture toughness transition temperature measured by these Mini-CT specimens is within the range of To values that were derived from various large fracture toughness specimens. Moreover, the scatter of the fracture toughness values measured by Mini-CT specimens perfectly follows the Weibull distribution function providing additional proof for validation of this geometry for the Master Curve evaluation of rector pressure vessel steels. Moreover, the International collaborative program has been developed to extend the assessment and validation efforts to irradiated weld metal. The program is underway and involves ORNL, CRIEPI, and EPRI.
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
Aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs. This uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical...... 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...... and permeability, where hydraulic opening is maximum for an angle of 15°. At this angle, the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress. Averaging the heterogeneous aperture to scale up...
Nanopatterning planar and non-planar mold surfaces for a polymer replication
DEFF Research Database (Denmark)
Cech, Jiri; Pranov, Henrik; Kofod, Guggi;
2013-01-01
, freestanding nickel foil with a reversed pattern. This foil is then used either as a direct master for polymer replication or as a master for an extremely high pressure embossing of such master onto a metallic injection mold cavity surface coated with special coating, which, when cured, forms robust and hard......, glass-like material. We have demonstrated nanopattern transfer on both planar and non-planar geometries and our nanopatterned mold coating can sustain more than 10.000 injection molding cycles. We can coat our nanopatterned mold surfaces with a monolayer of perfluorosilane to further reduce surface...
Mamun, A A; Shukla, P K
2009-09-01
Effects of the nonthermal distribution of electrons as well as the polarity of the net dust-charge number density on nonplanar (viz. cylindrical and spherical) dust-ion-acoustic solitary waves (DIASWs) are investigated by employing the reductive perturbation method. It is found that the basic features of the DIASWs are significantly modified by the effects of nonthermal electron distribution, polarity of net dust-charge number density, and nonplanar geometry. The implications of our results in some space and laboratory dusty plasma environments are briefly discussed.
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)
Analytical Modeling and Contradictions in Limestone Reservoirs: Breccias, Vugs, and Fractures
Directory of Open Access Journals (Sweden)
Nelson Barros-Galvis
2015-01-01
Full Text Available Modeling of limestone reservoirs is traditionally developed applying tectonic fractures concepts or planar discontinuities and has been simulated dynamically without considering nonplanar discontinuities as sedimentary breccias, vugs, fault breccias, and impact breccias, assuming that all these nonplanar discontinuities are tectonic fractures, causing confusion and contradictions in reservoirs characterization. The differences in geometry and connectivity in each discontinuity affect fluid flow, generating the challenge to develop specific analytical models that describe quantitatively hydrodynamic behavior in breccias, vugs, and fractures, focusing on oil flow in limestone reservoirs. This paper demonstrates the differences between types of discontinuities that affect limestone reservoirs and recommends that all discontinuities should be included in simulation and static-dynamic characterization, because they impact fluid flow. To demonstrate these differences, different analytic models are developed. Findings of this work are based on observations of cores, outcrops, and tomography and are validated with field data. The explanations and mathematical modeling developed here could be used as diagnostic tools to predict fluid velocity and fluid flow in limestone reservoirs, improving the complex reservoirs static-dynamic characterization.
Nonplanar ion-acoustic solitons collision in Xe+-F-- SF6- and Ar+-F-- SF6- plasmas
El-Tantawy, S. A.; Carbonaro, P.
2016-04-01
The solitons collision in nonplanar (cylindrical and spherical) plasmas consisting of positive ions, two different negative ions, and isothermal electrons is studied. For this purpose, the Poincaré-Lighthill-Kuo (PLK) method is used to obtain two-coupled nonplanar Korteweg-de Vries (nKdV) equations. Also, the nonplanar phase shifts are calculated. The physical parameters of two plasma experiments; namely Xe+-F-- SF6- and Ar+-F-- SF6- are used to examine the properties of the localized pulses and their phase shifts after collision. It is found that the present model gives rise to the propagation of positive and negative pulses. The effects of the total negative ions concentration, the density ratio of the second-negative ions, the temperature ratio, and the geometrical effects on the behavior of solitons collisions and their phase shifts are investigated. Furthermore, it is found that the phase shifts in the case of the Ar+-F-- SF6- plasma are much larger than those of the Xe+-F-- SF6- plasma. Also, for fixed plasma parameters, the solitons collision received the largest phase shift in spherical geometry, followed by the cylindrical and planar geometries.
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.
Nonplanar loops leave the Veneziano model photon massless
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.
Nonplanar loops leave the Veneziano model photon massless
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.
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.
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...... of the active material, the cross-sectional geometry was observed by field emission scanning electron microscopy and scanning transmission electron microscopy. The optical properties were carried out at room temperature using micro-photoluminescence setup. The results showed different deposition rates...... for openings oriented along [0-11] and [0-1-1] directions with higher rate along [0-1-1]. The fabricated active material was incorporated into photonic crystal waveguides....
Energy Technology Data Exchange (ETDEWEB)
Uddin, M. J., E-mail: josim.phys2007@gmail.com; Alam, M. S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-02-15
Nonplanar (cylindrical and spherical) positron-acoustic (PA) Gardner solitary waves (SWs) in an unmagnetized plasma system consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated. The modified Gardner equation is derived by using the reductive perturbation technique. The effects of cylindrical and spherical geometries, superthermal parameter of hot positrons and electrons, relative temperature ratios, and relative number density ratios on the PA Gardner SWs are studied by using the numerical simulations. The implications of our results in various space and laboratory plasma environments are briefly discussed.
Study of nonplanarity of peptide bond using theoretical calculations.
Selvarengan, P; Kolandaivel, P
2005-08-01
The conformational dependence of nonplanarity of the peptide bond of formylglycinamide has been studied using ab initio and density functional theory methods. Hartree-Fock self-consistent field theory (HF), Møller-Plesset perturbation theory (MP2) of ab initio and B3LYP level of theory of dft method have been used employing 6-31++G** basis set. The MP2 method predicts better results than HF and B3LYP levels of theory for conformational stability dependence of nonplanarity. Systematic dependence of planarity deviation has been observed in MP2 theory. The chemical hardness values successfully predict the conformational region, but fail to obey maximum hardness principle. It is concluded that the most reliable dft method could not successfully predict the planarity of peptide bond in comparison with electron correlated method of ab initio method.
Application of Random Ferns for non-planar object detection
Mastov, Alexey; Konovalenko, Ivan; Grigoryev, Anton
2015-12-01
The real time object detection task is considered as a part of a project devoted to development of autonomous ground robot. This problem has been successfully solved with Random Ferns algorithm, which belongs to keypoint-based method and uses fast machine learning algorithms for keypoint matching step. As objects in the real world are not always planar, in this article we describe experiments of applying this algorithm for non-planar objects. Also we introduce a method for fast detection of a special class of non-planar objects | those which can be decomposed into planar parts (e.g. faces of a box). This decomposition needs one detector for each side, which may significantly affect speed of detection. Proposed approach copes with it by omitting repeated steps for each detector and organizing special queue of detectors. It makes the algorithm three times faster than naive one.
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.
Dynamics of rotationally fissioned asteroids: non-planar case
Boldrin, L. A. G.; Scheeres, D. J.; Winter, O. C.
2016-10-01
The rotational fission of asteroids has been studied previously with simplified models restricted to planar motion. However, the observed physical configuration of contact binaries leads one to conclude that most of them are not in a planar configuration and hence would not be restricted to planar motion once they undergo rotational fission. This motivated a study of the evolution of initially non-planar binaries created by fission. Using a two-ellipsoid model, we performed simulations taking only gravitational interactions between components into account. We simulate 91 different initial inclinations of the equator of the secondary body for 19 different mass ratios. After disruption, the binary system dynamics are chaotic, as predicted from theory. Starting the system in a non-planar configuration leads to a larger energy and enhanced coupling between the rotation state of the smaller fissioned body and the evolving orbital system, and enables re-impact to occur. This leads to differences with previous planar studies, with collisions and secondary spin fission occurring for all mass ratios with inclinations θ0 ≥ 40o, and mimics a Lidov-Kozai mechanism. Out of 1729 studied cases, we found that ˜14 per cent result in secondary fission, ˜25 per cent result in collisions and ˜6 per cent have lifetimes longer than 200 yr. In Jacobson & Scheeres stable binaries only formed in cases with mass ratios q system should start in a non-planar configuration.
Longitudinal mode structure in a non-planar ring resonator
Directory of Open Access Journals (Sweden)
M Jaberi
2013-09-01
Full Text Available The structure of longitudinal modes of a passively Q-switched, non-planar unidirectional ring-resonator,with Nd:YAG active medium is described in this article. Two different techniques are used to study the longitudinal mode structure of the laser resonator. At first, the fast-fourier transform technique is applied for analyzing the mode beating of the optical fields by intensity frequency structure of the laser pulses to determine the number of longitudinal modes. Then, an analyzer etalon is used to observe Fabry-Perot fringes to compute the numbers of the resonator longitudinal modes. The results of two techniques are in good agreement with each other. Under the proper conditions, a reliable single longitudinal mode of the non-planar ring-resonator can be achieved with a good spatial mode profile that originates from the unidirectional travelling optical field propagation in the resonator having a very low sensitivity of the non-planar ring resonator to the optical elements misalignment.
A generalized Beraha conjecture for non-planar graphs
Energy Technology Data Exchange (ETDEWEB)
Jacobsen, Jesper Lykke, E-mail: jesper.jacobsen@ens.fr [Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris (France); Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris (France); Salas, Jesús, E-mail: jsalas@math.uc3m.es [Grupo de Modelización, Simulación Numérica y Matemática Industrial, Universidad Carlos III de Madrid, Avda. de la Universidad, 30, 28911 Leganés (Spain); Grupo de Teorías de Campos y Física Estadística, Instituto Gregorio Millán, Universidad Carlos III de Madrid, Unidad Asociada al IEM–CSIC, Madrid (Spain)
2013-10-21
We study the partition function Z{sub G(nk,k)}(Q,v) of the Q-state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its zeros in the plane (Q,v) for 1⩽k⩽7. We also consider two specializations of Z{sub G(nk,k)}, namely the chromatic polynomial P{sub G(nk,k)}(Q) (corresponding to v=−1), and the flow polynomial Φ{sub G(nk,k)}(Q) (corresponding to v=−Q). In these two cases, we study their zeros in the complex Q-plane for 1⩽k⩽7. We pay special attention to the accumulation loci of the corresponding zeros when n→∞. We observe that the Berker–Kadanoff phase that is present in two-dimensional Potts models, also exists for non-planar recursive graphs. Their qualitative features are the same; but the main difference is that the role played by the Beraha numbers for planar graphs is now played by the non-negative integers for non-planar graphs. At these integer values of Q, there are massive eigenvalue cancellations, in the same way as the eigenvalue cancellations that happen at the Beraha numbers for planar graphs.
Geometry from Information Geometry
Caticha, Ariel
2015-01-01
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
Physisorbed Films on Planar and Nonplanar Surfaces.
Cheng, E.
1990-01-01
In the case of multilayer liquid films on planar surfaces, we found that the widely used Frenkel-Halsey -Hill theory is the leading term of a many-body expansion of the more general Dzyaloshinskii-Lifshitz-Pitaevskii theory in the nonretardation limit. While the FHH theory is a good approximation in the thin film region, retardation has been shown to be important at thickness d >=q 100 A. A universal behavior of the retardation has also been found. Submonolayer He film on weak-binding substrate surfaces have been found to have unexpected and exciting new features. The weak binding of the substrate potential supports only low density monolayer He films so that the monolayer He solid can be eliminated. Meanwhile, the z -wise delocalization of He atoms reduces the He-He interaction and the lateral binding. It is possible that the 2D liquid film will be eliminated as well and a quasi-2D bose gas is expected. A further possibility is that no He monolayer film at all will be present on a weak-binding substrate. The possibility of using the fractal geometry to describe (global) surface roughness has been investigated. A power-law relation between the coverage and thickness is found on a fractally rough surface, with its exponent determined by the surface fractal dimension. A new and interesting phenomenon has been found: the adsorbed film "defractalizes" the substrate surface; this is observable by small angle x-ray and neutron scattering measurements. Adsorption inside a cylindrical pore and near an oblique corner have also been discussed.
Integrable system on phase space with nonplanar metrics
Bogdanov, E I
2001-01-01
The problem on the integrability of the evolution system on the phase spaces with the nonplanar metrics is studied. It is shown that in the case, when the phase space is a sphere, the system Hamiltonians are generated under the action of the Poisson operators on the variations of the phase space geodesic lines and the problem on the evolution system integrability is reduced to the task on the integrability of the repers motion equations on the phase space. The bihamiltonian representation of the evaluation systems is connected with the differential-geometric properties of the phase space
Seismic determination of saturation in fractured reservoirs
Brown, R.L.; Wiggins, M.L.; Gupta, A.
2002-01-01
Detecting the saturation of a fractured reservoir using shear waves is possible when the fractures have a geometry that induces a component of movement perpendicular to the fractures. When such geometry is present, vertically traveling shear waves can be used to examine the saturation of the fractured reservoir. Tilted, corrugated, and saw-tooth fracture models are potential examples.
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...
Banerjee, Sourav; Kundu, Tribikram
2008-03-01
Multilayered solid structures made of isotropic, transversely isotropic, or general anisotropic materials are frequently used in aerospace, mechanical, and civil structures. Ultrasonic fields developed in such structures by finite size transducers simulating actual experiments in laboratories or in the field have not been rigorously studied. Several attempts to compute the ultrasonic field inside solid media have been made based on approximate paraxial methods like the classical ray tracing and multi-Gaussian beam models. These approximate methods have several limitations. A new semianalytical method is adopted in this article to model elastic wave field in multilayered solid structures with planar or nonplanar interfaces generated by finite size transducers. A general formulation good for both isotropic and anisotropic solids is presented in this article. A variety of conditions have been incorporated in the formulation including irregularities at the interfaces. The method presented here requires frequency domain displacement and stress Green's functions. Due to the presence of different materials in the problem geometry various elastodynamic Green's functions for different materials are used in the formulation. Expressions of displacement and stress Green's functions for isotropic and anisotropic solids as well as for the fluid media are presented. Computed results are verified by checking the stress and displacement continuity conditions across the interface of two different solids of a bimetal plate and investigating if the results for a corrugated plate with very small corrugation match with the flat plate results.
Institute of Scientific and Technical Information of China (English)
侯冰; 谭鹏; 陈勉; 袁亮; 熊振宇; 许超兰
2016-01-01
Large-scale hydraulic fracturing technology is significant in the development of compact limestone reservoirs with low porosity and low permeability. The diagenesis, mineral composition and mechanical properties of the compact limestone reservoirs are greatly different from those of the compact sandstone ones. Hydraulic fracture geometry is complicated under different stress states and construction conditions. Based on the hydraulic fracturing simulation experiments on compact limestone outcrops carried out by using a true triaxial test system, the effects of multiple factors on fracture propagating laws of horizontal well in compact limestone are studied. The results show that hydraulic fractures likely interact with natural ones when the horizontal stress difference ranges from 2 to 8 MPa. A higher fracturing fluid viscosity reduces the possibility of shearing slip and filtration expansion of the natural fractures, forming a relatively less complex fracture network. Under the strike-slip fault stress state (HVhσ>σ>σ), the horizontal hydraulic fracture can be easily generated and propagates along the bedding plane, especially when the direction of borehole is parallel to the bedding plane. The fracturing with variable pump rates can reactivate more natural fractures, forming a more complicated fracture network. Acidizing treatment for openhole section can significantly reduce the fracture pressure, and the decrease range of fracture pressure gradually increases with the increase of acidizing treatment time. This study may provide a reference for field fracturing treatment.%开发低孔、低渗的致密灰岩储层需要进行大规模的水力压裂。致密灰岩的成岩过程、矿物组成以及岩石力学性质与致密砂岩等储层差异很大，在不同应力状态以及施工参数条件下水力裂缝扩展形态有待研究。采用真三轴水力压裂试验系统对致密灰岩露头展开压裂物模试验，研究地应力差、压裂液黏
Episodic slow slip events in a non-planar subduction fault model for northern Cascadia
Li, D.; Liu, Y.; Matsuzawa, T.; Shibazaki, B.
2014-12-01
Episodic tremor and slow slip (ETS) events have been detected along the Cascadia margin, as well as many other subduction zones, by increasingly dense seismic and geodetic networks over the past decade. In northern Cascadia, ETS events arise on the thrust fault interface of 30~50 km depth, coincident with metamorphic dehydration of the subducting oceanic slab around temperatures of 350. Previous numerical simulations (e.g., Liu and Rice 2007) suggested that near-lithostatic pore pressure in the rate-state friction stability transition zone could give rise to slow slip events (SSE) down-dip of the seismogenic zone, which provides a plausible physical mechanism for these phenomena. Here we present a 3-D numerical simulation of inter-seismic SSEs based on the rate- and state- friction law, incorporating a non-planar, realistic northern Cascadia slab geometry compiled by McCrory et al. (2012) using triangular dislocation elements. Preliminary results show that the width and pore pressure level of the transition zone can remarkably affect the recurrence of SSEs. With effective normal stress of ~1-2 MPa and characteristic slip distance of ~1.4 mm, inter-seismic SSEs can arise about every year. The duration of each event is about 2~3 weeks, with the propagating speed along strike in the range of km/day. Furthermore, the slab bending beneath southern Vancouver Island and northern Washington State appears to accelerate the along-strike propagation of SSEs. Our next step is to constrain the rate-state frictional properties using geodetic inversion of SSE slip and inter-SSE plate coupling from the Plate Boundary Observatory (PBO) GPS measurements. Incorporating the realistic fault geometry into a physics model constrained by geodetic data will enable us to transition from a conceptual towards a quantitative and predictive understanding of SSEs mechanism.
Comparative studies of the effect of polycyclic aromatic hydrocarbon geometry on the hydrolysis of diol epoxides The interaction of the diol epoxides (DEs) of both planar and non-planar PAHs with water have been examined using quantum mechanical and molecular dynamics. Th...
Ritz, E.; Pollard, D. D.
2011-12-01
Geological and geophysical investigations demonstrate that faults are geometrically complex structures, and that the nature and intensity of off-fault damage is spatially correlated with geometric irregularities of the slip surfaces. Geologic observations of exhumed meter-scale strike-slip faults in the Bear Creek drainage, central Sierra Nevada, CA, provide insight into the relationship between non-planar fault geometry and frictional slip at depth. We investigate natural fault geometries in an otherwise homogeneous and isotropic elastic material with a two-dimensional displacement discontinuity method (DDM). Although the DDM is a powerful tool, frictional contact problems are beyond the scope of the elementary implementation because it allows interpenetration of the crack surfaces. By incorporating a complementarity algorithm, we are able to enforce appropriate contact boundary conditions along the model faults and include variable friction and frictional strength. This tool allows us to model quasi-static slip on non-planar faults and the resulting deformation of the surrounding rock. Both field observations and numerical investigations indicate that sliding along geometrically discontinuous or irregular faults may lead to opening of the fault and the formation of new fractures, affecting permeability in the nearby rock mass and consequently impacting pore fluid pressure. Numerical simulations of natural fault geometries provide local stress fields that are correlated to the style and spatial distribution of off-fault damage. We also show how varying the friction and frictional strength along the model faults affects slip surface behavior and consequently influences the stress distributions in the adjacent material.
Rathbun, Alan M; Shardell, Michelle; Orwig, Denise; Hebel, J Richard; Hicks, Gregory E; Beck, Thomas J; Magaziner, Jay; Hochberg, Marc C
2016-11-01
Prior studies have shown that women have declines in bone structure and strength after hip fracture, but it is unclear whether men sustain similar changes. Therefore, the objective was to examine sex differences in proximal femur geometry following hip fracture. Hip structural analysis was used to derive metrics of bone structure and strength: aerial bone mineral density, cross-sectional bone area (CSA), cortical outer diameter, section modulus (SM), and buckling ratio (BR) from dual-energy x-ray absorptiometry scans performed at baseline (within 22days of hospital admission), two, six, or twelve months after hip fracture in men and women (n=282) enrolled in the Baltimore Hip Studies 7th cohort. Weighted estimating equations were used to evaluate sex differences at the narrow neck (NN), intertrochanteric (IT), and femoral shaft (FS). Men had significantly different one year NN changes compared to women in CSA: -6.33% (-12.47, -0.20) vs. 1.37% (-3.31, 6.43), P=0.049; SM: -4.98% (-11.08, 1.10) vs. 3.94% (-2.51, 10.42), P=0.042; and BR: 7.50% (0.65, 14.36) vs. -1.20% (-6.41, 4.00), P=0.044. One year IT changes displayed similar patterns, but the sex differences were not statistically significant for CSA: -4.07% (-10.83, 2.67) vs. 0.41% (-3.41, 4.24), P=0.252; SM: -4.78% (-12.10, 5.53) vs. -0.31 (-4.74, 4.11), P=0.287; and BR: 4.59% (-0.65, 9.84) vs. 1.52% (-4.23, 7.28), P=0.425. Differences in FS geometric parameters were even smaller in magnitude and not significantly different by sex. Women generally experienced non-significant increases in bone tissue and strength following hip fracture, while men had structural declines that were statistically greater at the NN region. Reductions in the mechanical strength of the proximal femur after hip fracture could put men at higher risk for subsequent fractures of the contralateral hip. Copyright © 2016 Elsevier Inc. All rights reserved.
Multi-projector auto-calibration and placement optimization for non-planar surfaces
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.
Energy Technology Data Exchange (ETDEWEB)
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Fabrication method for small-scale structures with non-planar features
Energy Technology Data Exchange (ETDEWEB)
Burckel, David Bruce; Ten Eyck, Gregory A.
2016-09-20
The fabrication of small-scale structures is disclosed. A unit-cell of a small-scale structure with non-planar features is fabricated by forming a membrane on a suitable material. A pattern is formed in the membrane and a portion of the substrate underneath the membrane is removed to form a cavity. Resonators are then directionally deposited on the wall or sides of the cavity. The cavity may be rotated during deposition to form closed-loop resonators. The resonators may be non-planar. The unit-cells can be formed in a layer that includes an array of unit-cells.
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.
Hydraulic fracture propagation modeling and data-based fracture identification
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
Directory of Open Access Journals (Sweden)
Omid Arjmandi-Tash
2012-12-01
Full Text Available Introduction: Atherosclerosis is a focal disease that susceptibly forms near bifurcations, anastomotic joints, side branches, and curved vessels along the arterial tree. In this study, pulsatile blood flow in a bifurcation model with a non-planar branch is investigated. Methods: Wall shear stress (WSS distributions along generating lines on vessels for different bifurcation angles are calculated during the pulse cycle. Results: The WSS at the outer side of the bifurcation plane vanishes especially for higher bifurcation angles but by increasing the bifurcation angle low WSS region squeezes. At the systolic phase there is a high possibility of formation of a separation region at the outer side of bifurcation plane for all the cases. WSS peaks exist on the inner side of bifurcation plane near the entry section of daughter vessels and these peaks drop as bifurcation angle is increased. Conclusion: It was found that non-planarity of the daughter vessel lowers the minimum WSS at the outer side of the bifurcation and increases the maximum WSS at the inner side. So it seems that the formation of atherosclerotic plaques at bifurcation region in direction of non-planar daughter vessel is more risky.
Beam model for non-planar orbits in synchrotrons
Energy Technology Data Exchange (ETDEWEB)
Month, M.
1984-03-26
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.
Static aeroelastic analysis of very flexible wings based on non-planar vortex lattice method
Institute of Scientific and Technical Information of China (English)
Xie Changchuan; Wang Libo; Yang Chao; Liu Yi
2013-01-01
A rapid and efficient method for static aeroelastic analysis of a flexible slender wing when considering the structural geometric nonlinearity has been developed in this paper.A non-planar vortex lattice method herein is used to compute the non-planar aerodynamics of flexible wings with large deformation.The finite element method is introduced for structural nonlinear statics analysis.The surface spline method is used for structure/aerodynamics coupling.The static aeroelastic characteristics of the wind tunnel model of a flexible wing are studied by the nonlinear method presented,and the nonlinear method is also evaluated by comparing the results with those obtained from two other methods and the wind tunnel test.The results indicate that the traditional linear method of static aeroelastic analysis is not applicable for cases with large deformation because it produces results that are not realistic.However,the nonlinear methodology,which involves combining the structure finite element method with the non-planar vortex lattice method,could be used to solve the aeroelastic deformation with considerable accuracy,which is in fair agreement with the test results.Moreover,the nonlinear finite element method could consider complex structures.The non-planar vortex lattice method has advantages in both the computational accuracy and efficiency.Consequently,the nonlinear method presented is suitable for the rapid and efficient analysis requirements of engineering practice.It could be used in the preliminary stage and also in the detailed stage of aircraft design.
Non-planar Feynman diagrams and Mellin-Barnes representations with AMBRE 3.0
Energy Technology Data Exchange (ETDEWEB)
Dubovyk, Ievgen [Institute of Electrophysics and Radiation Technologies, Kharkiv (Ukraine); Gluza, Janusz [Univ. of Silesia, Katowice (Poland). Inst. of Physics; Riemann, Tord
2016-04-15
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.
Structural templating in a nonplanar phthalocyanine using single crystal copper iodide
Rochford, L. A. (Luke A.); Ramadan, Alexandra J.; Keeble, Dean S.; Ryan, Mary P.; Heutz, Sandrine; Jones, T 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.
Temporal analysis of the coherent properties of optical images of rough nonplanar objects
Mandrosov, V. I.
2009-01-01
The possibility of using temporal analysis to find the relation between chromatic properties of probe radiation and coherent properties of the optical images of rough non-planar objects is substantiated. The analysis is based on the use of the time correlation function and on the study of the speckl
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
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
Bistatic SAR coherence over non-planar topographies
Andre, Daniel B.; Morrison, Keith
2012-05-01
Monostatic Synthetic Aperture Radar (SAR) Coherent Change Detection (CCD) has been found to be of great utility in detecting changes that occur on the ground. Detectable changes of interest include vehicle tracks and water flow. The CCD procedure involves performing repeat pass radar collections, to form a coherence product, where ground disturbances can induce detectable incoherence. However there is usually a difference in the radar collection geometry which can lead to incoherent energy noise entering the CCD, which reduces the detectability of tracks. When sensing flat terrain, the incoherence due to collection geometry difference can be removed through a conventional Fourier image support trimming process. However, it has been found that when the terrain contains non-flat topography, the optimal trimming process is substantially more involved, so much so that a new per-pixel SAR back-projection imaging algorithm has been developed. This algorithm trims off incoherent energy on a per-pixel basis according to the local topography. In order to validate the bistatic SAR generalization to the monostatic per-pixel formalism and algorithm, bistatic change detection measurements were conducted with the GB-SAR system, and these are reported here.
Non-planar vibrations of a string in the presence of a boundary obstacle
Singh, Harkirat; Wahi, Pankaj
2017-02-01
We analyze planar and non-planar motions of a string vibrating against a unilateral curved obstacle. Our model incorporates the change in tension due to stretching of the string, which introduces nonlinear coupling between motions in mutually perpendicular directions, as well as the wrapping nonlinearity due to the presence of the obstacle. The system of equations has been discretized by assuming functional form of the displacements which satisfies all the geometrical boundary conditions. This discretized system is then used to investigate the various motions possible both in the absence as well as the presence of the obstacle. In the absence of the obstacle, there are infinitely many planar and two non-planar motions viz. a circular trajectory and a precessing elliptical trajectory for a fixed magnitude of the disturbance. In contrast, the string has only one planar motion when the obstacle is present and two non-planar motions, either an oscillating orbit or a whirling orbit depending on the magnitude of the initial disturbance. To obtain the transition from oscillating to whirling orbits, we perform a stability analysis of the planar motion using Floquet theory. This analysis reveals that there exists a critical amplitude below which the planar motion is neutrally stable and the typical trajectories are ellipses with major and minor radii changing both in magnitude and direction. Beyond the critical amplitude, the planar motion is unstable and we get whirling trajectories which are precessing ellipses again with varying major and minor radii. We further study the effect of changing obstacle parameters on the critical amplitude, and obtain the stability boundaries in the space spanned by the obstacle parameters and the amplitude of the planar vibration. We obtain some interesting values of the obstacle parameters for which small and large amplitude planar motions are stable resulting in oscillating ellipses while motions with intermediate amplitudes are unstable
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.
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
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
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.
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...
Changes in Mitral Valve Annular Geometry After Repair: Saddle-Shaped Versus Flat Annuloplasty Rings
Mahmood, Feroze; Gorman, Joseph H.; Subramaniam, Balachundhar; Gorman, Robert C.; Panzica, Peter J.; Hagberg, Robert C.; Lerner, Adam B.; Hess, Philip E.; Maslow, Andrew; Khabbaz, Kamal R.
2011-01-01
Background Saddle-shaped annuloplasty rings are being increasingly used during mitral valve (MV) repair to conform the mitral annulus to a more nonplanar shape and possibly reduce leaflet stress. In this study utilizing three-dimensional transesophageal echocardiography we compared the effects of rigid flat rings with those of the saddle rings on the mitral annular geometry. Specifically we measured the changes in nonplanarity angle (NPA) before and after MV repair. Methods Geometric analysis on 38 patients undergoing MV repair for myxomatous and ischemic mitral regurgitation with full flat rings (n = 18) and saddle rings (n = 18) were performed. The acquired three-dimensional volumetric data were analyzed utilizing the “Image Arena” software (TomTec GmBH, Munich, Germany). Specifically, the degree of change in the NPA was calculated and compared before and after repair for both types of rings. Results Both types of annuloplasty rings resulted in significant changes in the geometric structure of the MV after repair. However, saddle rings lead to a decrease in the NPA (7% for ischemic and 8% for myxomatous MV repairs) (ie, made the annulus more nonplanar), whereas flat rings increased the NPA (7.9% for ischemic and 11.8% for myxomatous MV repairs) (ie, made the annulus less nonplanar); p value 0.001 or less. Conclusions Implantation of saddle-shaped rings during MV repair surgery is associated with augmentation of the nonplanar shape of the mitral annulus (ie, decreases NPA). This favorable change in the mitral annular geometry could possibly confer a structural advantage to MV repairs with the saddle rings. PMID:20868816
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
Analysis of thick, non-planar boundaries using the discontinuity analyser
Directory of Open Access Journals (Sweden)
M. W. Dunlop
Full Text Available The advent of missions comprised of phased arrays of spacecraft, with separation distances ranging down to at least mesoscales, provides the scientific community with an opportunity to accurately analyse the spatial and temporal dependencies of structures in space plasmas. Exploitation of the multi-point data sets, giving vastly more information than in previous missions, thereby allows unique study of their small-scale physics. It remains an outstanding problem, however, to understand in what way comparative information across spacecraft is best built into any analysis of the combined data. Different investigations appear to demand different methods of data co-ordination. Of the various multi-spacecraft data analysis techniques developed to affect this exploitation, the discontinuity analyser has been designed to investigate the macroscopic properties (topology and motion of boundaries, revealed by multi-spacecraft magnetometer data, where the possibility of at least mesoscale structure is considered. It has been found that the analysis of planar structures is more straightforward than the analysis of non-planar boundaries, where the effects of topology and motion become interwoven in the data, and we argue here that it becomes necessary to customise the analysis for non-planar events to the type of structure at hand. One issue central to the discontinuity analyser, for instance, is the calculation of normal vectors to the structure. In the case of planar and `thin' non-planar structures, the method of normal determination is well-defined, although subject to uncertainties arising from unwanted signatures. In the case of `thick', non-planar structures, however, the method of determination becomes particularly sensitive to the type of physical sampling that is present. It is the purpose of this article to firstly review the discontinuity analyser technique and secondly, to discuss the analysis of the normals to thick non-planar
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,
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
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
Extreme localized exhumation at syntaxes initiated by subduction geometry
Bendick, Rebecca; Ehlers, Todd A.
2014-08-01
Some of the highest and most localized rates of lithospheric deformation in the world are observed at the transition between adjacent plate boundary subduction segments. The initiating perturbation of this deformation has long been attributed to vigorous erosional processes as observed at Nanga Parbat and Namche Barwa in the Himalaya and at Mount St. Elias in Alaska. However, an erosion-dominated mechanism ignores the 3-D geometry of curved subducting plates. Here we present an alternative explanation for rapid exhumation at these locations based on the 3-D thermomechanical evolution of collisions between plates with nonplanar geometries. Comparison of model predictions with existing data reproduces the defining characteristics of these mountains and offers an explanation for their spatial correlation with arc termini. These results demonstrate a "bottom-up" tectonic rather than "top-down" erosional initiation of feedbacks between erosion and tectonic deformation; hence, the importance of 3-D subduction geometry.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
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
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
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
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...
Kreyszig, Erwin
1991-01-01
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
General Geometry and Geometry of Electromagnetism
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...
Nanoscale dielectric microscopy of non-planar samples by lift-mode electrostatic force microscopy.
Van Der Hofstadt, M; Fabregas, R; Biagi, M C; Fumagalli, L; Gomila, G
2016-10-01
Lift-mode electrostatic force microscopy (EFM) is one of the most convenient imaging modes to study the local dielectric properties of non-planar samples. Here we present the quantitative analysis of this imaging mode. We introduce a method to quantify and subtract the topographic crosstalk from the lift-mode EFM images, and a 3D numerical approach that allows for extracting the local dielectric constant with nanoscale spatial resolution free from topographic artifacts. We demonstrate this procedure by measuring the dielectric properties of micropatterned SiO2 pillars and of single bacteria cells, thus illustrating the wide applicability of our approach from materials science to biology.
Transverse modes of a diode-laser pumped monolithic unidirectional non-planar ring laser
Institute of Scientific and Technical Information of China (English)
Keying Wu(吴克瑛); Suhui Yang(杨苏辉); Guanghui Wei(魏光辉)
2003-01-01
Diode-laser pumped monolithic single-frequency non-planar ring laser has the advantages of compactness,reliability and high efficiency. But when the pump power is high enough, the thermal effect will be seriousand the high-order transverse modes will appear. Therefore the single-mode output power is limited. Inthis paper, the mechanism of generating the high-order transverse modes in the monolithic unidirectionalnon-planar ring cavity is analyzed using ray tracing method. The calculated results are in agreement withthe experiments.
Laser-diode-pumped 1319-nm monolithic non-planar ring single-frequency laser
Institute of Scientific and Technical Information of China (English)
Qing Wang(王青); Chunqing Gao(高春清); Yan Zhao(赵严); Suhui Yang(杨苏辉); Guanghui Wei(魏光辉); Dongmei Hong(洪冬梅)
2003-01-01
Single-frequency 1319-nm laser was obtained by using a laser-diode-pumped monolithic Nd:YAG crystalwith a non-planar ring oscillator (NPRO). When the NPRO laser was pumped by an 800-μm fiber coupledlaser diode, the output power of the single-frequency 1319-nm laser was 220 mW, and the slope efficiencywas 16%. With a 100-μm fiber coupled diode laser pumped, 99-mW single-frequency 1319-nm laser wasobtained with a slope efficiency of 29%.
Nanoscale dielectric microscopy of non-planar samples by lift-mode electrostatic force microscopy
Van Der Hofstadt, M.; Fabregas, R.; Biagi, M. C.; Fumagalli, L.; Gomila, G.
2016-10-01
Lift-mode electrostatic force microscopy (EFM) is one of the most convenient imaging modes to study the local dielectric properties of non-planar samples. Here we present the quantitative analysis of this imaging mode. We introduce a method to quantify and subtract the topographic crosstalk from the lift-mode EFM images, and a 3D numerical approach that allows for extracting the local dielectric constant with nanoscale spatial resolution free from topographic artifacts. We demonstrate this procedure by measuring the dielectric properties of micropatterned SiO2 pillars and of single bacteria cells, thus illustrating the wide applicability of our approach from materials science to biology.
Directory of Open Access Journals (Sweden)
Éimhín M. Ní Mhuircheartaigh
2011-01-01
Full Text Available The importance of molecular conformation to the nature and strength of noncovalent interactions existing between a series of increasingly nonplanar tetraphenylporphyrin (TPP derivatives and carbon nanotubes was systematically investigated experimentally in solution using a range of linear and nonlinear optical techniques. Additional complementary molecular dynamics studies were found to support the experimental observations. Convincing evidence of binding between single walled nanotubes (SWNTs and some of these porphyrins was discovered, and a nonplanar macrocycle conformation was found to increase the likelihood of noncovalent binding onto nanotubes. Nonlinear optical studies showed that the optical limiting behavior of the TPP derivatives deteriorated with increasing porphyrin nonplanarity, but that formation of nanotube composites dramatically improved the optical limiting properties of all molecules studied. It was also found that the significant photoluminescence quenching behavior reported in the literature for such porphyrin/SWNT composites is at least partly caused by photoluminescence and excitation self-absorption and is, therefore, an artifact of the system.
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
Álvarez, Celedonio M; Barbero, Héctor; Ferrero, Sergio
2016-09-18
The main purpose of this video is to show 6 reaction steps of a convergent synthesis and prepare a complex molecule containing up to three nonplanar polyaromatic units, which are two corannulene moieties and a racemic hexahelicene linking them. The compound described in this work is a good host for fullerenes. Several common organic reactions, such as free-radical reactions, C-C coupling or click chemistry, are employed demonstrating the versatility of functionalization that this compound can accept. All of these reactions work for planar aromatic molecules. With subtle modifications, it is possible to achieve similar results for nonplanar polyaromatic compounds.
Covalent functionalization of octagraphene with magnetic octahedral B6- and non-planar C6- clusters
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.
Conformal growth of anodic nanotubes for dye-sensitized solar cells: part II. Nonplanar electrode.
Sun, Lidong; Zhang, Sam; Wang, Qing
2014-02-01
Anodic titania nanotube array features highly ordered alignment as well as porous nature, and exhibits intriguing properties when employed in a variety of applications. All these profit from the continuous efforts on controlling the nanotube configurations. Recently, nonplanar electrodes have also been used to grow the nanotubes besides the conventional planar counterparts. As such, it is of great interest and significance to complete a picture to link the nanotubes grown on planar and various nonplanar electrodes for a comprehensive understanding of nanotube growing manners, in an attempt to boost their future applications. In the first part of this review, planar electrodes are focused with regard to nanotube growth and application in dye-sensitized solar cells. In this part, the nanotubes grown on patterned or curved surfaces are discussed first with reference to a similar structure of alumina nanopores, which are subsequently used to mirror the growth of nanotubes on cylindrical electrodes (i.e., titanium wires or meshes). The last section focuses on titanium tubular electrodes which are attractive for thermal fluids in view of the drastically reduced thermal conductivity in the presence of anodic nanotubes. As a recent hot topic, wire-shaped dye-sensitized solar cells are deliberated in terms of cell structure, efficiency calculation, merits, challenges and outlook.
Carlson, Warren; de Mello Koch, Robert; Lin, Hai
2011-03-01
In this article we study operators with a dimension Δ ˜ O( N) and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are two distinct classes of operators that we consider: operators labeled by Young diagrams with two long columns or two long rows. The main complication in working with restricted Schur polynomials is in building a projector from a given S n+ m irreducible representation to an S n × S m irreducible representation (both specified by the labels of the restricted Schur polynomial). We give an explicit construction of these projectors by reducing it to the simple problem of addition of angular momentum in ordinary non-relativistic quantum mechanics. The diagonalization of the dilatation operator reduces to solving three term recursion relations. The fact that the recursion relations have only three terms is a direct consequence of the weak mixing at one loop of the restricted Schur polynomials. The recursion relations can be solved exactly in terms of symmetric Kravchuk polynomials or in terms of Clebsch-Gordan coefficients. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable.
Carlson, Warren; Lin, Hai
2011-01-01
In this article we study operators with a dimension $\\Delta\\sim O(N)$ and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are two distinct classes of operators that we consider: operators labeled by Young diagrams with two long columns or two long rows. The main complication in working with restricted Schur polynomials is in building a projector from a given $S_{n+m}$ irreducible representation to an $S_n\\times S_m$ irreducible representation (both specified by the labels of the restricted Schur polynomial). We give an explicit construction of these projectors by reducing it to the simple problem of addition of angular momentum in ordinary non-relativistic quantum mechanics. The diagonalizationof the dilatation operator reduces to solving three term recursion relations. The fact that the recursion relations have only three terms is a direct consequence of the weak mixing at one loop of the restricte...
Diseases and Conditions Hip fracture By Mayo Clinic Staff A hip fracture is a serious injury, with complications that can be life-threatening. The risk of hip fracture rises with age. Older people are at a ...
Poroelastic modeling of seismic boundary conditions across a fracture.
Nakagawa, Seiji; Schoenberg, Michael A
2007-08-01
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Discrete modeling of hydraulic fracturing processes in a complex pre-existing fracture network
Kim, K.; Rutqvist, J.; Nakagawa, S.; Houseworth, J. E.; Birkholzer, J. T.
2015-12-01
Hydraulic fracturing and stimulation of fracture networks are widely used by the energy industry (e.g., shale gas extraction, enhanced geothermal systems) to increase permeability of geological formations. Numerous analytical and numerical models have been developed to help understand and predict the behavior of hydraulically induced fractures. However, many existing models assume simple fracturing scenarios with highly idealized fracture geometries (e.g., propagation of a single fracture with assumed shapes in a homogeneous medium). Modeling hydraulic fracture propagation in the presence of natural fractures and homogeneities can be very challenging because of the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and pre-existing natural fractures. In this study, the TOUGH-RBSN code for coupled hydro-mechanical modeling is utilized to simulate hydraulic fracture propagation and its interaction with pre-existing fracture networks. The simulation tool combines TOUGH2, a simulator of subsurface multiphase flow and mass transport based on the finite volume approach, with the implementation of a lattice modeling approach for geomechanical and fracture-damage behavior, named Rigid-Body-Spring Network (RBSN). The discrete fracture network (DFN) approach is facilitated in the Voronoi discretization via a fully automated modeling procedure. The numerical program is verified through a simple simulation for single fracture propagation, in which the resulting fracture geometry is compared to an analytical solution for given fracture length and aperture. Subsequently, predictive simulations are conducted for planned laboratory experiments using rock-analogue (soda-lime glass) samples containing a designed, pre-existing fracture network. The results of a preliminary simulation demonstrate selective fracturing and fluid infiltration along the pre-existing fractures, with additional fracturing in part
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 base
Vos, A.P. de; Horst, A.R.A. van der; Perel, M.
2001-01-01
Non-planar driver's side rear-view mirrors provide a wider field-of-view than planar mirrors, but produce a minified image. A field experiment was conducted to measure the performance of drivers when making lane change decisions based on mirror information. Four mirror types were included: a planar
Gauthier, B.D.M.; Bisdom, K.; Bertotti, G.
2012-01-01
The full 3D characterization of fracture networks is a key issue in naturally fractured reservoir modeling. Fracture geometry (e.g., orientation, size, spacing), fracture scale (e.g., bed-confined fractures, fracture corridors), lateral and vertical variations, need to be defined from limited, gener
[Geometry of the hip joint: methodology and guidelines].
Gaspar, Drago; Crnković, Tomislav
2013-03-01
An hip fracture is an significant personal, family and health issue of people older than 65 years. In the first year of the fracture up to 30% of the injured die and about 50% of them never regain their formal degree of independence in fulfilling day-to-day activities. Estimations are that throughout 30 years in the world there will be around 6 million hip fractures per year which is about four times the todays amount. Todays predictions of hip fractures based on the hip geometry have shown us that the hip geometry is an independent variable of the bone mineral density. The hip geometry is more resistant to the effect of various factors than the bone mineral density and the changes throu life are a lot slower. The uniqueness and the sensitivity of the hip geometry in predicting a fracture is high and acceptable in research results of most authors. In this review we present the previous relevant knowledge about the measures and factors which determines the hip geometry and the accepted amount of pictorial methods of hip display. We have compared the methodology and the patients of eleven randomly picked writings on predicting hip fracture based on the hip geometry. We highlight the need of further refinement of the methodology and the more balanced selection of patients for a greater conformity in future writings. The hip geometry has shown it self as an useful diagnostical instrument but there is still more room for its improvement.
Energy Technology Data Exchange (ETDEWEB)
Ito, Kazumasa; Yongkoo, Seol
2003-04-09
Water fluxes in unsaturated, fractured rock involve the physical processes occurring at fracture-matrix interfaces within fracture networks. Modeling these water fluxes using a discrete fracture network model is a complicated effort. Existing preprocessors for TOUGH2 are not suitable to generate grids for fracture networks with various orientations and inclinations. There are several 3-D discrete-fracture-network simulators for flow and transport, but most of them do not capture fracture-matrix interaction. We have developed a new 3-D discrete-fracture-network mesh generator, FRACMESH, to provide TOUGH2 with information about the fracture network configuration and fracture-matrix interactions. FRACMESH transforms a discrete fracture network into a 3 dimensional uniform mesh, in which fractures are considered as elements with unique rock material properties and connected to surrounding matrix elements. Using FRACMESH, individual fractures may have uniform or random aperture distributions to consider heterogeneity. Fracture element volumes and interfacial areas are calculated from fracture geometry within individual elements. By using FRACMESH and TOUGH2, fractures with various inclinations and orientations, and fracture-matrix interaction, can be incorporated. In this paper, results of flow and transport simulations in a fractured rock block utilizing FRACMESH are presented.
Non-planar and Non-linear Second Sound Waves in He Ⅱ
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; KIMURA Seiji; MURAKAMI Masahide; WANG Ru-zhu
2000-01-01
Non-planar and non-linear second sound wave are experimentally investigated in an open He Ⅱ bath. It is found that second sound wave characterized by a negative tail part in an open He Ⅱ bath is different from that propagating through a channel, and the shape of the negative tail part of second sound wave varies at different location in an open He Ⅱ bath. Theoretical consideration is also carried out based on two-fluid model and vortex evolution equation. It is found that experimental and theoretical results agree rather well with each other. Second sound wave may develop into the thermal shock wave provided that the heat flux is large.
Multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates.
Energy Technology Data Exchange (ETDEWEB)
Chen, Ken Shuang
2004-11-01
This report documents the author's efforts in the deterministic modeling of copper-sulfidation corrosion on non-planar substrates such as diodes and electrical connectors. A new framework based on Goma was developed for multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates. In this framework, the moving sulfidation front is explicitly tracked by treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and repeatedly performing re-meshing using CUBIT and re-mapping using MAPVAR. Three one-dimensional studies were performed for verifying the framework in asymptotic regimes. Limited model validation was also carried out by comparing computed copper-sulfide thickness with experimental data. The framework was first demonstrated in modeling one-dimensional copper sulfidation with charge separation. It was found that both the thickness of the space-charge layers and the electrical potential at the sulfidation surface decrease rapidly as the Cu{sub 2}S layer thickens initially but eventually reach equilibrium values as Cu{sub 2}S layer becomes sufficiently thick; it was also found that electroneutrality is a reasonable approximation and that the electro-migration flux may be estimated by using the equilibrium potential difference between the sulfidation and annihilation surfaces when the Cu{sub 2}S layer is sufficiently thick. The framework was then employed to model copper sulfidation in the solid-state-diffusion controlled regime (i.e. stage II sulfidation) on a prototypical diode until a continuous Cu{sub 2}S film was formed on the diode surface. The framework was also applied to model copper sulfidation on an intermittent electrical contact between a gold-plated copper pin and gold-plated copper pad; the presence of Cu{sub 2}S was found to raise the effective electrical resistance drastically. Lastly, future research needs in modeling atmospheric copper sulfidation are discussed.
Institute of Scientific and Technical Information of China (English)
Marte Gutierrez; Dong-Joon Youn
2015-01-01
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 distribu-tions 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.
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.
CONSTRAINT EFFECT IN FRACTURE WHAT IS IT
Energy Technology Data Exchange (ETDEWEB)
Lam, P; Prof. Yuh J. Chao, P
2008-10-29
The meaning of the phrase 'constraint effect in fracture' has changed in the past two decades from 'contained plasticity' to a broader description of 'dependence of fracture toughness value on geometry of test specimen or structure'. This paper will first elucidate the fundamental mechanics reasons for the apparent 'constraint effects in fracture', followed by outlining a straightforward approach to overcoming this problem in both brittle (elastic) and ductile (elastic-plastic) fracture. It is concluded by discussing the major difference in constraint effect on fracture event in elastic and elastic-plastic materials.
Schären, S; Jeanneret, B
1999-05-01
Fractures of the atlas account for 1-2% of all vertebral fractures. We divide atlas fractures into 5 groups: isolated fractures of the anterior arch of the atlas, isolated fractures of the posterior arch, combined fractures of the anterior and posterior arch (so-called Jefferson fractures), isolated fractures of the lateral mass and fractures of the transverse process. Isolated fractures of the anterior or posterior arch are benign and are treated conservatively with a soft collar until the neck pain has disappeared. Jefferson fractures are divided into stable and unstable fracture depending on the integrity of the transverse ligament. Stable Jefferson fractures are treated conservatively with good outcome while unstable Jefferson fractures are probably best treated operatively with a posterior atlanto-axial or occipito-axial stabilization and fusion. The authors preferred treatment modality is the immediate open reduction of the dislocated lateral masses combined with a stabilization in the reduced position using a transarticular screw fixation C1/C2 according to Magerl. This has the advantage of saving the atlanto-occipital joints and offering an immediate stability which makes immobilization in an halo or Minerva cast superfluous. In late instabilities C1/2 with incongruency of the lateral masses occurring after primary conservative treatment, an occipito-cervical fusion is indicated. Isolated fractures of the lateral masses are very rare and may, if the lateral mass is totally destroyed, be a reason for an occipito-cervical fusion. Fractures of the transverse processes may be the cause for a thrombosis of the vertebral artery. No treatment is necessary for the fracture itself.
Hydraulic fracturing model based on the discrete fracture model and the generalized J integral
Liu, Z. Q.; Liu, Z. F.; Wang, X. H.; Zeng, B.
2016-08-01
The hydraulic fracturing technique is an effective stimulation for low permeability reservoirs. In fracturing models, one key point is to accurately calculate the flux across the fracture surface and the stress intensity factor. To achieve high precision, the discrete fracture model is recommended to calculate the flux. Using the generalized J integral, the present work obtains an accurate simulation of the stress intensity factor. Based on the above factors, an alternative hydraulic fracturing model is presented. Examples are included to demonstrate the reliability of the proposed model and its ability to model the fracture propagation. Subsequently, the model is used to describe the relationship between the geometry of the fracture and the fracturing equipment parameters. The numerical results indicate that the working pressure and the pump power will significantly influence the fracturing process.
Fractal characterization of fracture surfaces in concrete
Saouma, V.E.; Barton, C.C.; Gamaleldin, N.A.
1990-01-01
Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.
High-Fidelity Aerostructural Optimization of Nonplanar Wings for Commercial Transport Aircraft
Khosravi, Shahriar
Although the aerospace sector is currently responsible for a relatively small portion of global anthropogenic greenhouse gas emissions, the growth of the airline industry raises serious concerns about the future of commercial aviation. As a result, the development of new aircraft design concepts with the potential to improve fuel efficiency remains an important priority. Numerical optimization based on high-fidelity physics has become an increasingly attractive tool over the past fifteen years in the search for environmentally friendly aircraft designs that reduce fuel consumption. This approach is able to discover novel design concepts and features that may never be considered without optimization. This can help reduce the economic costs and risks associated with developing new aircraft concepts by providing a more realistic assessment early in the design process. This thesis provides an assessment of the potential efficiency improvements obtained from nonplanar wings through the application of fully coupled high-fidelity aerostructural optimization. In this work, we conduct aerostructural optimization using the Euler equations to model the flow along with a viscous drag estimate based on the surface area. A major focus of the thesis is on finding the optimal shape and performance benefits of nonplanar wingtip devices. Two winglet configurations are considered: winglet-up and winglet-down. These are compared to optimized planar wings of the same projected span in order to quantify the possible drag reductions offered by winglets. In addition, the drooped wing is studied in the context of exploratory optimization. The main results show that the winglet-down configuration is the most efficient winglet shape, reducing the drag by approximately 2% at the same weight in comparison to a planar wing. There are two reasons for the superior performance of this design. First, this configuration moves the tip vortex further away from the wing. Second, the winglet
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.......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....
Energy Technology Data Exchange (ETDEWEB)
Mayout, Saliha; Tribeche, Mouloud, E-mail: mouloudtribeche@yahoo.fr [Plasma Physics Group (PPG), Theoretical Physics Laboratory (TPL), Faculty of Sciences- Physics, University of Bab-Ezzouar, U.S.T.H.B, B.P. 32, El Alia, Algiers 16111 (Algeria); Sahu, Biswajit [Department of Mathematics, West Bengal State University, Barasat, Kolkata-700126 (India)
2015-12-15
A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.
Fracture imaging with converted elastic waves
Energy Technology Data Exchange (ETDEWEB)
Nihei, K.T.; Nakagawa, S.; Myer, L.R.
2001-05-29
This paper examines the seismic signatures of discrete, finite-length fractures, and outlines an approach for elastic, prestack reverse-time imaging of discrete fractures. The results of this study highlight the importance of incorporating fracture-generated P-S converted waves into the imaging method, and presents an alternate imaging condition that can be used in elastic reverse-time imaging when a direct wave is recorded (e.g., for crosswell and VSP acquisition geometries).
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 ...
Characterization of borehole fractures by the body and interface waves
Henry, F.
2005-01-01
The success of the fracturing process in the oil and gas industry depends on our ability to define the hydraulic fracture geometry. To have a method of measurement for characterizing completely the fracture dimensions from a single well in reliable way, will be a primordial importance, in term of ec
Analysis of Fracturing Network Evolution Behaviors in Random Naturally Fractured Rock Blocks
Wang, Y.; Li, X.; Zhang, B.
2016-11-01
Shale gas has been discovered in the Upper Triassic Yanchang Formation, Ordos Basin, China. Due to the weak tectonic activities in the shale plays, core observations indicate abundant random non-tectonic micro-fractures in the producing shales. The role of micro-fractures in hydraulic fracturing for shale gas development is currently poorly understood yet potentially critical. In a series of scaled true triaxial laboratory experiments, we investigate the interaction of propagating fracturing network with natural fractures. The influence of dominating factors was studied and analyzed, with an emphasis on non-tectonic fracture density, injection rate, and stress ratio. A new index of P-SRV is proposed to evaluate the fracturing effectiveness. From the test results, three types of fracturing network geometry of radial random net-fractures, partly vertical fracture with random branches, and vertical main fracture with multiple branches were observed. It is suggested from qualitative and quantitative analysis that great micro-fracture density and injection rate tend to maximum the fracturing network; however, it tends to decrease the fracturing network with the increase in horizontal stress ratio. The function fitting results further proved that the injection rate has the most obvious influence on fracturing effectiveness.
High-Reliability Pump Module for Non-Planar Ring Oscillator Laser
Liu, Duncan T.; Qiu, Yueming; Wilson, Daniel W.; Dubovitsky, Serge; Forouhar, Siamak
2007-01-01
We propose and have demonstrated a prototype high-reliability pump module for pumping a Non-Planar Ring Oscillator (NPRO) laser suitable for space missions. The pump module consists of multiple fiber-coupled single-mode laser diodes and a fiber array micro-lens array based fiber combiner. The reported Single-Mode laser diode combiner laser pump module (LPM) provides a higher normalized brightness at the combined beam than multimode laser diode based LPMs. A higher brightness from the pump source is essential for efficient NPRO laser pumping and leads to higher reliability because higher efficiency requires a lower operating power for the laser diodes, which in turn increases the reliability and lifetime of the laser diodes. Single-mode laser diodes with Fiber Bragg Grating (FBG) stabilized wavelength permit the pump module to be operated without a thermal electric cooler (TEC) and this further improves the overall reliability of the pump module. The single-mode laser diode LPM is scalable in terms of the number of pump diodes and is capable of combining hundreds of fiber-coupled laser diodes. In the proof-of-concept demonstration, an e-beam written diffractive micro lens array, a custom fiber array, commercial 808nm single mode laser diodes, and a custom NPRO laser head are used. The reliability of the proposed LPM is discussed.
Patwardhan, Ardan
The objective of this study has been to examine the imaging properties of transmission electron microscopes when coherent non-planar illumination is used in conjunction with defocused specimens. This situation is reminiscent of what is commonly the case in electron microscopic phase-contrast studies of biologically relevant macromolecules, using a field emission gun as a coherent electron source. For the sake of simplicity, the imaging system has been idealized as a thin lens with properties that can be described by the Fresnel approximation of the Huygens-Fresnel principle. The resulting expressions show that the system magnification has a defocus dependent factor, as do the contrast transfer functions. These factors are normally not taken into account in conventional derivations. The defocus dependent factor can be minimized by using planar illumination. The factor approaches infinity as the crossover moves closer to the specimen, and it is in the region close to the specimen that this factor is most significant. These results can have serious implications for high-resolution single-particle cryo electron microscopy as this technique often relies on combining data taken at a range of defocus values.
Exact solution of planar and nonplanar weak shock wave problem in gasdynamics
Energy Technology Data Exchange (ETDEWEB)
Singh, L.P. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Ram, S.D., E-mail: sram.rs.apm@itbhu.ac.in [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Singh, D.B. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India)
2011-11-15
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.
Block Copolymer Directed Self-Assembly Approaches for Doping Planar and Non-Planar Semiconductors
Popere, Bhooshan; Russ, Boris; Heitsch, Andrew; Trefonas, Peter; Segalman, Rachel
As electronic circuits continue to shrink, reliable nanoscale doping of functional devices presents new challenges. While directed self-assembly (DSA) of block copolymers (BCPs) has enabled excellent pitch control for lithography, controlling the 3D dopant distribution remains a fundamental challenge. To this end, we have developed a BCP self-assembly approach to confine dopants to nanoscopic domains within a semiconductor. This relies on the supramolecular encapsulation of the dopants within the core of the block copolymer (PS- b-P4VP) micelles, self-assembly of these micelles on the substrate, followed by rapid thermal diffusion of the dopants into the underlying substrate. We show that the periodic nature of the BCP domains enables precise control over the dosage and spatial position of dopant atoms on the technologically relevant length scales (10-100 nm). Additionally, as the lateral density of 2D circuit elements approaches the Moore's limit, novel 3D architectures have emerged. We have utilized our BCP self-assembly approach towards understanding the self-assembly our micelles directed by such nanoscale non-planar features. We show that the geometric confinement imposed by the hard feature walls directs the assembly of these micelles.
Bär, Christian; Schwarz, Matthias
2012-01-01
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Ando, Ryosuke
2016-11-01
The elastodynamic boundary integral equation method (BIEM) in real space and in the temporal domain is an accurate semi-analytical tool to investigate the earthquake rupture dynamics on non-planar faults. However, its heavy computational demand for a historic integral generally increases with a time complexity of O(MN3)for the number of time steps N and elements M due to volume integration in the causality cone. In this study, we introduce an efficient BIEM, termed the `Fast Domain Partitioning Method' (FDPM), which enables us to reduce the computation time to the order of the surface integral, O(MN2), without degrading the accuracy. The memory requirement is also reduced to O(M2) from O(M2N). FDPM uses the physical nature of Green's function for stress to partition the causality cone into the domains of the P and S wave fronts, the domain in-between the P and S wave fronts, and the domain of the static equilibrium, where the latter two domains exhibit simpler dependences on time and/or space. The scalability of this method is demonstrated on the large-scale parallel computing environments of distributed memory systems. It is also shown that FDPM enables an efficient use of memory storage, which makes it possible to reduce computation times to a previously unprecedented level. We thus present FDPM as a powerful tool to break through the current fundamental difficulties in running dynamic simulations of coseismic ruptures and earthquake cycles under realistic conditions of fault geometries.
Compartmentalization analysis using discrete fracture network models
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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.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Gänsslen, A; Oestern, H J
2011-12-01
Treatment of acetabular fractures requires extensive knowledge of the bony anatomy, the amount of possible exposure of the bone with the selected approaches and fracture type-dependent indications of operative treatment. Classification of the fracture with detailed analysis of the fracture morphology is the basis for decision making and planning. The primary treatment aim is the anatomic reconstruction of the acetabulum which results in optimal long-term results.The basis of this overview is the presentation of standard treatment concepts in acetabular fracture surgery. Beside characteristics of the acetabular bony anatomy, biomechanical and pathomechanical principles and the relevant radiological anatomy, the treatment options, both conservative and operative and basic principles of the indications for standard surgical approaches will be discussed.The special fracture type is discussed in detail regarding incidence, injury mechanism, concomitant injuries, options for conservative and operative treatment, quality of operative reduction and long-term results.Furthermore, epidemiological data on typical postoperative complications are evaluated.
DeCoster, T. A.; Stevens, M. A.; Albright, J. P.
1994-01-01
Fractures occur in athletes and dramatically influence performance during competitive and recreational activities. Fractures occur in athletes as the result of repetitive stress, acute sports-related trauma and trauma outside of athletics. The literature provides general guidelines for treatment as well as a variety of statistics on the epidemiology of fractures by sport and level of participation. Athletes are healthy and motivated patients, and have high expectations regarding their level o...
Numerical investigation of blood flow in a deformable coronary bifurcation and non-planar branch
Razavi, Seyed Esmail; Omidi, Amir Ali; Saghafi Zanjani, Massoud
2014-01-01
Introduction: Among cardiovascular diseases, arterials stenosis is recognized more commonly than the others. Hemodynamic characteristics of blood play a key role in the incidence of stenosis. This paper numerically investigates the pulsatile blood flow in a coronary bifurcation with a non-planar branch. To create a more realistic analysis, the wall is assumed to be compliant. Furthermore, the flow is considered to be three-dimensional, incompressible, and laminar. Methods: The effects of non-Newtonian blood, compliant walls and different angles of bifurcation on hemodynamic characteristics of flow were evaluated. Shear thinning of blood was simulated with the Carreau-Yasuda model. The current research was mainly focused on the flow characteristics in bifurcations since atherosclerosis occurs mostly in bifurcations. Moreover, as the areas with low shear stresses are prone to stenosis, these areas were identified. Results: Our findings indicated that the compliant model of the wall, bifurcation’s angle, and other physical properties of flow have an impact on hemodynamics of blood flow. Lower wall shear stress was observed in the compliant wall than that in the rigid wall. The outer wall of bifurcation in all models had lower wall shear stress. In bifurcations with larger angles, wall shear stress was higher in outer walls, and lower in inner walls. Conclusion: The non-Newtonian blood vessels and different angles of bifurcation on hemodynamic characteristics of flow evaluation confirmed a lower wall shear stress in the compliant wall than that in the rigid wall, while the wall shear stress was higher in outer walls but lower in inner walls in the bifurcation regions with larger angles. PMID:25671176
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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
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.
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
Sarabia Condés, J M; Ibañez Martínez, L; Sánchez Carrasco, M A; Carrillo Julia, F J; Salmerón Martínez, E L
2015-01-01
The purpose of this paper is to present our experience in the treatment of the fractures of the hamate and to make a review of the literature on this topic. We retrospectively reviewed 10 patients treated in our clinic between 2005-2012 suffering from fractures of the hamate. Six cases were fractures of the body and four were fractures of the hamate. Five cases were of associated injuries. Diagnostic delay ranged from 30 days to 2 years. Patient follow-up ranged from 1 to 10 years. Patient satisfaction was evaluated using the DASH questionnaire. Five patients with a fracture of the body underwent surgery, and one was treated conservatively. Two patients with fracture of the hook of the hamate were treated with immobilization, and two more patients had the fragment removed. The grip strength and the digital clip were reduced in 2 cases. Flexion and extension of the wrist was limited in 3 cases. The mobility of the fingers was normal in all the cases, except in one. The results obtained from the DASH questionnaire were normal in all the cases, except in one case of fracture of the hamate, and in two cases of fracture of the body. The surgical treatment should reduce the dislocation and stabilize the injuries with osteosynthesis. The fractures of the hamate are usually diagnosed late, and the most recommended treatment is removal of the fragment, although it cannot be deduced from this study. Copyright © 2014 SECOT. Published by Elsevier Espana. All rights reserved.
Sánchez León, Belisario; Facultad de Medicina, Universidad Nacional Mayor de San Marcos, Lima, Perú
2014-01-01
Our expertise is the study of more than 2,000 cases of Colles' fractures. Colles name should in this case to synthesize the type of fractures of the lower end of the radius. There have been various proposed classifications according to the different fracture lines can be demonstrated radiologically in the region of the wrist. We believe that these ratings should only be retained if the concept of the articular fracture or not in the classical sense, since it has great value in the functional ...
Fracture of sandwiched composites
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Lin, Weh-Huei.
1989-01-01
Fracture of a pair of collinear cracks in various materials, such as an isotropic strip, an orthotropic strip, a bonded isotropic adhesive layer, and sandwiched orthotropic layers, is investigated. The crack surfaces are subjected to an arbitrary opening pressure p(x). The problems are formulated in terms of Fredholm integral equation of the second kind by making use the techniques of Fourier transform and finite Hilbert transform. In case of uniform opening pressure p(x)={sigma}, exact expressions for the stress intensity factors and the shape of deformed crack are obtained. Numerical calculations are carried out to study the effects of various boundary geometries and material properties on the fracture of the chosen materials.
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...
Institute of Scientific and Technical Information of China (English)
GUO Enli; MO Xiaohuan
2006-01-01
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
Gravity-Driven Hydraulic Fractures
Germanovich, L. N.; Garagash, D.; Murdoch, L. C.; Robinowitz, M.
2014-12-01
This study is motived by a new method for disposing of nuclear waste by injecting it as a dense slurry into a hydraulic fracture that grows downward to great enough depth to permanently isolate the waste. Disposing of nuclear waste using gravity-driven hydraulic fractures is mechanically similar to the upward growth of dikes filled with low density magma. A fundamental question in both applications is how the injected fluid controls the propagation dynamics and fracture geometry (depth and breadth) in three dimensions. Analog experiments in gelatin [e.g., Heimpel and Olson, 1994; Taisne and Tait, 2009] show that fracture breadth (the short horizontal dimension) remains nearly stationary when the process in the fracture "head" (where breadth is controlled) is dominated by solid toughness, whereas viscous fluid dissipation is dominant in the fracture tail. We model propagation of the resulting gravity-driven (buoyant or sinking), finger-like fracture of stationary breadth with slowly varying opening along the crack length. The elastic response to fluid loading in a horizontal cross-section is local and can be treated similar to the classical Perkins-Kern-Nordgren (PKN) model of hydraulic fracturing. The propagation condition for a finger-like crack is based on balancing the global energy release rate due to a unit crack extension with the rock fracture toughness. It allows us to relate the net fluid pressure at the tip to the fracture breadth and rock toughness. Unlike the PKN fracture, where breadth is known a priori, the final breadth of a finger-like fracture is a result of processes in the fracture head. Because the head is much more open than the tail, viscous pressure drop in the head can be neglected leading to a 3D analog of Weertman's hydrostatic pulse. This requires relaxing the local elasticity assumption of the PKN model in the fracture head. As a result, we resolve the breadth, and then match the viscosity-dominated tail with the 3-D, toughness
Slab1.0: A three-dimensional model of global subduction zone geometries
Hayes, G.P.; Wald, D.J.; Johnson, R.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. Copyright 2011 by the American Geophysical Union.
Modelling of Specimen Fracture
2013-09-23
the plate center. An end load of 1.0 MPa was applied. 1 2 3 Modelling of Specimen Fracture – Final Report 11 TR-13-47 Figure 2.5: Crack Geometry Figure...Christopher Bayley DRDC Atlantic Dockyard Laboratory Pacific CFB Esquimalt, Building 199 PO Box 17000, Station Forces Victoria, British Columbia Canada...q The weighting function, q , can be any arbitrary function within the J-integral domain, and must be zero on the domain boundary . An easy function
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...
Geometry essentials for dummies
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
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Symplectic geometries on supermanifolds
Lavrov, P M
2007-01-01
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.
Gualtieri, Marco
2010-01-01
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.
Methods for euclidean geometry
Byer, Owen; Smeltzer, Deirdre L
2010-01-01
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
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.
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...
Shannon, John L., Jr.
1986-01-01
The application of fracture mechanics to the design of ceramic structures will require the precise measurement of crack growth and fracture resistance of these materials over their entire range of anticipated service temperatures and standardized test methods for making such measurements. The development of a standard test for measuring the plane strain fracture toughness is sought. Stress intensity factor coefficients were determined for three varieties of chevron-notch specimens, and fracture toughness measurements were made on silicon nitrides, silicon carbides, and aluminum oxides to assess the performance of each specimen variety. It was determined that silicon nitride and silicon carbides have flat crack growth resistance curves, but aluminum oxide does not. Additionally, batch-to-batch differences were noticed for the aluminum oxide. Experiments are continuing to explain the rising crack growth resistance and batch-to-batch variations for the aluminum oxide.
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.
Challenges in Continuum Modelling of Intergranular Fracture
DEFF Research Database (Denmark)
Coffman, Valerie; Sethna, James P.; Ingraffea, A. R.;
2011-01-01
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......, 3D grain boundary geometries comprise a five-dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties...... 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....
Energy Technology Data Exchange (ETDEWEB)
Duanmu, Kaining; Truhlar, Donald G.
2015-04-30
We report a systematic study of small silver clusters, Agn, Agn+, and Agn–, n = 1–7. We studied all possible isomers of clusters with n = 5–7. We tested 42 exchange–correlation functionals, and we assess these functionals for their accuracy in three respects: geometries (quantitative prediction of internuclear distances), structures (the nature of the lowest-energy structure, for example, whether it is planar or nonplanar), and energies. We find that the ingredients of exchange–correlation functionals are indicators of their success in predicting geometries and structures: local exchange–correlation functionals are generally better than hybrid functionals for geometries; functionals depending on kinetic energy density are the best for predicting the lowest-energy isomer correctly, especially for predicting two-dimensional to three-dimenstional transitions correctly. The accuracy for energies is less sensitive to the ingredient list. Our findings could be useful for guiding the selection of methods for computational catalyst design.
Algorithms in Algebraic Geometry
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
Fundamental concepts of geometry
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.
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
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Introduction to finite geometries
Kárteszi, F
1976-01-01
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geo
basement reservoir geometry and properties
Walter, bastien; Geraud, yves; Diraison, marc
2017-04-01
Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre
DEFF Research Database (Denmark)
Bisdom, Kevin; Bertotti, Giovanni; Nick, Hamid
2016-01-01
Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling...
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
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.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
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.
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
2011-01-01
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
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.
Constraint corrected fracture mechanics in structural integrity assessment
Energy Technology Data Exchange (ETDEWEB)
Laukkanen, A.; Wallin, K. [VTT Industrial Systems, Espoo (Finland)
2004-07-01
Specimen size, crack depth and loading conditions may affect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the Master Curve standard ASTM E1921, which is based on technology developed at VTT Industrial Systems. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases this may lead to unnecessary repairs or even to an early 'retirement' of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J-small scale yielding correction (SSYC), Q-parameter and the T{sub stress}. (orig.)
Atesok, Kivanc I; Jupiter, Jesse B; Weiss, Arnold-Peter C
2011-10-01
Galeazzi fracture is a fracture of the radial diaphysis with disruption at the distal radioulnar joint (DRUJ). Typically, the mechanism of injury is forceful axial loading and torsion of the forearm. Diagnosis is established on radiographic evaluation. Underdiagnosis is common because disruption of the ligamentous restraints of the DRUJ may be overlooked. Nonsurgical management with anatomic reduction and immobilization in a long-arm cast has been successful in children. In adults, nonsurgical treatment typically fails because of deforming forces acting on the distal radius and DRUJ. Open reduction and internal fixation is the preferred surgical option. Anatomic reduction and rigid fixation should be followed by intraoperative assessment of the DRUJ. Further intraoperative interventions are based on the reducibility and postreduction stability of the DRUJ. Misdiagnosis or inadequate management of Galeazzi fracture may result in disabling complications, such as DRUJ instability, malunion, limited forearm range of motion, chronic wrist pain, and osteoarthritis.
Martin-Drumel, Marie-Aline; McCarthy, Michael C.; Patterson, David; Eibenberger, Sandra; Buckingham, Grant; Baraban, Joshua H.; Ellison, Barney; Stanton, John F.
2016-06-01
The preferred conformation of cis-1,3-butadiene (CH_2=CH-CH=CH_2) has been of long-standing importance in organic chemistry because of its role in Diels-Alder transition states. The molecule could adopt a planar s-cis conformation, in favor of conjugations in the carbon chain, or a non-planar gauche conformation, as a result of steric interactions between the terminal H atoms. To resolve this ambiguity, we have now measured the pure rotational spectrum of this isomer in the microwave region, unambiguously establishing a significant inertial defect, and therefore a gauche conformation. Experimental measurements of gauche-1,3-butadiene and several of its isotopologues using cavity Fourier-transform microwave (FTMW) spectroscopy in a supersonic expansion and chirped-pulse FTMW spectroscopy in a 4 K buffer gas cell will be summarized, as will new quantum chemical calculations.
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.
Task order #24 update: exploration of damage mechanisms in cylindrical geometry
Energy Technology Data Exchange (ETDEWEB)
Kaul, Ann M [Los Alamos National Laboratory
2011-01-14
A typical method of failure for ductile materials is spallation damage, which is caused by the nucleation, growth and coalescence of voids due to the presence of high tensile stress in the material. Spallation damage models, such as TEPLA, are currently implemented in hydrodynamic computer codes used at Los Alamos National Laboratory (LANL). Parameters for such constitutive models are derived from data sets obtained primarily from gas gun and shock-driven experiments, which are designed to allow one-dimensional analysis of the evolution of the failure characteristics. However, in a non-planar geometry, advanced failure models predict failure to be a multi-dimensional process. Additionally, a limited amount of data exists for the process of void nucleation, growth and coalescence. Another lightly researched area is the state of the material in the event that the spallation layer is recollected and voids are closed. The experiments described here are being conducted as part of a Campaign-l effort to provide data addressing these issues. The Russian Damage Experimental Series is designed to provide fundamental non-planar (cylindrical) spallation damage data, including early time processes (void nucleation, growth and coalescence) and late time processes (recollection of the spallation layer). Previous experiments produced data addressing some of the early time processes. This presentation will be provided to LANL and VNIIEF colleagues as a means of assessing the status of Task Order No.24 at the current time.
Riemann-Finsler Geometry with Applications to Information Geometry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Bonola, Roberto
2010-01-01
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
Santo, J
1999-01-01
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
Discrete and computational geometry
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 a
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
Simulation of Hydraulic and Natural Fracture Interaction Using a Coupled DFN-DEM Model
Energy Technology Data Exchange (ETDEWEB)
J. Zhou; H. Huang; M. Deo
2016-03-01
The presence of natural fractures will usually result in a complex fracture network due to the interactions between hydraulic and natural fracture. The reactivation of natural fractures can generally provide additional flow paths from formation to wellbore which play a crucial role in improving the hydrocarbon recovery in these ultra-low permeability reservoir. Thus, accurate description of the geometry of discrete fractures and bedding is highly desired for accurate flow and production predictions. Compared to conventional continuum models that implicitly represent the discrete feature, Discrete Fracture Network (DFN) models could realistically model the connectivity of discontinuities at both reservoir scale and well scale. In this work, a new hybrid numerical model that couples Discrete Fracture Network (DFN) and Dual-Lattice Discrete Element Method (DL-DEM) is proposed to investigate the interaction between hydraulic fracture and natural fractures. Based on the proposed model, the effects of natural fracture orientation, density and injection properties on hydraulic-natural fractures interaction are investigated.
... Z Videos Infographics Symptom Picker Anatomy Bones Joints Muscles Nerves Vessels Tendons About Hand Surgery What is a Hand Surgeon? What is ... serve as a framework. This framework supports the muscles that make the wrist ... When one of these hand bones is broken (fractured), it can prevent you ...
Directory of Open Access Journals (Sweden)
2003-07-01
Full Text Available The fracture properties of many different types of fibers are covered in a timely new book that will prove to be a tremendous source of information and references for researchers in the wide and diverse field of fibers and composites, says Bill Clegg.
... Commentary Recent News Scientists Working on Solar-Powered Prosthetic Limbs Exercise a Great Prescription to Help Older Hearts Bavencio Approved for Rare Skin Cancer Older Mothers May Raise Better-Behaved Kids, Study ... or a collapsed lung (pneumothorax—see Traumatic Pneumothorax ). An injury that fractures the lower ribs sometimes also damages the liver (see Liver ...
Freslon, M; Bouaka, D; Coipeau, P; Defossez, G; Leclercq, N; Nebout, J; Marteau, E; Poilbout, N; Prebet, R
2008-06-01
Thoracolumbar fractures are frequent and the functional outcomes are sometimes severe. This multicentric study, including five medical centers, was performed to evaluate the long-term outcomes of the patients. One hundred and thirty six patients with thoracolumbar fracture (T11 to L2) was evaluated with a minimal follow-up of two years. Every one had a clinical exam with a score of Oswestry and an X-Ray study (before and after treatment and at revision). Most of them presented compression fractures, the most often at L1 level. On X-rays, a gain was noted on the vertebral kyphosis immediately after surgery, but there is a loss of correction over time whatever the treatment. The clinical outcomes for the patients were great, with an Oswestry average score of 6,4. A correlation was noted between this functional score and vertebral kyphosis. So, an anterior column strengthening (isolated or performed during the surgery) could improve these functional outcomes. Moreover, the Thoraco Lumbar Injury Severity Score (TLISS) seems to be a simple organigram to determine the most appropriate treatment of these fractures, with particular attention to the distraction mechanism or posterior ligamentous complex lesions. However, RMI before surgery is necessary to evaluate these lesions.
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Kumaresan, S
2005-01-01
Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.
Lectures on Symplectic Geometry
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...
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Facilitating Understandings of Geometry.
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
Introduction to tropical geometry
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...
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
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.
Derived logarithmic geometry I
Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi
2016-01-01
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.
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.
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...
Hohmann, Manuel
2014-01-01
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.
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....
Intermediate algebra & analytic geometry
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
Schreiber, Urs
2016-01-01
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.
Punzi, Raffaele; Wohlfarth, Mattias N R
2008-01-01
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de
2008-12-11
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Description of Fracture Systems for External Criticality Reports
Energy Technology Data Exchange (ETDEWEB)
Jean-Philippe Nicot
2001-09-21
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.
A Spatial Clustering Approach for Stochastic Fracture Network Modelling
Seifollahi, S.; Dowd, P. A.; Xu, C.; Fadakar, A. Y.
2014-07-01
Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach
Nonlinear Fracture Mechanics and Plasticity of the Split Cylinder Test
DEFF Research Database (Denmark)
Olesen, John Forbes; Østergaard, Lennart; Stang, Henrik
2006-01-01
demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive......The split cylinder testis subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fracture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two...
Sources of hyperbolic geometry
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...
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
2014-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...
Computational synthetic geometry
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...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
2016-01-01
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
Wetterich, C
2012-01-01
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
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...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
2015-01-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
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...
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.
FROMS3D: New Software for 3-D Visualization of Fracture Network System in Fractured Rock Masses
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.
Hiszpanski, Anna Maria
Molecular semiconductors have generated significant interest for their potential use in lightweight and mechanically flexible electronic devices. Yet, predicting how new molecular semiconductors will perform in devices remains a challenge because devices are comprised of polycrystalline thin films of molecular semiconductors, and charge transport in these films depends greatly on the details of their microstructure whose heterogeneities can span multiple length scales. The microstructure typically evolves during deposition, and thus developing organic electronics not only hinges on the success of materials discovery, but also on the ability to fine-tune deposition and processing parameters to access the thin-film structure most conducive for charge transport. This thesis explores chemical modification of a non-planar organic semiconductor, contorted hexabenzocoronene, cHBC, to tune its optoelectronic properties and processing strategies to induce structural changes in thin films. We primarily explore fluorine- and chlorine-substitution at the peripheral aromatic rings of cHBC to lower its energy levels and optical bandgap, and we demonstrate such halogenated derivatives as electron acceptors in organic solar cells. Substitution with these larger atoms also increases cHBC's intramolecular steric hindrance, providing access to an alternative molecular conformation with an order of magnitude higher solubility and systematic shifts in absorption and emission characteristics. cHBC's non-planarity provides an added dimension of tunability as it frustrates crystallization during deposition, producing amorphous films that can be subsequently crystallized with post-deposition processing. Decoupling structural development from deposition allows us to fabricate transistors from differently treated cHBC films and elucidate the effects of changes in film structure on charge transport, as measured by the field-effect mobility. With different processing, the extent of c
Case study: the impact of VSB fracturing
Dillon, Brian; Norris, Tim
2008-05-01
Yield of a Variable Shaped Beam (VSB) created photomask is directly related to the quality of the fracture. The quality of a fracture is determined by three criteria: split CDs, slivers, and fracture consistency. Split CDs of figures whose widths are under the beam's shot size affect the quality due to adding an unnecessary shot registration error. Slivers, or extremely skinny shots, are harmful because they increase write time, adversely affect lithography patterning, and subsequently can cause inspection errors. Inconsistent fracturing of identical geometry compounds these issues that affect uniformity. Testmask structures devoted to grading the impact of slivers and consistency will be created, manufactured, and measured to enable statistical analysis of fracture data. These structures will be systematically designed to cover a wide range of sliver widths and feature geometries. The mean to target will be evaluated for these test structures, and from this, impact on CD linearity and CD uniformity can be judged. The effect of slivers on write time will be discussed in a more general scope. When evaluating the impact of slivers, five criteria should be investigated: sliver length, sliver width, proximity, avoidability, and location. Each of these criteria either affect lithography or write time. Determining how to define the maximum width of a sliver is fracture algorithm dependent, but this paper gives guidelines that should ease that process. The goal is to fracture identical geometry in an identical fashion, regardless of orientation or mirroring, while making the shots as large as possible and avoiding slivers; and when avoiding a sliver is impossible, trying to embed the sliver between large shots.
The Geometry of Conventionality
Weatherall, James Owen
2013-01-01
Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.
Bowyer, Adrian
1983-01-01
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
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
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Geometry of elastic hydrofracturing by injection of an over pressured non-Newtonian Fluid
Cerca, Mariano; Barrientos, Bernardino; Soto, Enrique; Mares, Carlos
2009-01-01
The nucleation and propagation of hydrofractures by injection of over pressured fluids in an elastic and isotropic medium are studied experimentally. Non-Newtonian fluids are injected inside a gelatine whose mechanical properties are assumed isotropic at the experimental strain rates. Linear elastic theory predicts that plastic deformation associated to breakage of gelatin bonds is limited to a small zone ahead of the tip of the propagating fracture and that propagation will be maintained while the fluid pressure exceeds the normal stress to the fracture walls (Ch\\'avez-\\'Alvarez,2008) (i.e., the minimum compressive stress), resulting in a single mode I fracture geometry. However, we observed the propagation of fractures type II and III as well as nucleation of secondary fractures, with oblique to perpendicular trajectories with respect to the initial fracture. In the Video (http://hdl.handle.net/1813/14122) experimental evidence shows that the fracture shape depends on the viscoelastic properties of gelatine...
DEFF Research Database (Denmark)
Mosthaf, Klaus; Rosenberg, L.; Balbarini, Nicola
approaches have been developed to describe contaminant transport in fractured media, such as the discrete fracture (with various fracture geometries), equivalent porous media (with and without anisotropy), and dual porosity models. However, these modeling concepts are not well tested for limestone geologies...... of field data is the determination of relevant hydraulic properties and interpretation of aqueous and solid phase contaminant concentration sampling data. Traditional water sampling has a bias towards fracture sampling, however concentrations in the limestone matrix are needed for assessing contaminant...
Non-planar femtosecond enhancement cavity for VUV frequency comb applications
Winkler, Georg; Seres, Jozsef; Seres, Enikoe; Schumm, Thorsten
2016-01-01
External passive femtosecond enhancement cavities (fsECs) are widely used to increase the efficiency of non-linear conversion processes like high harmonic generation (HHG) at high repetition rates. Their performance is often limited by beam ellipticity, caused by oblique incidence on spherical focusing mirrors. We introduce a novel three-dimensionally folded variant of the typical planar bow-tie resonator geometry that guarantees circular beam profiles, maintains linear polarization, and allows for a significantly tighter focus as well as a larger beam cross-section on the cavity mirrors. The scheme is applied to improve focusing in a Ti:Sapphire based VUV frequency comb system, targeting the 5th harmonic around 160 nm (7.8 eV) towards high-precision spectroscopy of the low-energy isomer state of Thorium-229. It will also be beneficial in fsEC-applications with even higher seeding and intracavity power where the damage threshold of the mirrors becomes a major concern.
Cox, Bryan D; Muccio, Donald D; Hamilton, Tracy P
2013-05-01
Retinoic acids and other vitamin A analogs contain a trimethylcyclohexenyl ring in conjugation with a polyene chain joined at carbon-6 (C6) and carbon-7 (C7). A MP2-SCS/cc-pVDZ// B3LYP/6-31G(d) 2-D potential energy surface was computed for all-trans retinoic acid, which had 6 minima (3 enantiomeric pairs). The global minima were distorted s-gauche enantiomers (6-7 = 53°) with half-chair conformations of the ring. Distorted s-gauche enantiomers (6-7 = 55°) with inverted half-chair ring conformations were 1.7 kJ/mol above the global minima. The s-trans enantiomers (6-7 = 164°) were 11.3 kJ/mol above the global minima. Steric energies were computed by the method of Guo and Karplus to identify key structural elements in retinoic acids which determines their conformation. Small molecule crystal structures in the CCDC database with trimethylcyclohexenyl ring and exocyclic double bonds have ring-chain geometries near to one of the 6 energy minima of retinoic acids, except for retinaldehyde iminium cations.
Universal correlators from geometry
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)
Universal Correlators from Geometry
Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Universal Correlators from Geometry
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-01-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
Sliding vane geometry turbines
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.
Diophantine geometry an introduction
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.
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.
Advanced geometries and regimes
Energy Technology Data Exchange (ETDEWEB)
Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
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".
Spacetime and Euclidean geometry
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.
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...
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…
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 ...
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.
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…
Danielson, Michelle E.; Beck, Thomas J.; Lian, YinJuan; Karlamangla, Arun S.; Greendale, Gail A; Ruppert, Kristine; Lo, Joan; Greenspan, Susan; Vuga, Marike; Cauley, Jane A.
2013-01-01
Racial/ethnic origin plays an important role in fracture risk. Racial/ethnic differences in fracture rates cannot be fully explained by bone mineral density (BMD). Studies examining the influence of bone geometry and strength on fracture risk have focused primarily on older adults and have not included people from diverse racial/ethnic backgrounds. Our goal was to explore racial/ethnic differences in hip geometry and strength in a large sample of midlife women. We performed Hip Structure Anal...
... the most widely used by doctors is the Salter-Harris system, described below. Type I Fractures These ... incidence of growth plate fractures peaks in adolescence. Salter-Harris classification of growth plate fractures. AAOS does ...
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.
Zou, Yi; Lin, Hongtao; Li, Lan; Moreel, Loise; Zhou, Jie; Du, Qingyang; Ogbuu, Okechukwu; Danto, Sylvain; Musgraves, J David; Richardson, Kathleen; Dobson, Kevin D; Birkmire, Robert; Hu, Juejun
2013-01-01
This paper reports a versatile, roll-to-roll and backend compatible technique for the fabrication of high-index-contrast photonic structures on both silicon and plastic substrates. The fabrication technique combines low-temperature chalcogenide glass film deposition and resist-free single-step thermal nanoimprint to process low-loss (1.6 dB/cm), sub-micron single-mode waveguides with a smooth surface finish using simple contact photolithography. Using this approach, the first chalcogenide glass micro-ring resonators are fabricated by thermal nanoimprint. The devices exhibit an ultra-high quality-factor of 400,000 near 1550 nm wavelength, which represents the highest value reported in chalcogenide glass micro-ring resonators. Furthermore, sub-micron nanoimprint of chalcogenide glass films on non-planar plastic substrates is demonstrated, which establishes the method as a facile route for monolithic fabrication of high-index-contrast devices on a wide array of unconventional substrates.
Badawi, Hassan M
2009-04-01
The structural stability and C-N internal rotations of phenylurea and phenylthiourea were investigated by DFT-B3LYP and ab initio MP2 and MP4//MP2 calculations with 6-311G** and/or 6-311+G** basis sets. The complex multirotor internal rotations in phenylurea and phenylthiourea were investigated at the B3LYP/6-311+G** level of theory from which several clear minima were predicted in the calculated potential energy scans of both molecules. For phenylurea two minima that correspond to non-planar- (CNCC dihedral angle of about 45 degrees ) cis (CNCO dihedral angle is near 0 degrees ) and trans (CNCO dihedral angle is near 180 degrees ) structures were predicted to have real frequency. For phenylthiourea only the non-planar-trans structure was predicted to be the low energy minimum for the molecule. The vibrational frequencies of the lowest energy non-planar-trans conformer of each of the two molecules were computed at the B3LYP level and tentative vibrational assignments were provided on the basis of normal coordinate analysis and experimental infrared and Raman data.
Badawi, Hassan M.
2009-04-01
The structural stability and C-N internal rotations of phenylurea and phenylthiourea were investigated by DFT-B3LYP and ab initio MP2 and MP4//MP2 calculations with 6-311G** and/or 6-311+G** basis sets. The complex multirotor internal rotations in phenylurea and phenylthiourea were investigated at the B3LYP/6-311+G** level of theory from which several clear minima were predicted in the calculated potential energy scans of both molecules. For phenylurea two minima that correspond to non-planar- (CNCC dihedral angle of about 45°) cis (CNCO dihedral angle is near 0°) and trans (CNCO dihedral angle is near 180°) structures were predicted to have real frequency. For phenylthiourea only the non- planar- trans structure was predicted to be the low energy minimum for the molecule. The vibrational frequencies of the lowest energy non-planar-trans conformer of each of the two molecules were computed at the B3LYP level and tentative vibrational assignments were provided on the basis of normal coordinate analysis and experimental infrared and Raman data.
An introduction to Minkowski geometries
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
Ghosh, Aritra; Ganguly, Ranjan; Schutzius, Thomas M; Megaridis, Constantine M
2014-05-07
Surface tension driven transport of liquids on open substrates offers an enabling tool for open micro total analysis systems that are becoming increasingly popular for low-cost biomedical diagnostic devices. The present study uses a facile wettability patterning method to produce open microfluidic tracks that - due to their shape, surface texture and chemistry - are capable of transporting a wide range of liquid volumes (~1-500 μL) on-chip, overcoming viscous and other opposing forces (e.g., gravity) at the pertinent length scales. Small volumes are handled as individual droplets, while larger volumes require repeated droplet transport. The concept is developed and demonstrated with coatings based on TiO2 filler particles, which, when present in adequate (~80 wt.%) quantities within a hydrophobic fluoroacrylic polymer matrix, form composites that are intrinsically superhydrophobic. Such composite coatings become superhydrophilic upon exposure to UV light (390 nm). A commercial laser printer-based photo-masking approach is used on the coating for spatially selective wettability conversion from superhydrophobic to superhydrophilic. Carefully designed wedge-patterned surface tension confined tracks on the open-air devices move liquid on them without power input, even when acting against gravity. Simple designs of wettability patterning are used on versatile substrates (e.g., metals, polymers, paper) to demonstrate complex droplet handling tasks, e.g., merging, splitting and metered dispensing, some of which occur in 3-D geometries. Fluid transport rates of up to 350 μL s(-1) are attained. Applicability of the design on metal substrates allows these devices to be used also for other microscale engineering applications, e.g., water management in fuel cells.
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.
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.
Klaue, Kaj
2004-09-01
The Chopart articular space was described by François Chopart (1743-1795) as a practical space for amputations in cases of distal foot necrosis. It corresponds to the limit between the anatomical hind-foot and the mid-foot. The bones involved are the talus and the calcaneus proximally, and the navicular and the cuboid distally. This space thus holds two functionally distinct entities, the anterior part of the coxa pedis (an essential functional joint) and the calcaneo-cuboidal joint,which can be considered to be an "adaptive joint" within a normal foot. Trauma to this region may cause fractures and/or dislocations and, in high energy trauma,compartment syndromes. Principles of treatment are immediate reduction of dislocations and realignment of the medial and lateral column of the foot in length and orientation. Open reduction and internal fixation of talus and navicular fractures are often indicated to restore the "coxa pedis". Open reconstruction or fusion in correct length of the calcaneo-cuboidal joint is occasionally indicated. Salvage procedures in malunions include navicular osteotomies and calcaneo-cuboidal bone block fusions. Treatment of joint destructions, especially involving the talo-navicular joint, include triple arthrodesis.
Electrical and Magnetic Imaging of Proppants in Shallow Hydraulic Fractures
Denison, J. L. S.; Murdoch, L. C.; LaBrecque, D. J.; Slack, W. W.
2015-12-01
Hydraulic fracturing is an important tool to increase the productivity of wells used for oil and gas production, water resources, and environmental remediation. Currently there are relatively few tools available to monitor the distribution of proppants within a hydraulic fracture, or the propagation of the fracture itself. We have been developing techniques for monitoring hydraulic fractures by injecting electrically conductive, dielectric, or magnetically permeable proppants. We then use the resulting contrast with the enveloping rock to image the proppants using geophysical methods. Based on coupled laboratory and numerical modeling studies, three types of proppants were selected for field evaluation. Eight hydraulic fractures were created near Clemson, SC in May of 2015 by injecting specialized proppants at a depth of 1.5 m. The injections created shallow sub-horizontal fractures extending several meters from the injection point.Each cell had a dense array of electrodes and magnetic sensors on the surface and four shallow vertical electrode arrays that were used to obtain data before and after hydraulic fracturing. Net vertical displacement and transient tilts were also measured. Cores from 130 boreholes were used to characterize the general geometries, and trenching was used to characterize the forms of two of the fractures in detail. Hydraulic fracture geometries were estimated by inverting pre- and post-injection geophysical data. Data from cores and trenching show that the hydraulic fractures were saucer-shaped with a preferred propagation direction. The geophysical inversions generated images that were remarkably similar in form, size, and location to the ground truth from direct observation. Displacement and tilt data appear promising as a constraint on fracture geometry.
Fracture characterisation using geoelectric null-arrays
Falco, Pierik; Negro, François; Szalai, Sándor; Milnes, Ellen
2013-06-01
The term "geoelectric null-array" is used for direct current electrode configurations yielding a potential difference of zero above a homogeneous half-space. This paper presents a comparative study of the behaviour of three null-arrays, midpoint null-array (MAN), Wenner-γ null-array and Schlumberger null-array in response to a fracture, both in profiling and in azimuthal mode. The main objective is to determine which array(s) best localise fractures or best identify their orientation. Forward modelling of the three null-arrays revealed that the Wenner-γ and Schlumberger null-arrays localise vertical fractures the most accurately, whilst the midpoint null-array combined with the Schlumberger null-array allows accurate orientation of a fracture. Numerical analysis then served as a basis to interpret the field results. Field test measurements were carried out above a quarry in Les Breuleux (Switzerland) with the three null-arrays and classical arrays. The results were cross-validated with quarry-wall geological mapping. In real field circumstances, the Wenner-γ null-array proved to be the most efficient and accurate in localising fractures. The orientations of the fractures according to the numerical results were most efficiently determined with the midpoint null-array, whilst the Schlumberger null-array adds accuracy to the results. This study shows that geoelectrical null-arrays are more suitable than classical arrays for the characterisation of fracture geometry.
Hydraulic fracture model comparison study: Complete results
Energy Technology Data Exchange (ETDEWEB)
Warpinski, N.R. [Sandia National Labs., Albuquerque, NM (United States); Abou-Sayed, I.S. [Mobil Exploration and Production Services (United States); Moschovidis, Z. [Amoco Production Co. (US); Parker, C. [CONOCO (US)
1993-02-01
Large quantities of natural gas exist in low permeability reservoirs throughout the US. Characteristics of these reservoirs, however, make production difficult and often economic and stimulation is required. Because of the diversity of application, hydraulic fracture design models must be able to account for widely varying rock properties, reservoir properties, in situ stresses, fracturing fluids, and proppant loads. As a result, fracture simulation has emerged as a highly complex endeavor that must be able to describe many different physical processes. The objective of this study was to develop a comparative study of hydraulic-fracture simulators in order to provide stimulation engineers with the necessary information to make rational decisions on the type of models most suited for their needs. This report compares the fracture modeling results of twelve different simulators, some of them run in different modes for eight separate design cases. Comparisons of length, width, height, net pressure, maximum width at the wellbore, average width at the wellbore, and average width in the fracture have been made, both for the final geometry and as a function of time. For the models in this study, differences in fracture length, height and width are often greater than a factor of two. In addition, several comparisons of the same model with different options show a large variability in model output depending upon the options chosen. Two comparisons were made of the same model run by different companies; in both cases the agreement was good. 41 refs., 54 figs., 83 tabs.
Fractures of the distal radius (Colles' fracture)
National Research Council Canada - National Science Library
João Carlos Belloti; João Baptista Gomes dos Santos; Álvaro Nagib Atallah; Walter Manna Albertoni; Flavio Faloppa
2007-01-01
CONTEXT AND OBJECTIVE: Although Colles' fracture is a common clinical situation for the orthopedist, we did not find any information in the literature that would allow safe decision-making on the best treatment for each fracture type...
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Spectral Geometry and Causality
Kopf, T
1996-01-01
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of...
Multivariate calculus and geometry
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.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Differential geometry and thermodynamics
Quevedo, H
2003-01-01
In this work we present the first steps of a new approach to the study of thermodynamics in the context of differential geometry. We introduce a fundamental differential 1-form and a metric on a pseudo-Euclidean manifold coordinatized by means of the extensive thermodynamic variables. The study of the connection and the curvature of these objects is initialized in this work by using Cartan structure equations. (Author)
Krauss, L M; 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.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
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 parame...... 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....
Integral geometry and holography
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.
Hilbert, completeness and geometry
Directory of Open Access Journals (Sweden)
Giorgio Venturi
2011-11-01
Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.
Integral geometry and valuations
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...
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
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
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,
Sliding contact fracture of dental ceramics: Principles and validation.
Ren, Linlin; Zhang, Yu
2014-07-01
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.
Martin-Short, R.; Edmiston, J. K.
2015-12-01
Typical hydraulic fracturing operations involve the use of a large quantity of water, which can be problematic for several reasons including possible formation (permeability) damage, disposal of waste water, and the use of precious local water resource. An alternate reservoir permeability enhancing technology not requiring water is cryogenic fracturing. This method induces controlled fracturing of rock formations by thermal shock and has potentially important applications in the geothermal and hydrocarbon industries. In this process, cryogenic fluid—such as liquid nitrogen—is injected into the subsurface, causing fracturing due to thermal gradients. These fractures may improve the formation permeability relative to that achievable by hydraulic fracturing alone. We conducted combined laboratory visualization and numerical simulations studies of thermal-shock-induced fracture initiation and propagation resulting from liquid nitrogen injection in rock and analog materials. The experiment used transparent soda-lime glass cubes to facilitate real-time visualization of fracture growth and the fracture network geometry. In this contribution, we report the effect of overall temperature difference between cryogenic fluid and solid material on the produced fracture network, by pre-heating the glass cubes to several temperatures and injecting liquid nitrogen. Temperatures are monitored at several points by thermocouple and the fracture evolution is captured visually by camera. The experiment was modeled using a customized, thermoelastic, fracture-capable numerical simulation code based on peridynamics. The performance of the numerical code was validated by the results of the laboratory experiments, and then the code was used to study the different factors affecting a cryogenic fracturing operation, including the evolution of residual stresses and constitutive relationships for material failure. In complex rock such as shale, understanding the process of cryogenic
Jayavelu, Perumal; Riaz, R; Tariq Salam, A R; Saravanan, B; Karthick, R
2016-10-01
Fracture of mandible can be classified according to its anatomical location, in which condylar fracture is the most common one overall and is missed on clinical examination. Due to the unique geometry of the mandible and temporomandibular joint, without treatment the fractures can result in marked pain, dysfunction, and deformity. The condylar fracture may be further classified depending on the sides involved: unilateral/bilateral, depending on the height of fracture: intracapsular (within the head of condyle), extracapsular - head and neck (high condyle fracture), and subcondylar (low condyle fracture), and depending on displacement: nondisplaced, displaced (anteromedially, medially, and lateral), and dislocated. The clinical features include swelling and tenderness over the temporomandibular joint region, restricted mouth opening, and anterior open bite. A 34-year-old male patient reported to the Department of Oral and Maxillofacial Surgery at Madha Dental College and Hospital; suffered fall trauma resulting in bilateral condyle fracture, dentoalveolar fracture in mandible with restricted mouth opening, and anterior open bite.
Effect of Natural Fractures on Hydraulic Fracturing
Ben, Y.; Wang, Y.; Shi, G.
2012-12-01
Hydraulic Fracturing has been used successfully in the oil and gas industry to enhance oil and gas production in the past few decades. Recent years have seen the great development of tight gas, coal bed methane and shale gas. Natural fractures are believed to play an important role in the hydraulic fracturing of such formations. Whether natural fractures can benefit the fracture propagation and enhance final production needs to be studied. Various methods have been used to study the effect of natural fractures on hydraulic fracturing. Discontinuous Deformation Analysis (DDA) is a numerical method which belongs to the family of discrete element methods. In this paper, DDA is coupled with a fluid pipe network model to simulate the pressure response in the formation during hydraulic fracturing. The focus is to study the effect of natural fractures on hydraulic fracturing. In particular, the effect of rock joint properties, joint orientations and rock properties on fracture initiation and propagation will be analyzed. The result shows that DDA is a promising tool to study such complex behavior of rocks. Finally, the advantages of disadvantages of our current model and future research directions will be discussed.
Nihei, Kurt T.; Yi, Weidong; Myer, Larry R.; Cook, Neville G. W.; Schoenberg, Michael
1999-03-01
The properties of guided waves which propagate between two parallel fractures are examined. Plane wave analysis is used to obtain a dispersion equation for the velocities of fracture channel waves. Analysis of this equation demonstrates that parallel fractures form an elastic waveguide that supports two symmetric and two antisymmetric dispersive Rayleigh channel waves, each with particle motions and velocities that are sensitive to the normal and tangential stiffnesses of the fractures. These fracture channel waves degenerate to shear waves when the fracture stiffnesses are large, to Rayleigh waves and Rayleigh-Lamb plate waves when the fracture stiffnesses are low, and to fracture interface waves when the fractures are either very closely spaced or widely separated. For intermediate fracture stiffnesses typical of fractured rock masses, fracture channel waves are dispersive and exhibit moderate to strong localization of guided wave energy between the fractures. The existence of these waves is examined using laboratory acoustic measurements on a fractured marble plate. This experiment confirms the distinct particle motion of the fundamental antisymmetric fracture channel wave (A0 mode) and demonstrates the ease with which a fracture channel wave can be generated and detected.
Traumatic thoracolumbar spine fractures
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
Shank, Nathaniel I; Pham, Ha H; Waggoner, Alan S; Armitage, Bruce A
2013-01-09
The cyanine dye thiazole orange (TO) is a well-known fluorogenic stain for DNA and RNA, but this property precludes its use as an intracellular fluorescent probe for non-nucleic acid biomolecules. Further, as is the case with many cyanines, the dye suffers from low photostability. Here, we report the synthesis of a bridge-substituted version of TO named α-CN-TO, where the central methine hydrogen of TO is replaced by an electron withdrawing cyano group, which was expected to decrease the susceptibility of the dye toward singlet oxygen-mediated degradation. An X-ray crystal structure shows that α-CN-TO is twisted drastically out of plane, in contrast to TO, which crystallizes in the planar conformation. α-CN-TO retains the fluorogenic behavior of the parent dye TO in viscous glycerol/water solvent, but direct irradiation and indirect bleaching studies showed that α-CN-TO is essentially inert to visible light and singlet oxygen. In addition, the twisted conformation of α-CN-TO mitigates nonspecific binding and fluorescence activation by DNA and a previously selected TO-binding protein and exhibits low background fluorescence in HeLa cell culture. α-CN-TO was then used to select a new protein that binds and activates fluorescence from the dye. The new α-CN-TO/protein fluoromodule exhibits superior photostability to an analogous TO/protein fluoromodule. These properties indicate that α-CN-TO will be a useful fluorogenic dye in combination with specific RNA and protein binding partners for both in vitro and cell-based applications. More broadly, structural features that promote nonplanar conformations can provide an effective method for reducing nonspecific binding of cationic dyes to nucleic acids and other biomolecules.
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
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Geometry for the Secondary School
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Linear connections on matrix geometries
Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad
1994-01-01
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.
Energy Technology Data Exchange (ETDEWEB)
Kanis, John A. [WHO Collaborating Centre for Metabolic Bone Diseases, University of Sheffield Medical School, Beech Hill Road, Sheffield S10 2RX (United Kingdom)], E-mail: w.j.pontefract@sheffield.ac.uk; Johansson, Helena; Oden, Anders [WHO Collaborating Centre for Metabolic Bone Diseases, University of Sheffield Medical School, Beech Hill Road, Sheffield S10 2RX (United Kingdom); McCloskey, Eugene V. [WHO Collaborating Centre for Metabolic Bone Diseases, University of Sheffield Medical School, Beech Hill Road, Sheffield S10 2RX (United Kingdom); Osteoporosis Centre, Northern General Hospital, Sheffield (United Kingdom)
2009-09-15
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.
Editors, LearningExpress
2010-01-01
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of 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 is an invaluable resource for both students and adults.
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
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
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
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
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
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.
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
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
[Periprosthetic Acetabulum Fractures].
Schreiner, A J; Stuby, F; de Zwart, P M; Ochs, B G
2016-12-01
In contrast to periprosthetic fractures of the femur, periprosthetic fractures of the acetabulum are rare complications - both primary fractures and fractures in revision surgery. This topic is largely under-reported in the literature; there are a few case reports and no long term results. Due to an increase in life expectancy, the level of patients' activity and the number of primary joint replacements, one has to expect a rise in periprosthetic complications in general and periprosthetic acetabular fractures in particular. This kind of fracture can be intra-, peri- or postoperative. Intraoperative fractures are especially associated with insertion of cementless press-fit acetabular components or revision surgery. Postoperative periprosthetic fractures of the acetabulum are usually related to osteolysis, for example, due to polyethylene wear. There are also traumatic fractures and fractures missed intraoperatively that lead to some kind of insufficiency fracture. Periprosthetic fractures of the acetabulum are treated conservatively if the implant is stable and the fracture is not dislocated. If surgery is needed, there are many possible different surgical techniques and challenging approaches. That is why periprosthetic fractures of the acetabulum should be treated by experts in pelvic surgery as well as revision arthroplasty and the features specific to the patient, fracture and prosthetic must always be considered. Georg Thieme Verlag KG Stuttgart · New York.
Simulation of the nutrient supply in fracture healing.
Chen, G; Niemeyer, F; Wehner, T; Simon, U; Schuetz, M A; Pearcy, M J; Claes, L E
2009-11-13
The healing process for bone fractures is sensitive to mechanical stability and blood supply at the fracture site. Most currently available mechanobiological algorithms of bone healing are based solely on mechanical stimuli, while the explicit analysis of revascularization and its influences on the healing process have not been thoroughly investigated in the literature. In this paper, revascularization was described by two separate processes: angiogenesis and nutrition supply. The mathematical models for angiogenesis and nutrition supply have been proposed and integrated into an existing fuzzy algorithm of fracture healing. The computational algorithm of fracture healing, consisting of stress analysis, analyses of angiogenesis and nutrient supply, and tissue differentiation, has been tested on and compared with animal experimental results published previously. The simulation results showed that, for a small and medium-sized fracture gap, the nutrient supply is sufficient for bone healing, for a large fracture gap, non-union may be induced either by deficient nutrient supply or inadequate mechanical conditions. The comparisons with experimental results demonstrated that the improved computational algorithm is able to simulate a broad spectrum of fracture healing cases and to predict and explain delayed unions and non-union induced by large gap sizes and different mechanical conditions. The new algorithm will allow the simulation of more realistic clinical fracture healing cases with various fracture gaps and geometries and may be helpful to optimise implants and methods for fracture fixation.
Analytic crack solutions for tilt fields around hydraulic fractures
Energy Technology Data Exchange (ETDEWEB)
Warpinski, N.R.
2000-01-05
The recent development of downhole tiltmeter arrays for monitoring hydraulic fractures has provided new information on fracture growth and geometry. These downhole arrays offer the significant advantages of being close to the fracture (large signal) and being unaffected by the free surface. As with surface tiltmeter data, analysis of these measurements requires the inversion of a crack or dislocation model. To supplement the dislocation models of Davis [1983], Okada [1992] and others, this work has extended several elastic crack solutions to provide tilt calculations. The solutions include constant-pressure 2D, penny-shaped, and 3D-elliptic cracks and a 2D-variable-pressure crack. Equations are developed for an arbitrary inclined fracture in an infinite elastic space. Effects of fracture height, fracture length, fracture dip, fracture azimuth, fracture width and monitoring distance on the tilt distribution are given, as well as comparisons with the dislocation model. The results show that the tilt measurements are very sensitive to the fracture dimensions, but also that it is difficult to separate the competing effects of the various parameters.
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.
Akagi, T; Bonis, J; Chaikovska, I; Chiche, R; Cizeron, R; Cohen, M; Cormier, E; Cornebise, P; Delerue, N; Flaminio, R; Funahashi, S; Jehanno, D; Honda, Y; Labaye, F; Lacroix, M; Marie, R; Miyoshi, S; Nagata, S; Omori, T; Peinaud, Y; Pinard, L; Shimizu, H; Soskov, V; Takahashi, T; Tanaka, R; Terunuma, T; Urakawa, J; Variola, A; Zomer, F
2011-01-01
As part of the positron source R&D for future $e^+-e^-$ colliders and Compton based compact light sources, a high finesse non-planar four-mirror Fabry-Perot cavity has recently been installed at the ATF (KEK, Tsukuba, Japan). The first measurements of the gamma ray flux produced with a such cavity using a pulsed laser is presented here. We demonstrate the production of a flux of 2.7 $\\pm$ 0.2 gamma rays per bunch crossing ($\\sim3\\times10^6$ gammas per second) during the commissioning.
Directory of Open Access Journals (Sweden)
STOYAN SLAVOV
2015-12-01
Full Text Available The paper presents the design of a specialized instrument for formation different types of regular microshape roughness on functional surfaces of parts with non-planar macroshape by using the process, called “surface plastic deformation”. The elements of which it is constructed are explained and the results from carried out strength and deformation analysis, obtained by Finite Element Method, conducted using the Simulation module of the SolidWorks are also represented. On this basis some advantages and limitations of some of the surface plastic deformation process technological parameters are identified and recommendations for its implementation are given.
Analysis of fracture patterns and local stress field variations in fractured reservoirs
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
Imaging of vertebral fractures
Directory of Open Access Journals (Sweden)
Ananya Panda
2014-01-01
Full Text Available Vertebral fracture is a common clinical problem. Osteoporosis is the leading cause of non-traumatic vertebral fracture. Often, vertebral fractures are not clinically suspected due to nonspecific presentation and are overlooked during routine interpretation of radiologic investigations. Moreover, once detected, many a times the radiologist fails to convey to the clinician in a meaningful way. Hence, vertebral fractures are a constant cause of morbidity and mortality. Presence of vertebral fracture increases the chance of fracture in another vertebra and also increases the risk of subsequent hip fracture. Early detection can lead to immediate therapeutic intervention improving further the quality of life. So, in this review, we wish to present a comprehensive overview of vertebral fracture imaging along with an algorithm of evaluation of vertebral fractures.
Comparison of Measured and Modelled Hydraulic Conductivities of Fractured Sandstone Cores
Baraka-Lokmane, S.; Liedl, R.; Teutsch, G.
- A new method for characterising the detailed fracture geometry in sandstone cores is presented. This method is based on the impregnation of samples with coloured resin, without significant disturbance of the fractures. The fractures are made clearly visible by the resin, thus allowing the fracture geometry to be examined digitally. In order to model the bulk hydraulic conductivity, the samples are sectioned serially perpendicular to the flow direction. The hydraulic conductivity of individual sections is estimated by summing the contribution of the matrix and each fracture from the digital data. Finally, the hydraulic conductivity of the bulk sample is estimated by a harmonic average in series along the flow path. Results of this geometrical method are compared with actual physical conductivity values measured from fluid experiments carried out prior to sectioning. The predicted conductivity from the fracture geometry parameters (e.g., fracture aperture, fracture width, fracture length and fracture relative roughness all measured using an optical method) is in good agreement with the independent physical measurements, thereby validating the approach.
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
Byron, S.
1985-03-01
The low pressure gas-filled thyratron is scalable in the long dimension. Internally the tube is formed as a tetrode, with an auxiliary grid placed between the cathode and the control grid. A dc or pulsed power source drives the auxiliary grid both to insure uniform cathode emission and to provide a grid-cathode plasma prior to commutation. The high voltage holdoff structure consists of the anode, the control grid and its electrostatic shielding baffles, and a main quartz insulator. A small gas flow supply and exhaust system is used that eliminates the need for a hydrogen reservoir and permits other gases, such as helium, to be used. The thyratron provides a low inductance, high current, long lifetime switch configuration: useful for switch-on applications involving large scale lasers and other similar loads that are distributed in a linear geometry.
Critique of information geometry
Energy Technology Data Exchange (ETDEWEB)
Skilling, John, E-mail: skilling@eircom.net [Maximum Entropy Data Consultants Ltd, Kenmare (Ireland)
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
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.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Stockem, A.; Fiuza, F.; Silva, L. O.; Antici, P.; Margarone, D.; Korn, G.
2013-08-01
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project. At the request of the Proceedings Editors and Dr. Stepan Bulanov, University of California, Berkeley, the above article has been updated to include three additional authors: A. Stockem, F. Fiuza, and L. O. Silva. All additional authors have consented to their name being added to the paper. Furthermore, the updated article PDF contains amendments to a number of references as detailed within the pages attached to the end of the updated article PDF file. The updated article was re-published on 8 August 2013.
Fracture Criterion for Fracture Mechanics of Magnets
Institute of Scientific and Technical Information of China (English)
潘灏; 杨文涛
2003-01-01
The applicability and limitation of some fracture criteria in the fracture mechanics of magnets are studied.It is shown that the magnetic field intensity factor can be used as a fracture criterion when the crack in a magnet is only affected by a magnetic field. For some magnetostrictive materials in which the components of magnetostriction strain do not satisfy the compatibility equation of deformation, the stress intensity factor can no longer be effectively applicable as a fracture criterion when the crack in a magnet is affected by a magnetic field and mechanical loads simultaneously.
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Klein geometries, parabolic geometries and differential equations of finite type
Abadoglu, Ender
2009-01-01
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).
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.
Higher geometry an introduction to advanced methods in analytic geometry
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
Alierta, J A; Pérez, M A; Seral, B; García-Aznar, J M
2016-09-01
The aim of this study is to evaluate the fracture union or non-union for a specific patient that presented oblique fractures in tibia and fibula, using a mechanistic-based bone healing model. Normally, this kind of fractures can be treated through an intramedullary nail using two possible configurations that depends on the mechanical stabilisation: static and dynamic. Both cases are simulated under different fracture geometries in order to understand the effect of the mechanical stabilisation on the fracture healing outcome. The results of both simulations are in good agreement with previous clinical experience. From the results, it is demonstrated that the dynamization of the fracture improves healing in comparison with a static or rigid fixation of the fracture. This work shows the versatility and potential of a mechanistic-based bone healing model to predict the final outcome (union, non-union, delayed union) of realistic 3D fractures where even more than one bone is involved.
Triaxial coreflood study of the hydraulic fracturing of Utica Shale
Carey, J. W.; Frash, L.; Viswanathan, H. S.
2015-12-01
One of the central questions in unconventional oil and gas production research is the cause of limited recovery of hydrocarbon. There are many hypotheses including: 1) inadequate penetration of fractures within the stimulated volume; 2) limited proppant delivery; 3) multiphase flow phenomena that blocks hydrocarbon migration; etc. Underlying any solution to this problem must be an understanding of the hydrologic properties of hydraulically fractured shale. In this study, we conduct triaxial coreflood experiments using a gasket sealing mechanism to characterize hydraulic fracture development and permeability of Utica Shale samples. Our approach also includes fracture propagation with proppants. The triaxial coreflood experiments were conducted with an integrated x-ray tomography system that allows direct observation of fracture development using x-ray video radiography and x-ray computed tomography at elevated pressure. A semi-circular, fracture initiation notch was cut into an end-face of the cylindrical samples (1"-diameter with lengths from 0.375 to 1"). The notch was aligned parallel with the x-ray beam to allow video radiography of fracture growth as a function of injection pressure. The proppants included tungsten powder that provided good x-ray contrast for tracing proppant delivery and distribution within the fracture system. Fractures were propagated at injection pressures in excess of the confining pressure and permeability measurements were made in samples where the fractures propagated through the length of the sample, ideally without penetrating the sample sides. Following fracture development, permeability was characterized as a function of hydrostatic pressure and injection pressure. X-ray video radioadiography was used to study changes in fracture aperture in relation to permeability and proppant embedment. X-ray tomography was collected at steady-state conditions to fully characterize fracture geometry and proppant distribution.
Directory of Open Access Journals (Sweden)
Shanyong Liu
2016-05-01
Full Text Available Volume fracturing in shale gas forms complex fracture networks and increases stimulated reservoir volume through large-scale fracturing operation with plug-perforation technology. However, some perforation clusters are stimulated unevenly after fracturing. This study aims to solve this problem by analyzing the shortcomings of the conventional fracturing model and developing a coupled model based on the 2D fracture motion equation, energy conservation law, linear elastic mechanics, and stress superposition principle. First, a multi-fracture in-situ stress model was built by studying the induced stress produced by the fracture initiation to deduce the multi-fracture induced stress impact factor on the basis of the stress superposition principle. Then, the classical Perkins–Kern–Nordgren model was utilized with the crustal stress model. Finally, a precise fracturing design method was used to optimize perforation and fracturing parameters under the new model. Results demonstrate that the interference effect among fractures is the major factor causing the non-uniform propagation of each fracture. Compression on the main horizontal stress increases the net pressure. Therefore, both the degree of operation difficulty and the complexity of fracture geometry are improved. After applying the optimal design, the production is increased by 20%, and the cost is reduced by 15%.
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.
An introduction to incidence geometry
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...
Micromechanical Aspects of Hydraulic Fracturing Processes
Galindo-torres, S. A.; Behraftar, S.; Scheuermann, A.; Li, L.; Williams, D.
2014-12-01
A micromechanical model is developed to simulate the hydraulic fracturing process. The model comprises two key components. Firstly, the solid matrix, assumed as a rock mass with pre-fabricated cracks, is represented by an array of bonded particles simulated by the Discrete Element Model (DEM)[1]. The interaction is ruled by the spheropolyhedra method, which was introduced by the authors previously and has been shown to realistically represent many of the features found in fracturing and communition processes. The second component is the fluid, which is modelled by the Lattice Boltzmann Method (LBM). It was recently coupled with the spheropolyhedra by the authors and validated. An advantage of this coupled LBM-DEM model is the control of many of the parameters of the fracturing fluid, such as its viscosity and the injection rate. To the best of the authors' knowledge this is the first application of such a coupled scheme for studying hydraulic fracturing[2]. In this first implementation, results are presented for a two-dimensional situation. Fig. 1 shows one snapshot of the LBM-DEM coupled simulation for the hydraulic fracturing where the elements with broken bonds can be identified and the fracture geometry quantified. The simulation involves a variation of the underground stress, particularly the difference between the two principal components of the stress tensor, to explore the effect on the fracture path. A second study focuses on the fluid viscosity to examine the effect of the time scales of different injection plans on the fracture geometry. The developed tool and the presented results have important implications for future studies of the hydraulic fracturing process and technology. references 1. Galindo-Torres, S.A., et al., Breaking processes in three-dimensional bonded granular materials with general shapes. Computer Physics Communications, 2012. 183(2): p. 266-277. 2. Galindo-Torres, S.A., A coupled Discrete Element Lattice Boltzmann Method for the
Jia, Pin; Cheng, Linsong; Huang, Shijun; Wu, Yonghui
2016-06-01
This paper presents a semi-analytical model for the flow behavior of naturally fractured formations with multi-scale fracture networks. The model dynamically couples an analytical dual-porosity model with a numerical discrete fracture model. The small-scale fractures with the matrix are idealized as a dual-porosity continuum and an analytical flow solution is derived based on source functions in Laplace domain. The large-scale fractures are represented explicitly as the major fluid conduits and the flow is numerically modeled, also in Laplace domain. This approach allows us to include finer details of the fracture network characteristics while keeping the computational work manageable. For example, the large-scale fracture network may have complex geometry and varying conductivity, and the computations can be done at predetermined, discrete times, without any grids in the dual-porosity continuum. The validation of the semi-analytical model is demonstrated in comparison to the solution of ECLIPSE reservoir simulator. The simulation is fast, gridless and enables rapid model setup. On the basis of the model, we provide detailed analysis of the flow behavior of a horizontal production well in fractured reservoir with multi-scale fracture networks. The study has shown that the system may exhibit six flow regimes: large-scale fracture network linear flow, bilinear flow, small-scale fracture network linear flow, pseudosteady-state flow, interporosity flow and pseudoradial flow. During the first four flow periods, the large-scale fracture network behaves as if it only drains in the small-scale fracture network; that is, the effect of the matrix is negligibly small. The characteristics of the bilinear flow and the small-scale fracture network linear flow are predominantly determined by the dimensionless large-scale fracture conductivity. And low dimensionless fracture conductivity will generate large pressure drops in the large-scale fractures surrounding the wellbore. With
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......, 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...
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
Finding Proofs in Tarskian Geometry
Beeson, Michael; Wos, Larry
2016-01-01
We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some \\Otter proofs in Tarskian geometry (solving challenges issued in Wos's 1998...
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
2012-01-01
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Tibia (Shinbone) Shaft Fractures
... energy collisions, such as an automobile or motorcycle crash, are common causes of tibial sha fractures. In cases like these, the bone can be broken into several pieces (comminuted fracture). Sports injuries, such as a fall while skiing or running ...
Fractures in anisotropic media
Shao, Siyi
Rocks may be composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties of a rock to be anisotropic. Coexisting fractures and layers in rock give rise to competing mechanisms of anisotropy. For example: (1) at low fracture stiffness, apparent shear-wave anisotropy induced by matrix layering can be masked or enhanced by the presence of a fracture, depending on the fracture orientation with respect to layering, and (2) compressional-wave guided modes generated by parallel fractures can also mask the presence of matrix layerings for particular fracture orientations and fracture specific stiffness. This report focuses on two anisotropic sources that are widely encountered in rock engineering: fractures (mechanical discontinuity) and matrix layering (impedance discontinuity), by investigating: (1) matrix property characterization, i.e., to determine elastic constants in anisotropic solids, (2) interface wave behavior in single-fractured anisotropic media, (3) compressional wave guided modes in parallel-fractured anisotropic media (single fracture orientation) and (4) the elastic response of orthogonal fracture networks. Elastic constants of a medium are required to understand and quantify wave propagation in anisotropic media but are affected by fractures and matrix properties. Experimental observations and analytical analysis demonstrate that behaviors of both fracture interface waves and compressional-wave guided modes for fractures in anisotropic media, are affected by fracture specific stiffness (controlled by external stresses), signal frequency and relative orientation between layerings in the matrix and fractures. A fractured layered medium exhibits: (1) fracture-dominated anisotropy when the fractures are weakly coupled; (2) isotropic behavior when fractures delay waves that are usually fast in a layered medium; and (3) matrix-dominated anisotropy when the fractures are closed and no longer delay the signal. The
Sprains, Strains and Fractures
... Young Physicians Annual Scientific Meeting Webinars Careers in Podiatry APMA 2040 Student Profiles CPME REdRC Manage Your ... and fractures. Many fractures and sprains occur during sports. Football players are particularly vulnerable to foot and ...
... this page: //medlineplus.gov/ency/patientinstructions/000168.htm Hip fracture - discharge To use the sharing features on this page, please enable JavaScript. Hip fracture surgery is done to repair a break in ...
... neck fracture repair; Trochanteric fracture repair; Hip pinning surgery; Osteoarthritis - hip ... You may receive general anesthesia for this surgery. This means you ... spinal anesthesia . With this kind of anesthesia, medicine is ...
Metatarsal stress fractures - aftercare
... page: //medlineplus.gov/ency/patientinstructions/000553.htm Metatarsal stress fractures - aftercare To use the sharing features on ... that connect your ankle to your toes. A stress fracture is a break in the bone that ...
Periprosthetic acetabular fractures.
Benazzo, Francesco; Formagnana, Mario; Bargagliotti, Marco; Perticarini, Loris
2015-10-01
The aim of this article is to propose a diagnostic and therapeutic algorithm for the acetabular periprosthetic fractures. This article explores the current literature on the epidemiology, causes and classification of periprosthetic acetabular fractures. Integrating data with the experience of the authors, it offers a guide to diagnosis and possible therapeutic strategies. Intra-operative fractures can occur during rasping, reaming or implant impaction, and they must be treated immediately if the component(s) is (are) unstable. Post-operative fractures can be due to major trauma (acute fractures) or minor forces in bone osteolysis; it is possible to plan reconstruction and fixation according to fracture characteristics. Treatment choice depends upon fracture site and implant stability. Periprosthetic acetabular fractures are uncommon complications that can occur intra-operatively or post-operatively, and a reconstructive surgeon must be able to manage the procedure. Accurate planning and reconstruction implant are necessary to achieve good cup stability.
ModeⅠrock fracture toughness with different types of brazilian disc
Institute of Scientific and Technical Information of China (English)
YU Hai-yong; JIN Zhi-xin; JING Hai-he
2004-01-01
According to the results evaluated by researchers for mode Ⅰ rock fracture toughness measurement, a series of comparison tests with different types Brazilian discs were conducted in order to search for the simplest geometry specimens by which accurate,comparable and consistent mode Ⅰ rock fracture toughness could obtain.
The influence of lead length on the fractures associated with leading corners and sidings
CSIR Research Space (South Africa)
Turner, PA
1989-02-01
Full Text Available Stopes on three reef horizons and at various depths were examined in the vicinity of inter-panel leads. The general geometry of fractures in the vicinity of inter-panels leads is outlined. The extend of fracturing parallel to the siding between...
Planetary Image Geometry Library
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
Digital geometry in image processing
Mukhopadhyay, Jayanta
2013-01-01
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of
Initiation to global Finslerian geometry
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
Identifying osteoporotic vertebral fracture
Griffith, James F.
2015-01-01
Osteoporosis per se is not a harmful disease. It is the sequela of osteoporosis and most particularly the occurrence of osteoporotic fracture that makes osteoporosis a serious medical condition. All of the preventative measures, investigations, treatment and research into osteoporosis have one primary goal and that is to prevent the occurrence of osteoporotic fracture. Vertebral fracture is by far and away the most prevalent osteoporotic fracture. The significance and diagnosis of vertebral f...
Bone mass and microarchitecture in CKD patients with fracture.
Nickolas, Thomas L; Stein, Emily; Cohen, Adi; Thomas, Valerie; Staron, Ronald B; McMahon, Donald J; Leonard, Mary B; Shane, Elizabeth
2010-08-01
Patients with predialysis chronic kidney disease (CKD) have increased risk for fracture, but the structural mechanisms underlying this increased skeletal fragility are unknown. We measured areal bone mineral density (aBMD) by dual-energy x-ray absorptiometry at the spine, hip, and radius, and we measured volumetric BMD (vBMD), geometry, and microarchitecture by high-resolution peripheral quantitative computed tomography (HR-pQCT) at the radius and tibia in patients with CKD: 32 with fracture and 59 without fracture. Patients with fracture had lower aBMD at the spine, total hip, femoral neck, and the ultradistal radius, the last having the strongest association with fracture. By HR-pQCT of the radius, patients with fracture had lower cortical area and thickness, total and trabecular vBMD, and trabecular number and greater trabecular separation and network heterogeneity. At the tibia, patients with fracture had significantly lower cortical area, thickness, and total and cortical density. Total vBMD at both radius and tibia most strongly associated with fracture. By receiver operator characteristic curve analysis, patients with longer duration of CKD had area under the curve of >0.75 for aBMD at both hip sites and the ultradistal radius, vBMD and geometry at the radius and tibia, and microarchitecture at the tibia. In summary, patients with predialysis CKD and fractures have lower aBMD by dual-energy x-ray absorptiometry and lower vBMD, thinner cortices, and trabecular loss by HR-pQCT. These density and structural differences may underlie the increased susceptibility to fracture among patients with CKD.
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
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.
Functional integration over geometries
Mottola, E
1995-01-01
The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal 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 \\cal G, the functional measure on the coset space {\\cal M}/{\\cal 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 \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it 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 me...
Itin, Yakov
2007-01-01
The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Ma...
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.
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
Optimum Stirling engine geometry
Energy Technology Data Exchange (ETDEWEB)
Senft, J.R. [University of Wisconsin, River Walls, WI (United States). Mathematics Dept.
2002-07-01
This paper combines the author's work on mechanical efficiency of reciprocating engines with the classic Schmidt thermodynamic model for Stirling engines and revisits the problem of identifying optimal engine geometry. All previous optimizations using the Schmidt theory focused on obtaining a maximal specific indicated cyclic work. This does not necessarily produce the highest shaft output. Indeed, some optima based upon indicated work would yield engines that cannot run at all due to excessive intrinsic mechanical losses. The analysis presented in this paper shows how to optimize for shaft or brake work output. Specifically, it presents solutions to the problem of finding the piston-to-displacer swept volume ratio and phase angle which will give the maximum brake output for a given total swept volume, given temperature extremes, a given mean operating pressure, and a given engine mechanism effectiveness. The paper covers the split-cylinder or gamma-type Stirling in detail, serving as a model for similar analysis of the other Stirling engine configurations. (author)
Geusens, PP; Sambrook, P.N.; Lems, W.F.
2009-01-01
The lifetime risk of experiencing a fracture in 50-year-old men is lower (20%) than the risk in women (50%). Consequently, much less research has been carried out on osteoporosis and fracture risk in men. Differences in the risk and incidence of fractures between men and women are related to differe
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.
A Comprehensive Numerical Model for Simulating Fluid Transport in Nanopores
Zhang, Yuan; Yu, Wei; Sepehrnoori, Kamy; di, Yuan
2017-01-01
Since a large amount of nanopores exist in tight oil reservoirs, fluid transport in nanopores is complex due to large capillary pressure. Recent studies only focus on the effect of nanopore confinement on single-well performance with simple planar fractures in tight oil reservoirs. Its impacts on multi-well performance with complex fracture geometries have not been reported. In this study, a numerical model was developed to investigate the effect of confined phase behavior on cumulative oil and gas production of four horizontal wells with different fracture geometries. Its pore sizes were divided into five regions based on nanopore size distribution. Then, fluid properties were evaluated under different levels of capillary pressure using Peng-Robinson equation of state. Afterwards, an efficient approach of Embedded Discrete Fracture Model (EDFM) was applied to explicitly model hydraulic and natural fractures in the reservoirs. Finally, three fracture geometries, i.e. non-planar hydraulic fractures, non-planar hydraulic fractures with one set natural fractures, and non-planar hydraulic fractures with two sets natural fractures, are evaluated. The multi-well performance with confined phase behavior is analyzed with permeabilities of 0.01 md and 0.1 md. This work improves the analysis of capillarity effect on multi-well performance with complex fracture geometries in tight oil reservoirs.
Some effects of stress, friction and fluid flow on hydraulic fracturing
Energy Technology Data Exchange (ETDEWEB)
Hanson, M.E.; Anderson, G.D.; Shaffer, R.J.; Thorson, L.D.
1981-03-01
We are conducting a DOE funded research program which is aimed at understanding the hydraulic fracturing process, especially those phenomena and parameters which strongly affect or control the fracture geometry. Our theoretical and experimental studies consistently confirm the well known fact that in-situ stress has a primary effect on fracture geometry and that fractures propagate perpendicular to the least principal stress. In addition, we find that frictional interfaces in reservoirs can affect fracturing. We have also quantified some of the effects on fracture geometry due to frictional slippage along interfaces. We found that variation of friction along an interface can result in abrupt steps in the fracture path. These effects have been seen in the mine back of emplaced fractures and are demonstrated both theoretically and in the laboratory. Further experiments and calculations are starting to indicate the possible control of the fracture height by the vertical change in the cables to X-608A wells should be replaced, and develop v across categories of persons affected. Respondents were selected according to a purposive sampling strategy, wn are also included. The management plan for the operation of the plant is discussed. (DMC)
Large Influence of Subduction Geometry on Extreme Exhumation in Orogen Syntaxes
Ehlers, T. A.; Bendick, R. O.
2014-12-01
Some of the highest and most localized rates of lithospheric deformation in the world are observed at the transition between adjacent plate boundary subduction segments (syntaxes). The initiating perturbation of this deformation has long been attributed to vigorous, climate driven, erosional processes as observed at Nanga Parbat and Namche Barwa in the Himalaya and at Mt. St. Elias in Alaska. However, an erosion-dominated mechanism ignores the 3D geometry of curved subducting plates and changes in paleoclimate. Here we present an alternative explanation for rapid exhumation at these locations based on the 3D thermo-mechanical evolution of collisions between plates with nonplanar geometries. A set of numerical solutions and thermochronometer observations are presented for the interaction between a rigid indenter between subduction segments with an overriding viscous material. The model setup is intentionally simplified to identify how the 3D geometry of a subducting plate influences upper plate deformation, and therefore omits many of the complexities of collision interfaces, such as the transfer of mass between the downgoing and overriding plates. Temperatures are calculated using the 3D advection diffusion equation with radiogenic heat production and shear heating. The thermal and Stokes flow solutions are fully coupled and evolve throughout the simulation. Model predicted cooling ages are compared to observed cooling ages from published bedrock and detrital thermochronometer studies by calculating cooling rate dependent thermochronometer ages. Comparison of model predictions with existing thermochronometer data reproduces the defining characteristics of these mountains such as a localized "bulls-eye" pattern of rapid exhumation and young cooling ages above the rigid indenter between subduction segments. These results demonstrate a 'bottom up' tectonic rather than 'top down' erosional initiation of feedbacks between erosion and tectonic deformation. While the role
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....
Analytic Geometry, A Tentative Guide.
Helwig, G. Alfred; And Others
This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…
Price, Matthew C; Horn, Pamela L; Latshaw, James C
2013-01-01
Proximal humerus fractures are among the most common fractures associated with osteoporosis. With an aging population, incidence of these fractures will only increase. The proximal humerus not only forms the lateral portion of the shoulder articulation but also has significant associations with musculoskeletal and neurovascular structures. As a result, fractures of the proximal humerus can significantly impact not only the function of the shoulder joint, but the health and function of the entire upper extremity as well. Understanding of these fractures, the management options, and associated nursing care, can help reduce morbidity rate and improve functional outcomes.
McCormick, Frank; Nwachukwu, Benedict U; Provencher, Matthew T
2012-04-01
Stress fractures are a relatively common entity in athletes, in particular, runners. Physicians and health care providers should maintain a high index of suspicion for stress fractures in runners presenting with insidious onset of focal bone tenderness associated with recent changes in training intensity or regimen. It is particularly important to recognize “high-risk” fractures, as these are associated with an increased risk of complication. A patient with confirmed radiographic evidence of a high-risk stress fracture should be evaluated by an orthopedic surgeon. Runners may benefit from orthotics, cushioned sneakers, interval training, and vitamin/calcium supplementation as a means of stress fracture prevention.
Role of MRI in hip fractures, including stress fractures, occult fractures, avulsion fractures
Energy Technology Data Exchange (ETDEWEB)
Nachtrab, O. [Department of Radiology, The Robert Jones and Agnes Hunt Orthopaedic Hospital, Gobowen, Oswestry Shropshire SY10 7AG (United Kingdom); Cassar-Pullicino, V.N., E-mail: Victor.Pullicino@rjah.nhs.uk [Department of Radiology, The Robert Jones and Agnes Hunt Orthopaedic Hospital, Gobowen, Oswestry Shropshire SY10 7AG (United Kingdom); Lalam, R.; Tins, B.; Tyrrell, P.N.M.; Singh, J. [Department of Radiology, The Robert Jones and Agnes Hunt Orthopaedic Hospital, Gobowen, Oswestry Shropshire SY10 7AG (United Kingdom)
2012-12-15
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.
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 increased...... with increasing age and disease duration. Among 34 deceased MS patients 4 had had fractures. These findings are discussed in relation to physical and cognitive impairment in MS. A case-control study is recommended....
Fluid trapping during capillary displacement in fractures
Yang, Zhibing; Neuweiler, Insa; Méheust, Yves; Fagerlund, Fritjof; Niemi, Auli
2016-09-01
The spatial distribution of fluid phases and the geometry of fluid-fluid interfaces resulting from immiscible displacement in fractures cast decisive influence on a range of macroscopic flow parameters. Most importantly, these are the relative permeabilities of the fluids as well as the macroscopic irreducible saturations. They also influence parameters for component (solute) transport, as it usually occurs through one of the fluid phase only. Here, we present a numerical investigation on the critical role of aperture variation and spatial correlation on fluid trapping and the morphology of fluid phase distributions in a geological fracture. We consider drainage in the capillary dominated regime. The correlation scale, that is, the scale over which the two facing fracture walls are matched, varies among the investigated geometries between L/256 and L (self-affine fields), L being the domain/fracture length. The aperture variability is quantified by the coefficient of variation (δ), ranging among the various geometries from 0.05 to 0.25. We use an invasion percolation based model which has been shown to properly reproduce displacement patterns observed in previous experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. We show that when the in-plane curvature is considered, the amount of trapped fluid mass first increases with increasing correlation scale Lc and then decreases as Lc further increases from some intermediate scale towards the domain length scale L. The in-plane curvature contributes to smoothening the invasion front and to dampening the entrapment of fluid clusters of a certain size range that depends on the combination of random aperture standard deviation and spatial correlation.
In Vitro Fracture of Human Cortical Bone: Local Fracture Criteria and Toughening Mechanisms
Energy Technology Data Exchange (ETDEWEB)
Nalla, R; Stolken, J; Kinney, J; Ritchie, R
2004-08-18
A micro-mechanistic understanding of bone fracture that encompasses how cracks interact with the underlying microstructure and defines their local failure mode is lacking, despite extensive research on the response of bone to a variety of factors like aging, loading, and/or disease. Micro-mechanical models for fracture incorporating such local failure criteria have been widely developed for metallic and ceramic materials systems; however, few such deliberations have been undertaken for the fracture of bone. In fact, although the fracture event in mineralized tissues such as bone is commonly believed to be locally strain controlled, until recently there has been little experimental evidence to support this widely held belief. In the present study, a series of in vitro experiments involving a double-notch bend test geometry are performed in order to shed further light on the nature of the local cracking events that precede catastrophic fracture in bone and to define their relationship to the microstructure. Specifically, crack-microstructure interactions are examined to determine the salient toughening mechanisms in human cortical bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micro-mechanical models of these processes, in particular crack deflection and uncracked ligament bridging, the relative importance of these toughening mechanisms is established.
Monitoring hydraulic fracturing with seismic emission volume
Niu, F.; Tang, Y.; Chen, H.; TAO, K.; Levander, A.
2014-12-01
Recent developments in horizontal drilling and hydraulic fracturing have made it possible to access the reservoirs that are not available for massive production in the past. Hydraulic fracturing is designed to enhance rock permeability and reservoir drainage through the creation of fracture networks. Microseismic monitoring has been proven to be an effective and valuable technology to image hydraulic fracture geometry. Based on data acquisition, seismic monitoring techniques have been divided into two categories: downhole and surface monitoring. Surface monitoring is challenging because of the extremely low signal-to-noise ratio of the raw data. We applied the techniques used in earthquake seismology and developed an integrated monitoring system for mapping hydraulic fractures. The system consists of 20 to 30 state-of-the-art broadband seismographs, which are generally about hundreds times more sensible than regular geophones. We have conducted two experiments in two basins with very different geology and formation mechanism in China. In each case, we observed clear microseismic events, which may correspond to the induced seismicity directly associated with fracturing and the triggered ones at pre-existing faults. However, the magnitude of these events is generally larger than magnitude -1, approximately one to two magnitudes larger than those detected by downhole instruments. Spectrum-frequency analysis of the continuous surface recordings indicated high seismic energy associated with injection stages. The seismic energy can be back-projected to a volume that surrounds each injection stage. Imaging seismic emission volume (SEV) appears to be an effective way to map the stimulated reservior volume, as well as natural fractures.
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...
Index Theorems on Torsional Geometries
Kimura, Tetsuji
2007-01-01
We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.
Lögters, T; Windolf, J
2016-10-01
Fractures of the carpal bones are uncommon. On standard radiographs fractures are often not recognized and a computed tomography (CT) scan is the diagnostic method of choice. The aim of treatment is to restore pain-free and full functioning of the hand. A distinction is made between stable and unstable carpal fractures. Stable non-displaced fractures can be treated conservatively. Unstable and displaced fractures have an increased risk of arthritis and non-union and should be stabilized by screws or k‑wires. If treated adequately, fractures of the carpal bones have a good prognosis. Unstable and dislocated fractures have an increased risk for non-union. The subsequent development of carpal collapse with arthrosis is a severe consequence of non-union, which has a heterogeneous prognosis.
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
DEFF Research Database (Denmark)
Takai, Hirokazu; Konstantinidis, Lukas; Schmal, Hagen
2016-01-01
Purpose. Anderson type III odontoid fractures have traditionally been considered stable and treated conservatively. However, unstable cases with unfavorable results following conservative treatment have been reported. Methods. We present the cases of two patients who sustained minimally displaced...... Anderson type III fractures with a characteristic fracture pattern that we refer to as "oblique type axis body fracture." Results. The female patients aged 90 and 72 years, respectively, were both diagnosed with minimally displaced Anderson type III fractures. Both fractures had a characteristic "oblique...... type" fracture pattern. The first patient was treated conservatively with cervical spine immobilization in a semirigid collar. However, gross displacement was noted at the 6-week follow-up visit. The second patient was therefore treated operatively by C1-C3/4 posterior fusion and the course...
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
Hydraulic fracture during epithelial stretching
Casares, Laura; Vincent, Romaric; Zalvidea, Dobryna; Campillo, Noelia; Navajas, Daniel; Arroyo, Marino; Trepat, Xavier
2015-03-01
The origin of fracture in epithelial cell sheets subject to stretch is commonly attributed to excess tension in the cells’ cytoskeleton, in the plasma membrane, or in cell-cell contacts. Here, we demonstrate that for a variety of synthetic and physiological hydrogel substrates the formation of epithelial cracks is caused by tissue stretching independently of epithelial tension. We show that the origin of the cracks is hydraulic; they result from a transient pressure build-up in the substrate during stretch and compression manoeuvres. After pressure equilibration, cracks heal readily through actomyosin-dependent mechanisms. The observed phenomenology is captured by the theory of poroelasticity, which predicts the size and healing dynamics of epithelial cracks as a function of the stiffness, geometry and composition of the hydrogel substrate. Our findings demonstrate that epithelial integrity is determined in a tension-independent manner by the coupling between tissue stretching and matrix hydraulics.
Klammler, Harald; Hatfield, Kirk; Newman, Mark A.; Cho, Jaehyun; Annable, Michael D.; Parker, Beth L.; Cherry, John A.; Perminova, Irina
2016-07-01
This paper presents the fundamental theory and laboratory test results on a new device that is deployed in boreholes in fractured rock aquifers to characterize vertical distributions of water and contaminant fluxes, aquifer hydraulic properties, and fracture network properties (e.g., active fracture density and orientation). The device, a fractured rock passive flux meter (FRPFM), consists of an inflatable core assembled with upper and lower packers that isolate the zone of interest from vertical gradients within the borehole. The outer layer of the core consists of an elastic fabric mesh equilibrated with a visible dye which is used to provide visual indications of active fractures and measures of fracture location, orientation, groundwater flux, and the direction of that flux. Beneath the outer layer is a permeable sorbent that is preloaded with known amounts of water soluble tracers which are eluted at rates proportional to groundwater flow. This sorbent also captures target contaminants present in intercepted groundwater. The mass of contaminant sorbed is used to quantify cumulative contaminant flux; whereas, the mass fractions of resident tracers lost are used to provide measures of water flux. In this paper, the FRPFM is bench tested over a range of fracture velocities (2-20 m/day) using a single fracture flow apparatus (fracture aperture = 0.5 mm). Test results show a discoloration in visible dye corresponding to the location of the active fracture. The geometry of the discoloration can be used to discern fracture orientation as well as direction and magnitude of flow in the fracture. Average contaminant fluxes were measured within 16% and water fluxes within 25% of known imposed fluxes.
Plas, van der S.A.; Sundberg, H.; Berg, van den H.; Scheu, G.; Wester, P.; Jensen, S.; Bergman, A.; Boer, de J.; Koeman, J.H.; Brouwer, A.
2000-01-01
The hepatic tumor promoting activity of the planar 0–1 ortho (~9.7 /w) and the nonplanar 2–4 ortho (~90.3 /w) fraction of the commercial PCB mixture Aroclor 1260 was studied using a medium-term two-stage initiation/promotion bioassay in female Sprague–Dawley rats. Fractionation was carried out on an
Particle Swarm Transport in Fracture Networks
Pyrak-Nolte, L. J.; Mackin, T.; Boomsma, E.
2012-12-01
Colloidal particles of many types occur in fractures in the subsurface as a result of both natural and industrial processes (e.g., environmental influences, synthetic nano- & micro-particles from consumer products, chemical and mechanical erosion of geologic material, proppants used in gas and oil extraction, etc.). The degree of localization and speed of transport of such particles depends on the transport mechanisms, the chemical and physical properties of the particles and the surrounding rock, and the flow path geometry through the fracture. In this study, we investigated the transport of particle swarms through artificial fracture networks. A synthetic fracture network was created using an Objet Eden 350V 3D printer to build a network of fractures. Each fracture in the network had a rectangular cross-sectional area with a constant depth of 7 mm but with widths that ranged from 2 mm to 11 mm. The overall dimensions of the network were 132 mm by 166 mm. The fracture network had 7 ports that were used either as the inlet or outlet for fluid flow through the sample or for introducing a particle swarm. Water flow rates through the fracture were controlled with a syringe pump, and ranged from zero flow to 6 ml/min. Swarms were composed of a dilute suspension (2% by mass) of 3 μm fluorescent polystyrene beads in water. Swarms with volumes of 5, 10, 20, 30 and 60 μl were used and delivered into the network using a second syringe pump. The swarm behavior was imaged using an optical fluorescent imaging system illuminated by green (525 nm) LED arrays and captured by a CCD camera. For fracture networks with quiescent fluids, particle swarms fell under gravity and remained localized within the network. Large swarms (30-60 μl) were observed to bifurcate at shallower depths resulting in a broader dispersal of the particles than for smaller swarm volumes. For all swarm volumes studied, particle swarms tended to bifurcate at the intersection between fractures. These
Determination of in-situ fracture apertures from digital borehole images
Energy Technology Data Exchange (ETDEWEB)
Johansson, Maria C.; Stephansson, O. [Royal Inst. of Tech., Stockholm (Sweden). Engineering Geology
1998-09-01
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 4 refs, 4 figs
Merrien-Soukatchoff, V.; Korini, T.; Thoraval, A.
2012-03-01
The paper presents the Discrete Fracture Network code RESOBLOK, which couples geometrical block system construction and a quick iterative stability analysis in the same package. The deterministic or stochastic geometry of a fractured rock mass can be represented and interactively displayed in 3D using two different fracture generators: one mainly used for hydraulic purposes and another designed to allow block stability evaluation. RESOBLOK has downstream modules that can quickly compute stability (based on limit equilibrium or energy-based analysis), display geometric information and create links to other discrete software. The advantage of the code is that it couples stochastic geometrical representation and a quick iterative stability analysis to allow risk-analysis with or without reinforcement and, for the worst cases, more accurate analysis using stress-strain analysis computer codes. These different aspects are detailed for embankment and underground works.
Energy Technology Data Exchange (ETDEWEB)
Choi, Shin Beom; Kim, Young Jin [Sungkyunkwan University, Suwon (Korea, Republic of); Chang, Yoon-Suk [Kyung Hee University, Yongin (Korea, Republic of); Kim, Min Chul; Lee, Bong Sang [Korea Atomic Energy Reserch Institute, Daejeon (Korea, Republic of)
2010-03-15
The aim of this paper is to suggest an approach to generate master curves by using miniature specimens, especially pre-cracked Charpy V-notched (PCVN) specimen, made of SA508 carbon steel. Firstly, fracture toughness diagram is derived from comparing finite element analyses results with the fixed mesh size at crack tip between standard compact tension and PCVN specimens. To compensate the constraint effects from different geometry, further examination based on the fracture toughness diagram was performed. In this context, a scale factor to deal with specimen size effects is proposed by statistically manipulating the numerical analysis data. Finally, the proposed scale factor is applied to calculate reference temperature which affects on the master curve. We expect that the approach can be applicable to compensate the geometrical constraint effects on fracture toughness of SA508 carbon steel when the PCVN specimen is used
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.
The Geometry Description Markup Language
Institute of Scientific and Technical Information of China (English)
RadovanChytracek
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.This article 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.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
[Fracture endoprosthesis of distal humerus fractures].
Müller, L P; Wegmann, K; Burkhart, K J
2013-08-01
The treatment of choice for fractures of the distal humerus is double plate osteosynthesis. Due to anatomical preshaped angle stable plates the primary stability and management of soft tissues has been improved. However, osteoporotic comminuted fractures in the elderly are often not amenable to stable osteosynthesis and total elbow arthroplasty has been established as an alternative therapy. Although complication rates have been reduced, complications of total elbow arthroplasty are still much more frequent than in total hip replacement. Furthermore, patients are advised not to exceed a weight bearing of 5 kg. Therefore, the indications for elbow arthroplasty must be evaluated very strictly and should be reserved for comminuted distal humeral fractures in the elderly with poor bone quality that are not amenable to stable osteosynthesis or for simple fractures in cases of preexisting symptomatic osteoarthritis. This article introduces and discusses modern concepts of elbow arthroplasty, such as modular convertible prosthesis systems, hemiarthroplasty and radial head replacement in total elbow arthroplasty.
Injection-driven deformation of a fractured material
MacMinn, C. W.; Wettlaufer, J. S.
2014-12-01
Hydraulic fracturing, or fracking, involves injecting fluid into a low-permeability reservoir rock at high pressure in order to open a network of fractures, which act as high-permeability pathways. However, most reservoir rocks have a pre-existing network of natural fractures. The impact of these existing fractures on the hydraulic fracturing process is difficult to predict, involving the nonlinear coupling of fluid flow with rock deformation and failure in a complex (fractured) geometry. Here, we study this problem experimentally in a model system: fluid injection into a cemented packing of soft particles, which behaves as a cohesive poroelastic material. We insert "natural" fractures into the system by manually cutting the bonds between particles in specific places. We then inject fluid into the packing at a constant rate and measure the dynamic strain field at high resolution using particle tracking. Comparison of the strain field with and without pre-existing fractures reveals their strong and nonlocal impact on both flow and deformation.
Hip axis length is a FRAX- and bone density-independent risk factor for hip fracture in women.
Leslie, William D; Lix, Lisa M; Morin, Suzanne N; Johansson, Helena; Odén, Anders; McCloskey, Eugene V; Kanis, John A
2015-05-01
Bone mineral density (BMD) measurement from dual-energy X-ray absorptiometry (DXA) is widely used to assess skeletal strength in clinical practice, but DXA instruments can also measure biomechanical parameters related to skeletal shape. The objective of the study was to determine whether DXA-derived hip geometry measures provide information on fracture prediction that is independent of hip fracture probability determined from the fracture risk assessment tool (FRAX) algorithm. This was a retrospective registry study using BMD results for Manitoba, Canada. Women aged 40 years and older with baseline hip DXA, derived hip geometry measures, and FRAX scores (n = 50 420) participated in the study. Hospitalized hip fracture (n = 1020) diagnosed during 319 137 person-years of follow-up (median 6.4 y) was measured. Among the hip geometry measures, hip axis length (HAL) showed a consistent association with hip fracture risk when adjusted for age [hazard ratio (HR) 1.30 per SD increase, 95% confidence interval (CI) 1.22-1.38], and this was unaffected by further adjustment for BMD or FRAX score. Adjusted for FRAX score with BMD, there was a significant effect of increasing HAL quintile on hip fracture risk (linear trend P hip geometry measurements are associated with incident hip fracture risk, but many do not confer significant independent predictive information. HAL was found to predict hip fractures when adjusted for BMD or FRAX score and may be of clinical value in refining hip fracture risk.
Yushi, Zou; Xinfang, Ma; Shicheng, Zhang; Tong, Zhou; Han, Li
2016-09-01
Shale formations are often characterized by low matrix permeability and contain numerous bedding planes (BPs) and natural fractures (NFs). Massive hydraulic fracturing is an important technology for the economic development of shale formations in which a large-scale hydraulic fracture network (HFN) is generated for hydrocarbon flow. In this study, HFN propagation is numerically investigated in a horizontally layered and naturally fractured shale formation by using a newly developed complex fracturing model based on the 3D discrete element method. In this model, a succession of continuous horizontal BP interfaces and vertical NFs is explicitly represented and a shale matrix block is considered impermeable, transversely isotropic, and linearly elastic. A series of simulations is performed to illustrate the influence of anisotropy, associated with the presence of BPs, on the HFN propagation geometry in shale formations. Modeling results reveal that the presence of BP interfaces increases the injection pressure during fracturing. HF deflection into a BP interface tends to occur under high strength and elastic anisotropy as well as in low vertical stress anisotropy conditions, which generate a T-shaped or horizontal fracture. Opened BP interfaces may limit the growth of the fracture upward and downward, resulting in a very low stimulated thickness. However, the opened BP interfaces favor fracture complexity because of the improved connection between HFs and NFs horizontally under moderate vertical stress anisotropy. This study may help predict the HF growth geometry and optimize the fracturing treatment designs in shale formations with complex depositional heterogeneity.
Hull, C. M.
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Ho...
Linear algebra, geometry and transformation
Solomon, Bruce
2014-01-01
Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg
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
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
Adler, Irving
1967-01-01
This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
Quantum Consequences of Parameterizing Geometry
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
Hull, C M
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)
Thermal Phase in Bubbling Geometries
Institute of Scientific and Technical Information of China (English)
LIU Chang-Yong
2008-01-01
We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
How Does The Bone Shaft Geometry Affect its Bending Properties?
Directory of Open Access Journals (Sweden)
Kaveh P. Saffar
2009-01-01
Full Text Available In this research, ten fresh specimens of sheep tibiae were provided from slaughtered animals. Whole bone specimens were loaded in three-point bending according to standard wet bone test protocols. Mechanical properties were determined and compared with the results which were obtained from two dry bone tests. The results showed that fracture bending moment and bone extrinsic stiffness had significant relations with fracture cross-section dependent parameters (i.e., cross-section area and area moment of inertia. Where, fracture energy and ultimate strength did not have such a relation with these parameters. Finite element modeling of bone shaft was made with simplified geometry (neglecting cross-section variations along bone shaft in two steps: First, by elliptical cross-section and second, by circular cross-section, assuming linear elastic and isotropic properties for the specimens. Elastic (Youngs modulus and fracture load, evaluated from curves obtained from tests, were applied to the finite element model and close results of maximum stress in both test specimen and first (elliptical cross-section model showed up. There was an average difference of about 2% between ultimate strength of wet bone specimens and maximum (tensile stress occurred in the elliptical models. However, this value for circular models was about 16%.
Origin of Permeability and Structure of Flows in Fractured Media
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
Flow and transport in single fracture with roughness.
Olkiewicz, Piotr; Dabrowski, Marcin
2016-04-01
Fracture flow may dominate in rocks with low porosity and it can accompany both industrial and natural processes. Typical examples of such processes are natural flows in crystalline rocks and industrial flows in geothermal systems or hydraulic fracturing. Fracture flow provides an important mechanism for transporting mass and energy. For example, geothermal energy is primarily transported by the flow of the heated water or steam rather than by the thermal diffusion. The geometry of the fracture network and the distribution of the mean apertures of individual fractures are the key parameters with regard to the fracture network transmissivity. Transport in fractures can occur through the combination of advection and diffusion processes like in the case of dissolved chemical components. The local distribution of the fracture aperture may play an important role for both flow and transport processes. In this work, we compare numerical solution for flow and transport processes in a single fracture in 2D and 3D. Fracture aperture distributions are generated by random correlated field method. We examine a single-phase flow of an incompressible viscous Newtonian fluid in the low Reynolds number limit. The velocity field is found using the Stokes equations with periodic boundary condition and a gravity force is imposed in the background. We systematically compare the obtained velocity field to the results obtained by solving the Reynolds equation, where pressure difference is imposed in the background. This allows us to examine the impact of the aperture distribution on the permeability of the medium and the local velocity distribution for two different mathematical descriptions of the fracture flow. Furthermore, we analyse the impact of aperture distribution on the front characteristics.
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.
Characterization of hydraulic fractures and reservoir properties of shale using natural tracers
Heath, J. E.; Gardner, P.; Kuhlman, K. L.; Malama, B.
2013-12-01
Hydraulic fracturing plays a major role in the economic production of hydrocarbon from shale. Current fracture characterization techniques are limited in diagnosing the transport properties of the fractures on the near wellbore scale to that of the entire stimulated reservoir volume. Microseismic reveals information on fracture geometries, but not transport properties. Production analysis (e.g., rate transient analysis using produced fluids) estimates fracture and reservoir flow characteristics, but often relies on simplified models in terms of fracture geometries and fluid storage and transport. We present the approach and potential benefits of incorporating natural tracers with production data analysis for fracture and reservoir characterization. Hydraulic fracturing releases omnipresent natural tracers that accumulate in low permeability rocks over geologic time (e.g., radiogenic 4He and 40Ar). Key reservoir characteristics govern the tracer release, which include: the number, connectivity, and geometry of fractures; the distribution of fracture-surface-area to matrix-block-volume; and the nature of hydrocarbon phases within the reservoir (e.g., methane dissolved in groundwater or present as a separate gas phase). We explore natural tracer systematics using numerical techniques under relevant shale-reservoir conditions. We evaluate the impact on natural tracer transport due to a variety of conceptual models of reservoir-transport properties and boundary conditions. Favorable attributes for analysis of natural tracers include the following: tracer concentrations start with a well-defined initial condition (i.e., equilibrium between matrix and any natural fractures); there is a large suite of tracers that cover a range of at least 7x in diffusion coefficients; and diffusive mass-transfer out of the matrix into hydraulic fractures will cause elemental and isotopic fractionation. Sandia National Laboratories is a multi-program laboratory managed and operated by
Massiot, Cécile; Nicol, Andrew; Townend, John; McNamara, David D.; Garcia-Sellés, David; Conway, Chris E.; Archibald, Garth
2017-07-01
Permeability hosted in andesitic lava flows is dominantly controlled by fracture systems, with geometries that are often poorly constrained. This paper explores the fracture system geometry of an andesitic lava flow formed during its emplacement and cooling over gentle paleo-topography, on the active Ruapehu volcano, New Zealand. The fracture system comprises column-forming and platy fractures within the blocky interior of the lava flow, bounded by autobreccias partially observed at the base and top of the outcrop. We use a terrestrial laser scanner (TLS) dataset to extract column-forming fractures directly from the point-cloud shape over an outcrop area of ∼3090 m2. Fracture processing is validated using manual scanlines and high-resolution panoramic photographs. Column-forming fractures are either steeply or gently dipping with no preferred strike orientation. Geometric analysis of fractures derived from the TLS, in combination with virtual scanlines and trace maps, reveals that: (1) steeply dipping column-forming fracture lengths follow a scale-dependent exponential or log-normal distribution rather than a scale-independent power-law; (2) fracture intensities (combining density and size) vary throughout the blocky zone but have similar mean values up and along the lava flow; and (3) the areal fracture intensity is higher in the autobreccia than in the blocky zone. The inter-connected fracture network has a connected porosity of ∼0.5 % that promote fluid flow vertically and laterally within the blocky zone, and is partially connected to the autobreccias. Autobreccias may act either as lateral permeability connections or barriers in reservoirs, depending on burial and alteration history. A discrete fracture network model generated from these geometrical parameters yields a highly connected fracture network, consistent with outcrop observations.
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...
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Siddharth Gautam; S Mitra; R Mukhopadhyay
2008-10-01
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 scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
An introduction to differential geometry
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.
Instability of supersymmetric microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
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......Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first......, 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...
Advances in discrete differential geometry
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, ...
Kotilainen, R; Kärjä, J; Kullaa-Mikkonen, A
1990-03-01
From a total of 350 jaw fractures treated in 1980-1984 at Kuopio University Central Hospital, 20% were in children. These injuries were evaluated retrospectively regarding age, sex, incidence and etiology. Forty-five of the patients were boys and 25 girls. The frequency of maxillary and mandibular fractures in 70 young patients was 28.6%. The most common type of bone fractures was fracture of the alveolar process, which was prevalent in persons with mixed dentition. Before the age of 7 years, falls from height were the common causes of jaw fractures. The major cause of the jaw fractures in children from 7 to 15 years old was road accidents (47.1%), especially in boys. Most of these were cycling accidents, only a few patients were victims of automobile accidents. In addition, about one third (25.7%) of the patients were treated in the hospital because of multiple injuries to other organs.
Directory of Open Access Journals (Sweden)
Mihajlović Miljan H.
2006-01-01
Full Text Available Background. Growing skull fracture or craniocerebral erosion is a rare complication of linear skull fracture in childhood. It is characterized by progressive diastatic enlargement of the fracture line, which leads to a cranial defect, dural cleft, and cerebral herniation. It is presented as a soft pulsabile scalp swelling above the fracture, with a clear cranial defect. Case report. In this paper we presented a patient, an 8-month-old boy with the growing skull fracture revealed four weeks after the injury. After the surgical treatment, the boy was in a good general condition without the presence of neurologic impairment. Conclusion. Early recognition of craniocerebral erosion is very important. Timely detection prevents further progression of the disease and the evolution of neurological impairment. Surgery is the method of choice for treating a growing skull fracture .
Paper Interfaces for Learning Geometry
Bonnard, Quentin; Verma, Himanshu; Kaplan, Frédéric; Dillenbourg, Pierre
2012-01-01
Paper interfaces offer tremendous possibilities for geometry education in primary schools. Existing computer interfaces designed to learn geometry do not consider the integration of conventional school tools, which form the part of the curriculum. Moreover, most of computer tools are designed specifically for individual learning, some propose group activities, but most disregard classroom-level learning, thus impeding their adoption. We present an augmented reality based tabletop system with ...
Courant Algebroids in Parabolic Geometry
Armstrong, Stuart
2011-01-01
To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.
Topology and geometry for physicists
Nash, Charles
2011-01-01
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
Higgs mass in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)
2014-09-11
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A new equi-dimensional fracture model using polyhedral cells for microseismic data sets
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.
Energy Technology Data Exchange (ETDEWEB)
Archambeau, C.B. [Univ. of Colorado, Boulder, CO (United States)
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.
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.
Pelvic fractures and mortality.
K.H. Chong; DeCoster, T.; Osler, T.; Robinson, B.
1997-01-01
A retrospective study of all patients (N = 343) with pelvic fractures admitted to our trauma service was conducted to evaluate the impact of pelvic fractures on mortality. All patients sustained additional injuries with an average Injury Severity Score (ISS) of twenty. Thirty-six patients died. This group had more severe pelvic fractures as graded by the Tile classification as well as a greater number and severity of associated injuries. Six patients died as a direct result of pelvic hemorrha...
DEFF Research Database (Denmark)
Takai, Hirokazu; Konstantinidis, Lukas; Schmal, Hagen;
2016-01-01
was uneventful. Conclusions. Oblique type axis body fractures resemble a highly unstable subtype of Anderson type III fractures with the potential of severe secondary deformity following conservative treatment, irrespective of initial grade of displacement. The authors therefore warrant a high index of suspicion......Purpose. Anderson type III odontoid fractures have traditionally been considered stable and treated conservatively. However, unstable cases with unfavorable results following conservative treatment have been reported. Methods. We present the cases of two patients who sustained minimally displaced...
The Common Geometry Module (CGM).
Energy Technology Data Exchange (ETDEWEB)
Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
[(Impending) pathological fracture].
Sutter, P M; Regazzoni, P
2002-01-01
Pathological fractures will be encountered in increasing frequency due to more patients with cancer, surviving a longer period. The skeleton is the third most frequent localization for metastases. Breast cancer is still the most common primary tumor, but bone metastases from lung cancer seem to be diagnosed more and more. Despite of finding metastases most often in the spinal column, fractures are seen mostly at the femoral site. A pathological fracture and, in almost all cases, an impending fracture are absolute indication for operation. An exact definition of an "impending fracture" is still lacking; it is widely accepted, that 50 per cent of bone mass must be destroyed before visualization in X-ray is possible, thus defining an impending fracture. The score system by Mirels estimates the fracture risk by means of four parameters (localization, per cent of destructed bone mass, type of metastasis, pain). Improving quality of life, relieving pain, preferably with a single operation and a short length of stay are the goals of (operative) treatment. For fractures of the proximal femur, prosthetic replacement, for fractures of the subtrochanteric region or the shaft, intramedullary nails are recommended. Postoperative radiation therapy possibly avoids tumor progression. In patient with a good long term prognosis, tumor should be removed locally aggressive.
Fracture mechanics safety approaches
Energy Technology Data Exchange (ETDEWEB)
Roos, E.; Schuler, X.; Eisele, U. [Materials Testing Inst. (MPA), Univ. of Stuttgart (Germany)
2004-07-01
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.)
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.
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.
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.
New software for 3D fracture network analysis and visualization
Song, J.; Noh, Y.; Choi, Y.; Um, J.; Hwang, S.
2013-12-01
This study presents new software to perform analysis and visualization of the fracture network system in 3D. The developed software modules for the analysis and visualization, such as BOUNDARY, DISK3D, FNTWK3D, CSECT and BDM, have been developed using Microsoft Visual Basic.NET and Visualization TookKit (VTK) open-source library. Two case studies revealed that each module plays a role in construction of analysis domain, visualization of fracture geometry in 3D, calculation of equivalent pipes, production of cross-section map and management of borehole data, respectively. The developed software for analysis and visualization of the 3D fractured rock mass can be used to tackle the geomechanical problems related to strength, deformability and hydraulic behaviors of the fractured rock masses.
Evoluton of polygonal fracture patterns in lava flows.
Aydin, A; Degraff, J M
1988-01-29
Cooling-induced fractures, also known as columnar joints, divide basaltic lava flows into prismatic columns with polygonal cross sections. The regularity and symmetry of the fracture patterns have long fascinated naturalists. In view of the recent selection of two candidate nuclear waste sites in areas where polygonally fractured volcanic rocks are located, a better understanding of the fracture patterns is required. Field data indicate that the tetragonal networks at flow surfaces evolve systematically to hexagonal networks as the joints grow inward during solidification of lava. This evolution occurs by the gradual change of most orthogonal intersections to nonorthogonal intersections of about 120 degrees. The surface features and intersection geometries of columnar joints show that joint segments at any given level form sequentially yet harmoniously.
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
FRACTAL PROPERTIES OF ROCK FRACTURE SURFACES
Institute of Scientific and Technical Information of China (English)
王金安; 谢和平; MarekA．KWASNIEWSKI
1996-01-01
To give a better understanding of the morphological features of rock fracture surfaces within the framework of fractal geometry, the fractal characters of the rough surfaces in" rock are analyzed according to the variogram method. The study elaborates the significance of the geometric parameters-fractal dimension D and the intercept A on a log-log plot to the surface structure. Investigation extends to the anisotropy and heterogeneity of rock fracture surfaces, and the scale effect on the fractal estimation. The present study indicates that fractal dimension alone may not be sufficient to characterize the surface roughness of rock joints. A reliable estimation should take into account the combination of D and A.
Hip Fractures among Older Adults
... online training for health care providers. Learn More Hip Fractures Among Older Adults Recommend on Facebook Tweet Share ... get older. What You Can Do to Prevent Hip Fractures You can prevent hip fractures by taking steps ...
Simulation of Solute Flow and Transport in a Geostatistically Generated Fractured Porous System
Assteerawatt, A.; Helmig, R.; Haegland, H.; Bárdossy, A.
2007-12-01
Fractured aquifer systems have provided important natural resources such as petroleum, gas, water and geothermal energy and have also been recently under investigation for their suitability as storage sites for high-level nuclear waste. The resource exploitation and potential utilization have led to extensive studies aiming of understanding, characterizing and finally predicting the behavior of fractured aquifer systems. By applying a discrete model approach to study flow and transport processes, fractures are determined discretely and the effect of individual fractures can be explicitly investigated. The critical step for the discrete model is the generation of a representative fracture network since the development of flow paths within a fractured system strongly depends on its structure. The geostatistical fracture generation (GFG) developed in this study aims to create a representative fracture network, which combines the spatial structures and connectivity of a fracture network, and the statistical distribution of fracture geometries. The spatial characteristics are characterized from indicator fields, which are evaluated from fracture trace maps. A global optimization, Simulated annealing, is utilized as a generation technique and the spatial characteristics are formulated to its objective function. We apply the GFG to a case study at a Pliezhausen field block, which is a sandstone of a high fracture density. The generated fracture network from the GFG are compared with the statistically generated fracture network in term of structure and hydraulic behavior. As the GFG is based on a stochastic concept, several realizations of the same descriptions can be generated, hence, an overall behavior of the fracture-matrix system have to be investigated from various realizations which leads to a problem of computational demand. In order to overcome this problem, a streamline method for a solute transport in a fracture porous system is presented. The results obtained
Pneumothorax complicating isolated clavicle fracture.
Hani, Redouane; Ennaciri, Badr; Jeddi, Idriss; El Bardouni, Ahmed; Mahfoud, Mustapha; Berrada, Mohamed Saleh
2015-01-01
Isolated clavicle fractures are among the commonest of traumatic fractures in the emergency department. Complications of isolated clavicle fractures are rare. Pneumothorax has been described as a complication of a fractured clavicle only rarely in English literature. In all the reported cases, the pneumothorax was treated by a thoracostomy and the clavicle fracture was treated conservatively. In our case, the pneumothorax required a chest drain insertion and the clavicle fracture was treated surgically with good result.
High Resolution Geophysical Characterization of Fractures within a Granitic Pluton
Pérez-Estaún, A.; Carbonell, R.
2007-12-01
The FEBEX underground gallery was excavated in the Aar Granite (Switzerland), a heterogeneous granite containing from very leucocratic facies to granodiorites. The geology of the gallery shows the existence of various sets of fractures with different attributes: geometry, kinematics, fracture infilling, etc. The study of the structural data, new observations on the FEBEX gallery itself and borehole televiewer data acquired in the newly drilled boreholes, have allowed to identify four sets of fractures. The first group of fractures has a typical distribution and characteristics of en echelon tension fractures and were formed in late magmatic stages, according with the paragenesis of the minerals that filled the craks. The main strike is around 300 (280-300). These fractures are deformed and displaced by the other group of faults. The second group corresponds to the lamprophyre dikes, of mantelic origin, with an orientation oblique to the tunnel, and slightly oblique to the first group of fractures (strike, 310-330). They were formed during an extension event well evidenced by their irregular margins and flame structures into the granite. The margins of these dikes show several reactivations as strike slip faults. Geophysical data has been acquired to characterized the fracture network of the surrounding volume within the FEBEX gallery. The geophysic data include new borehole logging such as Natural Gamma and Borehole Ground Penetrating radar. The processing and integration of these different data sets indicates that the GPR record can provide images of a third set of fractures, which are probably fluid filled. This set of fractures a subparallel to the tunnel axis and appear to intersect older boreholes which are nearly perpendicular to the axis of the FEBEX gallery.
DEFF Research Database (Denmark)
2008-01-01
Vertebral Fracture Prediction A method of processing data derived from an image of at least part of a spine is provided for estimating the risk of a future fracture in vertebraeof the spine. Position data relating to at least four neighbouring vertebrae of the spine is processed. The curvature...
Radial head fracture - aftercare
... Philadelphia, PA: Elsevier Saunders; 2015:chap 6. Prawer A. Radius and ulna fractures. In: Eiff M, Hatch R, eds. Fracture Management for Primary Care . 3rd ed. Philadelphia, PA: Elsevier Saunders; 2012:chap ... PhD, and the A.D.A.M. Editorial team. Related MedlinePlus Health ...
Della Rocca, Gregory J
2013-10-01
Displaced patella fractures often result in disruption of the extensor mechanism of the knee. An intact extensor mechanism is a requirement for unassisted gait. Therefore, operative treatment of the displaced patella fracture is generally recommended. The evaluation of the patella fracture patient includes examination of extensor mechanism integrity. Operative management of patella fractures normally includes open reduction with internal fixation, although partial patellectomy is occasionally performed, with advancement of quadriceps tendon or patellar ligament to the fracture bed. Open reduction with internal fixation has historically been performed utilizing anterior tension band wiring, although comminution of the fracture occasionally makes this fixation construct inadequate. Supplementation or replacement of the tension band wire construct with interfragmentary screws, cerclage wire or suture, and/or plate-and-screw constructs may add to the stability of the fixation construct. Arthrosis of the patellofemoral joint is very common after healing of patella fractures, and substantial functional deficits may persist long after fracture healing has occurred. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.
Institute of Scientific and Technical Information of China (English)
戴力扬
2001-01-01
Objective. To investigate the unique characteristics and treatment of thoracic spine fractures.Methods. Severty-seven patients with thoracic spine fractures were retrospectively reviewed. Of these, therewere 37 compressior fractures, 34 fracture-dislocations, 3 burst fractures and 3 burst-dislocations. Twenty-six pa-tients had a complete lesion of the spinal cord, 14 sustained a neurologically incomplete injury, and 37 wereneurologically intact. Fifty-three patients were treated nonoperatively and 24 treated operatively.Results. All patients were followed up for 2 ～ 15 years. None of the 26 patients with a complete lesion recov-ered any significant function. Of 37 neurologically intact patients, 13 had local pain although all of them re-mained normal function. Two of 14 patients with incomplete paraplegia returned to normal, 7 recovered some func-tion and 5 did not recovered.Conclusions. E ecause of the unique anatomy and biomechanics of the thoracic spine, the classification common-ly applied to thoracolumbar fractures is not suitable for thoracic fractures. Fusion and instrumentation are indicat-ed when the fractures are unstable, while patients with incomplete lesion of the spinal cord may be the candidatesfor supplemented decompression.
Characterization of fracture aperture field heterogeneity by electrical resistance measurement.
Boschan, A; Ippolito, I; Chertcoff, R; Hulin, J P; Auradou, H
2011-04-01
We use electrical resistance measurements to characterize the aperture field in a rough fracture. This is done by performing displacement experiments using two miscible fluids of different electrical resistivity and monitoring the time variation of the overall fracture resistance. Two fractures have been used: their complementary rough walls are identical but have different relative shear displacements which create "channel" or "barrier" structures in the aperture field, respectively parallel or perpendicular to the mean flow velocity U(→). In the "channel" geometry, the resistance displays an initial linear variation followed by a tail part which reflects the velocity contrast between slow and fast flow channels. In the "barrier" geometry, a change in the slope between two linear zones suggests the existence of domains of different characteristic aperture along the fracture. These variations are well reproduced analytically and numerically using simple flow models. For each geometry, we present then a data inversion procedure that allows one to extract the key features of the heterogeneity from the resistance measurement. Copyright © 2010 Elsevier B.V. All rights reserved.
Contaminant transport in fractured fine-grained glacigene sediments
Energy Technology Data Exchange (ETDEWEB)
Tsakiroglou, C.D. [Foundation for Research and Technology Hellas, Patras (Greece). Inst. of Chemical Engineering and High Temperature Chemical Processes; Klint, K.E.S.; Gravesen, P. [Geological Survey of Denmark and Greenland, Copenhagen (Denmark); Laroche, C.; Le Thiez, P. [Inst. Francaise du Petrole, Rueil-Malmaison (France)
2003-07-01
In this study, multi-scale geological information was collected during extensive fieldwork on a fractured clay-till site situated in Denmark (Ringe site). Meso-scale field data such as fracture spacing/connectivity and hydraulic ''in situ'' tests were combined with micro-scale laboratory studies of mechanical fracture apertures and pore network geometry of fractures and matrix so that a conceptual macro-pore model was established. At the small scale, pore network modeling approach was used to simulate the two-phase flow in single fractures and fracture networks, in the capillary dominated regime. Up-scaling from the pore to the fracture network allowed the estimation of average transport properties and their introduction into a macroscopic simulator of contaminant transport in dual porosity media (SIMUSCOPP). This macroscopic simulator is used for the long-term forecasting of the spatial and temporal evolution of the distribution of a typical LNAPL (creosote) over an extended area around the contaminated site.
Fracture of composite-adhesive-composite systems
Ripling, E. J.; Santner, J. S.; Crosley, P. B.
1984-01-01
This program was undertaken to initiate the development of a test method for testing adhesive joints in metal-adhesive-composite systems. The uniform double cantilever beam (UDCB) and the width tapered beam (WTB) specimen geometries were evaluated for measuring Mode I fracture toughness in these systems. The WTB specimen is the preferred geometry in spite of the fact that it is more costly to machine than the UDCB specimen. The use of loading tabs attached to thin sheets of composites proved to be experimentally unsatisfactory. Consequently, a new system was developed to load thin sheets of adherends. This system allows for the direct measurement of displacement along the load line. In well made joints separation occurred between the plies rather than in the adhesive.
Transphyseal Distal Humerus Fracture.
Abzug, Joshua; Ho, Christine Ann; Ritzman, Todd F; Brighton, Brian
2016-01-01
Transphyseal distal humerus fractures typically occur in children younger than 3 years secondary to birth trauma, nonaccidental trauma, or a fall from a small height. Prompt and accurate diagnosis of a transphyseal distal humerus fracture is crucial for a successful outcome. Recognizing that the forearm is not aligned with the humerus on plain radiographs may aid in the diagnosis of a transphyseal distal humerus fracture. Surgical management is most commonly performed with the aid of an arthrogram. Closed reduction and percutaneous pinning techniques similar to those used for supracondylar humerus fractures are employed. Cubitus varus caused by a malunion, osteonecrosis of the medial condyle, or growth arrest is the most common complication encountered in the treatment of transphyseal distal humerus fractures. A corrective lateral closing wedge osteotomy can be performed to restore a nearly normal carrying angle.
Galeazzi fracture-dislocations.
Mikić, Z D
1975-12-01
Among 125 patients with the Galeazzi-type fracture-dislocation of the forearm, there were fourteen children and eighty-six adults with the classic Galeazzi lesion, and twenty-five patients with a special type -- fracture of both bones and dislocation of the distal radio-ulnar joint. Conservative management was successful only in children. In adults this method resulted in failure in 80 per cent of cases. The results of operative treatment were much better. The fracture fragments of the radius and the dislocation of the radio-ulnar joint in this complex injury are very unstable, especially in the lesion with fractures of the radius and ulna, and it appears that rigid internal fixation is necessary for the dislocation as well as the fracture. With combined fixation over half of the results were excellent.
Kobayashi, A. S.; Ramulu, M.
1985-01-01
Dynamic fracture and crack propagation concepts for ductile materials are reviewed. The equations for calculating dynamic stress integrity and the dynamic energy release rate in order to study dynamic crack propagation are provided. The stress intensity factor versus crack velocity relation is investigated. The uses of optical experimental techniques and finite element methods for fracture analyses are described. The fracture criteria for a rapidly propagating crack under mixed mode conditions are discussed; crack extension and fracture criteria under combined tension and shear loading are based on maximum circumferential stress or energy criteria such as strain energy density. The development and use of a Dugdale model and finite element models to represent crack and fracture dynamics are examined.
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...
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.
General Construction of Tubular Geometry
Mukhopadhyay, Partha
2016-01-01
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Conventionalism and integrable Weyl geometry
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Wave propagation on microstate geometries
Keir, Joseph
2016-01-01
Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...
Euclidean geometry and its subgeometries
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...
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Heide, Marcus; Bihlmayer, Gustav; Blügel, Stefan
2011-04-01
The basic micromagnetic models of Landau, Lifshitz, and Dzyaloshinskii, are extended by an anisotropy term with two independent parameters. The resulting ground states of the magnetic domains and the domain-wall profiles are discussed for crystal lattices with orthorhombic unit cells. In these simple geometries, the magnetization is not confined to a single plane. Depending on the relations between the spin-stiffness, anisotropy, and Dzyaloshinskii-Moriya interaction several different zero-temperature phases of the magnetic structure are found. The corresponding phase diagrams are obtained numerically. Analytical results are given for some special cases. The studied model is of particular relevance for magnetic wires, nanostripes and ultrathin magnetic films deposited on non-magnetic surfaces.
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
The influence of fault geometry on small strike-slip fault mechanics
Ritz, Elizabeth; Pollard, David D.; Ferris, Michael
2015-04-01
Meter-scale subvertical strike-slip fault traces in the central Californian Sierra Nevada exhibit geometric complexities that significantly contribute to their mechanical behavior. Sections of faults that opened at depth channelized fluid flow, as evidenced by hydrothermal mineral infillings and alteration haloes. Thin sections show a variation in the style of ductile deformation of infill along the fault, with greater intensities of deformation along restraining bends. Orthorectified photomosaics of outcrops provide model geometries and parameter constraints used in a two-dimensional displacement discontinuity model incorporating a complementarity algorithm. Model results show that fault shape influences the distribution of opening, and consequently the spatial distribution of fluid conduits. Geometric irregularities are present at many scales, and sections of opening occur along both releasing and restraining bends. Model sensitivity tests focus on boundary conditions along the fault: frictional properties on closed sections and fluid pressure within sections of opening. The influence of the remote stress state varies along a non-planar fault, complicating the relationships between remote stresses, frictional properties, slip, and opening. Discontinuous sections of opening along model faults are similar in spatial distribution and aperture to the epidote infill assemblages observed in the field.
Thermal front propagation in variable aperture fracture-matrix system: A numerical study
Indian Academy of Sciences (India)
Nikhil Bagalkot; G Suresh Kumar
2015-04-01
A numerical study on the effect of complex fracture aperture geometry on propagation of thermal front in a coupled single fracture-matrix system has been carried out. Sinusoidal and logarithmic functions have been used to capture the variation in fracture aperture. Modifications have been made to existing coupled partial differential governing equations to consider the variation of fracture aperture. Effect of temperature on the thermal and physical properties of rock have been incorporated. A fully implicit finite difference scheme has been used to discretize the coupled governing equations. Thermal convection, dispersion and conduction are the major transport processes within fracture, while conduction is the major transport process within rock matrix. The results suggest that variation of fracture aperture increases the heat transfer rate at the fracture-matrix interface. Sensitivity analysis on rock thermal conductivity and fracture aperture have been carried out. The results suggest that the heat transfer from rock matrix to fracture for the case of the parallel plate model is greatly dependent on the rock thermal conductivity (m) as compared to variable aperture model. Further, the thermal front propagation for both parallel plate model and variable aperture model is sensitive to changes in fracture aperture. The heat transfer rate at the interface is greater at smaller fracture apertures and decreases with increase in aperture.
Atypical subtrochanteric femoral shaft fractures: role for mechanics and bone quality.
van der Meulen, Marjolein C H; Boskey, Adele L
2012-08-29
Bisphosphonates are highly effective agents for reducing osteoporotic fractures in women and men, decreasing fracture incidence at the hip and spine up to 50%. In a small subset of patients, however, these agents have recently been associated with 'atypical femoral fractures' (AFFs) in the subtrochanteric region or the diaphysis. These fractures have several atypical characteristics, including occurrence with minimal trauma; younger age than typical osteoporotic fractures; occurrence at cortical, rather than cancellous sites; early radiographic appearance similar to that of a stress fracture; transverse fracture pattern rather than the familiar spiral or transverse-oblique morphologies; initiation on the lateral cortex; and high risk of fracture on the contralateral side, at the same location as the initial fracture. Fracture is a mechanical phenomenon that occurs when the loads applied to a structure such as a long bone exceed its load-bearing capacity, either due to a single catastrophic overload (traumatic failure) or as a result of accumulated damage and crack propagation at sub-failure loads (fatigue failure). The association of AFFs with no or minimal trauma suggests a fatigue-based mechanism that depends on cortical cross-sectional geometry and tissue material properties. In the case of AFFs, bisphosphonate treatment may alter cortical tissue properties, as these agents are known to alter bone remodeling. This review discusses the use of bisphosphonates, their effects on bone remodeling, mechanics and tissue composition, their significance as an effective therapy for osteoporosis, and why these agents may increase fracture risk in a small population of patients.