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
Molecular motion in restricted geometries
Indian Academy of Sciences (India)
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time ...
The VSEPR model of molecular geometry
Gillespie, Ronald J
2012-01-01
Valence Shell Electron Pair Repulsion (VSEPR) theory is a simple technique for predicting the geometry of atomic centers in small molecules and molecular ions. This authoritative reference was written by Istvan Hartiggai and the developer of VSEPR theory, Ronald J. Gillespie. In addition to its value as a text for courses in molecular geometry and chemistry, it constitutes a classic reference for professionals.Starting with coverage of the broader aspects of VSEPR, this volume narrows its focus to a succinct survey of the methods of structural determination. Additional topics include the appli
Tuning spin transport properties and molecular magnetoresistance through contact geometry
Ulman, Kanchan; Narasimhan, Shobhana; Delin, Anna
2014-01-01
Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green's function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its "closed" and "open" conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ˜5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ˜400%.
Tuning spin transport properties and molecular magnetoresistance through contact geometry
International Nuclear Information System (INIS)
Ulman, Kanchan; Narasimhan, Shobhana; Delin, Anna
2014-01-01
Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green's function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its “closed” and “open” conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%
Tuning spin transport properties and molecular magnetoresistance through contact geometry.
Ulman, Kanchan; Narasimhan, Shobhana; Delin, Anna
2014-01-28
Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green's function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its "closed" and "open" conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%.
Graph-drawing algorithms geometries versus molecular mechanics in fullereness
Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.
1996-09-01
The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.
Hybridization and molecular geometry: A number game | Ojha ...
African Journals Online (AJOL)
Present article emphasize the new pedagogy to learn the hybridization and molecular geometry. It is always a challenge for the students to remember the hybridization and geometry of the molecule correctly. This topic has several importance in subjective and objective type questions and answers since in most of the ...
The use of direct geometry spectrometers in molecular spectroscopy
International Nuclear Information System (INIS)
Parker, Stewart F; Ramirez-Cuesta, Anibal J; Albers, Peter W; Lennon, David
2014-01-01
The advantages and disadvantages of the use of direct geometry spectrometers for molecular spectroscopy and catalysis studies are described. We show that both direct and indirect geometry INS spectrometers are important tools for the study of industrially relevant areas such as catalysis, proton conductors and gas separation. We propose a novel hybrid instrument, Cerberus, that would offer high sensitivity and high-to-reasonable resolution across the entire 'mid-infrared' spectral range that would effectively advance research in these areas
NMR determinations of molecular geometries in liquid crystal media
International Nuclear Information System (INIS)
Long, R.C.; Goldstein, J.H.
1983-01-01
The application of NMR spectroscopy in oriented media to the determination of molecular geometries is illustrated by results for three distinctly different molecules: naphthalene, ethylene oxide and spiropentane. The need for systematic application of vibrational corrections is emphasized and some of the effects associated with the different choices of solvent media are considered
Transient Changes in Molecular Geometries and How to Model Them
DEFF Research Database (Denmark)
Dohn, Asmus Ougaard
Light-induced chemical processes are accompanied by molecular motion on the femtosecond time scale. Uncovering this dynamical motion is central to understanding the chemical reaction on a fundamental level. This thesis focuses on the aspects of excess excitation energy dissipation via dynamic...... observe how the wide distribution of ground state geometries is responsible for decoherence, and that the solvent cage actually facilitates coherent motion, by blocking the newly discovered vibrational mode. We furthermore observe a non-specific, rotational solvent response to the excitation. The second...
Sossinsky, A B
2012-01-01
The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...
Indian Academy of Sciences (India)
. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...
Prasolov, V V
2015-01-01
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.
Molecular Diffusion Coefficients: Experimental Determination and Demonstration.
Fate, Gwendolyn; Lynn, David G.
1990-01-01
Presented are laboratory methods which allow the demonstration and determination of the diffusion coefficients of compounds ranging in size from water to small proteins. Included are the procedures involving the use of a spectrometer, UV cell, triterated agar, and oxygen diffusion. Results including quantification are described. (CW)
Programmable molecular recognition based on the geometry of DNA nanostructures.
Woo, Sungwook; Rothemund, Paul W K
2011-07-10
From ligand-receptor binding to DNA hybridization, molecular recognition plays a central role in biology. Over the past several decades, chemists have successfully reproduced the exquisite specificity of biomolecular interactions. However, engineering multiple specific interactions in synthetic systems remains difficult. DNA retains its position as the best medium with which to create orthogonal, isoenergetic interactions, based on the complementarity of Watson-Crick binding. Here we show that DNA can be used to create diverse bonds using an entirely different principle: the geometric arrangement of blunt-end stacking interactions. We show that both binary codes and shape complementarity can serve as a basis for such stacking bonds, and explore their specificity, thermodynamics and binding rules. Orthogonal stacking bonds were used to connect five distinct DNA origami. This work, which demonstrates how a single attractive interaction can be developed to create diverse bonds, may guide strategies for molecular recognition in systems beyond DNA nanostructures.
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
Pereira, L. R.; Jardim, D. F.; da Silva, J. M.
2017-12-01
The teaching and learning of Mathematics contents have been challenging along the history of the education, both for the teacher, in his dedicated task of teaching, as for the student, in his arduous and constant task of learning. One of the topics that are most discussed in these contents is the difference between the concepts of proof and demonstration. This work presents an interesting discussion about such concepts considering the use of the mathematical modeling approach for teaching, applied to some examples developed in the classroom with a group of students enrolled in the discipline of Geometry of the Mathematics curse of UFVJM.
Some simulation aspects, from molecular systems to stochastic geometries of pebble bed reactors
International Nuclear Information System (INIS)
Mazzolo, A.
2009-06-01
After a brief presentation of his teaching and supervising activities, the author gives an overview of his research activities: investigation of atoms under high intensity magnetic field (investigation of the electronic structure under these fields), studies of theoretical and numerical electrochemistry (simulation coupling molecular dynamics and quantum calculations, comprehensive simulations of molecular dynamics), and studies relating stochastic geometry and neutron science
Geometry optimization of zirconium sulfophenylphosphonate layers by molecular simulation methods
Czech Academy of Sciences Publication Activity Database
Škoda, J.; Pospíšil, M.; Kovář, P.; Melánová, Klára; Svoboda, J.; Beneš, L.; Zima, Vítězslav
2018-01-01
Roč. 24, č. 1 (2018), s. 1-12, č. článku 10. ISSN 1610-2940 R&D Projects: GA ČR(CZ) GA14-13368S; GA ČR(CZ) GA17-10639S Institutional support: RVO:61389013 Keywords : zirconium sulfophenylphosphonate * intercalation * molecular simulation Subject RIV: CA - Inorganic Chemistry OBOR OECD: Inorganic and nuclear chemistry Impact factor: 1.425, year: 2016
Molecular Geometry And Vibrational Spectra of 2'-chloroacetanilide
International Nuclear Information System (INIS)
Gokce, H.
2008-01-01
The molecular structure, vibrational frequencies and the corresponding vibrational assingments of 2'-chloroacetanilide in the ground state have been calculated by using Hartree-Fock (HF) and Density Functional Theory (DFT/B3LYP) methods with 6-311++G(d,p) basis set. The obtained vibrational frequencies and optimized geometric parameters (bond lenghts and angles) are in very good agreement with the experimental data. The comparison of the observed and calculated vibrational frequencies assignments of 2'-chloroacetanilide exhibit that the scaled DFT/B3LYP method is superior to be scaled HF method. Furthermore the calculated Infrared and Raman intensities are also reported
Designing an educative curriculum unit for teaching molecular geometry in high school chemistry
Makarious, Nader N.
Chemistry is a highly abstract discipline that is taught and learned with the aid of various models. Among the most challenging, yet a fundamental topic in general chemistry at the high school level, is molecular geometry. This study focused on developing exemplary educative curriculum materials pertaining to the topic of molecular geometry. The methodology used in this study consisted of several steps. First, a diverse set of models were analyzed to determine to what extent each model serves its purpose in teaching molecular geometry. Second, a number of high school teachers and college chemistry professors were asked to share their experiences on using models in teaching molecular geometry through an online questionnaire. Third, findings from the comparative analysis of models, teachers’ experiences, literature review on models and students’ misconceptions, the curriculum expectations of the Next Generation Science Standards and their emphasis on three-dimensional learning and nature of science (NOS) contributed to the development of the molecular geometry unit. Fourth, the developed unit was reviewed by fellow teachers and doctoral-level science education experts and was revised to further improve its coherence and clarity in support of teaching and learning of the molecular geometry concepts. The produced educative curriculum materials focus on the scientific practice of developing and using models as promoted in the Next Generations Science Standards (NGSS) while also addressing nature of science (NOS) goals. The educative features of the newly developed unit support teachers’ pedagogical knowledge (PK) and pedagogical content knowledge (PCK). The unit includes an overview, teacher’s guide, and eight detailed lesson plans with inquiry oriented modeling activities replete with models and suggestions for teachers, as well as formative and summative assessment tasks. The unit design process serves as a model for redesigning other instructional units in
Saritas, M. T.
2015-01-01
The meaningful knowledge creation about molecular geometry has always been the challenge of chemistry learning. In particular, microscopic world of chemistry science (example, atoms, molecules, structures) used in traditional two dimensional way of chemistry teaching can lead to such problem as students create misconceptions. In recent years,…
An algorithm for mass matrix calculation of internally constrained molecular geometries.
Aryanpour, Masoud; Dhanda, Abhishek; Pitsch, Heinz
2008-01-28
Dynamic models for molecular systems require the determination of corresponding mass matrix. For constrained geometries, these computations are often not trivial but need special considerations. Here, assembling the mass matrix of internally constrained molecular structures is formulated as an optimization problem. Analytical expressions are derived for the solution of the different possible cases depending on the rank of the constraint matrix. Geometrical interpretations are further used to enhance the solution concept. As an application, we evaluate the mass matrix for a constrained molecule undergoing an electron-transfer reaction. The preexponential factor for this reaction is computed based on the harmonic model.
An algorithm for mass matrix calculation of internally constrained molecular geometries
International Nuclear Information System (INIS)
Aryanpour, Masoud; Dhanda, Abhishek; Pitsch, Heinz
2008-01-01
Dynamic models for molecular systems require the determination of corresponding mass matrix. For constrained geometries, these computations are often not trivial but need special considerations. Here, assembling the mass matrix of internally constrained molecular structures is formulated as an optimization problem. Analytical expressions are derived for the solution of the different possible cases depending on the rank of the constraint matrix. Geometrical interpretations are further used to enhance the solution concept. As an application, we evaluate the mass matrix for a constrained molecule undergoing an electron-transfer reaction. The preexponential factor for this reaction is computed based on the harmonic model
Polarizability of acetanilide and RDX in the crystal: effect of molecular geometry
Tsiaousis, D.; Munn, R. W.; Smith, P. J.; Popelier, P. L. A.
2004-10-01
Density-functional theory with the B3LYP functional at the 6-311++G** level is used to calculate the dipole moment and the static polarizability for acetanilide and 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) in their in-crystal structures. For acetanilide the dipole moment is 2{1}/{2}% larger than for the gas-phase structure and for RDX (where there is a gross geometry change) it is 15% larger. The polarizability for the in-crystal structure is smaller than for the gas-phase structure by 3% for both species, whereas the in-crystal effective optical polarizability is larger than the gas-phase static polarizability for both crystals. Hence, effects in addition to the molecular geometry change in the crystal must be considered in order to interpret the effective polarizability completely.
International Nuclear Information System (INIS)
Seibt, J.; Marquetand, P.; Engel, Volker; Chen, Z.; Dehm, V.; Wuerthner, F.
2006-01-01
We study spectroscopic properties of molecular dimers coupled by dipole-dipole interactions within the framework of time-dependent quantum mechanics. A systematic variation of the dimer geometry allows to establish relationships between the latter and structures in the absorption spectrum. The theoretical model is constructed with the purpose to characterize the changes in absorption and emission properties arising upon aggregation of perylene bisimides. Measured and calculated spectra are compared, thereby addressing the question if a simple exciton model is capable to describe excited state properties of nanoaggregates of these molecules
van Roosmalen, Jarno; Beekman, Freek J.; Goorden, Marlies C.
2018-01-01
Imaging of 99mTc-labelled tracers is gaining popularity for detecting breast tumours. Recently, we proposed a novel design for molecular breast tomosynthesis (MBT) based on two sliding focusing multi-pinhole collimators that scan a modestly compressed breast. Simulation studies indicate that MBT has the potential to improve the tumour-to-background contrast-to-noise ratio significantly over state-of-the-art planar molecular breast imaging. The aim of the present paper is to optimize the collimator-detector geometry of MBT. Using analytical models, we first optimized sensitivity at different fixed system resolutions (ranging from 5 to 12 mm) by tuning the pinhole diameters and the distance between breast and detector for a whole series of automatically generated multi-pinhole designs. We evaluated both MBT with a conventional continuous crystal detector with 3.2 mm intrinsic resolution and with a pixelated detector with 1.6 mm pixels. Subsequently, full system simulations of a breast phantom containing several lesions were performed for the optimized geometry at each system resolution for both types of detector. From these simulations, we found that tumour-to-background contrast-to-noise ratio was highest for systems in the 7 mm-10 mm system resolution range over which it hardly varied. No significant differences between the two detector types were found.
Iversen, Birger
1992-01-01
Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics
International Nuclear Information System (INIS)
Cui, Yi; Chen, Zengtao
2015-01-01
The effect of initial void geometry on damage progression in a thin aluminum film under uniaxial load is studied via molecular dynamics (MD) method. The embedded voids are with different initial geometries regarding shape, porosity and intervoid ligament distance (ILD). Major simulations are run upon twelve MD geometries with each containing 8–27 million atoms. The corresponding stress–strain relation is monitored during the microstructure evolution of the specimens. The critical stress to trigger the dislocation emission is found in line with the prediction of the Lubarda model. The simulation results reveal that the initial void geometry has substantial impact on the stress–strain relation especially for a specimen with larger initial porosity. (paper)
Validation and extraction of molecular-geometry information from small-molecule databases.
Long, Fei; Nicholls, Robert A; Emsley, Paul; Graǽulis, Saulius; Merkys, Andrius; Vaitkus, Antanas; Murshudov, Garib N
2017-02-01
A freely available small-molecule structure database, the Crystallography Open Database (COD), is used for the extraction of molecular-geometry information on small-molecule compounds. The results are used for the generation of new ligand descriptions, which are subsequently used by macromolecular model-building and structure-refinement software. To increase the reliability of the derived data, and therefore the new ligand descriptions, the entries from this database were subjected to very strict validation. The selection criteria made sure that the crystal structures used to derive atom types, bond and angle classes are of sufficiently high quality. Any suspicious entries at a crystal or molecular level were removed from further consideration. The selection criteria included (i) the resolution of the data used for refinement (entries solved at 0.84 Å resolution or higher) and (ii) the structure-solution method (structures must be from a single-crystal experiment and all atoms of generated molecules must have full occupancies), as well as basic sanity checks such as (iii) consistency between the valences and the number of connections between atoms, (iv) acceptable bond-length deviations from the expected values and (v) detection of atomic collisions. The derived atom types and bond classes were then validated using high-order moment-based statistical techniques. The results of the statistical analyses were fed back to fine-tune the atom typing. The developed procedure was repeated four times, resulting in fine-grained atom typing, bond and angle classes. The procedure will be repeated in the future as and when new entries are deposited in the COD. The whole procedure can also be applied to any source of small-molecule structures, including the Cambridge Structural Database and the ZINC database.
Motta, Mario; Zhang, Shiwei
2018-05-01
We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.
Molecular geometries and relative stabilities of titanium oxide and gold-titanium oxide clusters
Energy Technology Data Exchange (ETDEWEB)
Hudson, Rohan J.; Falcinella, Alexander; Metha, Gregory F., E-mail: greg.metha@adelaide.edu.au
2016-09-30
Titanium oxide and gold-titanium oxide clusters of stoichiometry M{sub x}O{sub y} (M{sub x} = Ti{sub 3}, Ti{sub 4} & AuTi{sub 3}; y = 0 − (2x + 2)) have been investigated using density functional theory. Geometries of determined global energy minimum structures are reported and other isomers predicted up to 0.5 eV higher in energy. The Ti{sub 3}O{sub n} geometries build upon a triangular Ti{sub 3} motif, while Ti{sub 4}O{sub n} stoichiometries template upon a pseudo-tetrahedral Ti{sub 4} structure. Addition of a gold atom to the Ti{sub 3}O{sub n} series does not significantly alter the cluster geometry, with the gold atom preferentially binding to titanium atoms over oxygen atoms. Adiabatic ionization energies, electron affinities and HOMO/LUMO energies increase in magnitude with increasing oxygenation. The HOMO-LUMO energy gaps reach the bulk anatase band gap energy at stoichiometry (Au)Ti{sub m}O{sub 2m−1}, and increase above this upon further oxygen addition. The most stable structural moieties are found to be a cage-like, C{sub 3v} symmetric Ti{sub 4}O{sub 6/7} geometry and a Ti{sub 3}O{sub 6} structure with an η{sup 3}-bound oxygen atom.
Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method
DEFF Research Database (Denmark)
Christensen, A. S.; Svendsen, Casper Steinmann; Fedorov, D. G.
2014-01-01
while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta...
3D Printing of Molecular Models with Calculated Geometries and p Orbital Isosurfaces
Carroll, Felix A.; Blauch, David N.
2017-01-01
3D printing was used to prepare models of the calculated geometries of unsaturated organic structures. Incorporation of p orbital isosurfaces into the models enables students in introductory organic chemistry courses to have hands-on experience with the concept of orbital alignment in strained and unstrained p systems.
Energy Technology Data Exchange (ETDEWEB)
Xie, Wen Jun; Yang, Yi Isaac; Gao, Yi Qin, E-mail: gaoyq@pku.edu.cn [Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering and Biodynamic Optical Imaging Center, Peking University, Beijing 100871 (China)
2015-12-14
In this study, we examine how complex ions such as oxyanions influence the dynamic properties of water and whether differences exist between simple halide anions and oxyanions. Nitrate anion is taken as an example to investigate the hydration properties of oxyanions. Reorientation relaxation of its hydration water can occur through two different routes: water can either break its hydrogen bond with the nitrate to form one with another water or switch between two oxygen atoms of the same nitrate. The latter molecular mechanism increases the residence time of oxyanion’s hydration water and thus nitrate anion slows down the translational motion of neighbouring water. But it is also a “structure breaker” in that it accelerates the reorientation relaxation of hydration water. Such a result illustrates that differences do exist between the hydration of oxyanions and simple halide anions as a result of different molecular geometries. Furthermore, the rotation of the nitrate solute is coupled with the hydrogen bond rearrangement of its hydration water. The nitrate anion can either tilt along the axis perpendicularly to the plane or rotate in the plane. We find that the two reorientation relaxation routes of the hydration water lead to different relaxation dynamics in each of the two above movements of the nitrate solute. The current study suggests that molecular geometry could play an important role in solute hydration and dynamics.
International Nuclear Information System (INIS)
Xie, Wen Jun; Yang, Yi Isaac; Gao, Yi Qin
2015-01-01
In this study, we examine how complex ions such as oxyanions influence the dynamic properties of water and whether differences exist between simple halide anions and oxyanions. Nitrate anion is taken as an example to investigate the hydration properties of oxyanions. Reorientation relaxation of its hydration water can occur through two different routes: water can either break its hydrogen bond with the nitrate to form one with another water or switch between two oxygen atoms of the same nitrate. The latter molecular mechanism increases the residence time of oxyanion’s hydration water and thus nitrate anion slows down the translational motion of neighbouring water. But it is also a “structure breaker” in that it accelerates the reorientation relaxation of hydration water. Such a result illustrates that differences do exist between the hydration of oxyanions and simple halide anions as a result of different molecular geometries. Furthermore, the rotation of the nitrate solute is coupled with the hydrogen bond rearrangement of its hydration water. The nitrate anion can either tilt along the axis perpendicularly to the plane or rotate in the plane. We find that the two reorientation relaxation routes of the hydration water lead to different relaxation dynamics in each of the two above movements of the nitrate solute. The current study suggests that molecular geometry could play an important role in solute hydration and dynamics
DEFF Research Database (Denmark)
Wang, Yanwei; Peters, Günther H.J.; Hansen, Flemming Yssing
2008-01-01
structures (CABS), allows the computation of equilibrium partition coefficients as a function of confinement size solely based on a single sampling of the configuration space of a macromolecule in bulk. Superior in computational speed to previous computational methods, CABS is capable of handling slits...... parameter for characterization of spatial confinement effects on macromolecules. Results for the equilibrium partition coefficient in the weak confinement regime depend only on the ratio ofR-s to the confinement size regardless of molecular details....
Directory of Open Access Journals (Sweden)
Mohammad Firoz Khan
2016-12-01
Full Text Available Ab initio calculations were carried out to study the geometry, solvation free energy, dipole moment, molecular electrostatic potential (MESP, Mulliken and Natural charge distribution, polarizability, hyperpolarizability, Natural Bond Orbital (NBO energetic and different molecular properties like global reactivity descriptors (chemical hardness, softness, chemical potential, electronegativity, electrophilicity index of 2-methylimidazole. B3LYP/6-31G(d,p level of theory was used to optimize the structure both in the gas phase and in solution. The solvation free energy, dipole moment and molecular properties were calculated by applying the Solvation Model on Density (SMD in four solvent systems, namely water, dimethylsulfoxide (DMSO, n-octanol and chloroform. The computed bond distances, bond angles and dihedral angles of 2-methylimidazole agreed reasonably well with the experimental data except for C(2-N(1, C(4-C(5 and N(1-H(7 bond lengths and N(1-C(5-C(4 bond angle. The solvation free energy, dipole moment, polarizability, first order hyperpolarizability, chemical potential, electronegativity and electrophilicity index of 2-methylimidazole increased on going from non-polar to polar solvents. Chemical hardness also increased with increasing polarity of the solvent and the opposite relation was found in the case of softness. These results provide better understanding of the stability and reactivity of 2-methylimidazole in different solvent systems.
Directory of Open Access Journals (Sweden)
Gianvito Grasso
Full Text Available The success of medical threatments with DNA and silencing interference RNA is strongly related to the design of efficient delivery technologies. Cationic polymers represent an attractive strategy to serve as nucleic-acid carriers with the envisioned advantages of efficient complexation, low cost, ease of production, well-defined size, and low polydispersity index. However, the balance between efficacy and toxicity (safety of these polymers is a challenge and in need of improvement. With the aim of designing more effective polycationic-based gene carriers, many parameters such as carrier morphology, size, molecular weight, surface chemistry, and flexibility/rigidity ratio need to be taken into consideration. In the present work, the binding mechanism of three cationic polymers (polyarginine, polylysine and polyethyleneimine to a model siRNA target is computationally investigated at the atomistic level. In order to better understand the polycationic carrier-siRNA interactions, replica exchange molecular dynamic simulations were carried out to provide an exhaustive exploration of all the possible binding sites, taking fully into account the siRNA flexibility together with the presence of explicit solvent and ions. Moreover, well-tempered metadynamics simulations were employed to elucidate how molecular geometry, polycation flexibility, and charge neutralization affect the siRNA-polycations free energy landscape in term of low-energy binding modes and unbinding free energy barriers. Significant differences among polymer binding modes have been detected, revealing the advantageous binding properties of polyarginine and polylysine compared to polyethyleneimine.
International Nuclear Information System (INIS)
Ye Fuqiu; Fan Zhiqiang; He Jun; Peng Jun; Tang Liming
2012-01-01
Applying nonequilibrium Green's functions in combination with the first-principles density-functional theory, we investigate electronic transport properties of an all-carbon molecular device consisting of one phenalenyl molecule and two zigzag graphene nanoribbons. The results show that the electronic transport properties are strongly dependent on the contact geometry and device's currents can drop obviously when the connect sites change from second-nearest sites from the central atom of the molecule (S site) to third-nearest sites from the central atom of the molecule (T site). More importantly, the negative differential resistance behavior is only observed on the negative bias region when the molecule connects the graphene nanoribbons through two T sites.
Spinning geometry = Twisted geometry
International Nuclear Information System (INIS)
Freidel, Laurent; Ziprick, Jonathan
2014-01-01
It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms of twisted geometries. These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but the resulting geometries are not continuous across the faces. Here we show that this phase space can also be represented by continuous, piecewise-flat three-geometries called spinning geometries. These are composed of metric-flat three-cells glued together consistently. The geometry of each cell and the manner in which they are glued is compatible with the choice of fluxes and holonomies. We first remark that the fluxes provide each edge with an angular momentum. By studying the piecewise-flat geometries which minimize edge lengths, we show that these angular momenta can be literally interpreted as the spin of the edges: the geometries of all edges are necessarily helices. We also show that the compatibility of the gluing maps with the holonomy data results in the same conclusion. This shows that a spinning geometry represents a way to glue together the three-cells of a twisted geometry to form a continuous geometry which represents a point in the loop gravity phase space. (paper)
Demonstration of molecular beam epitaxy and a semiconducting band structure for I-Mn-V compounds
International Nuclear Information System (INIS)
Jungwirth, T.; Novak, V.; Cukr, M.; Zemek, J.; Marti, X.; Horodyska, P.; Nemec, P.; Holy, V.; Maca, F.; Shick, A. B.; Masek, J.; Kuzel, P.; Nemec, I.; Gallagher, B. L.; Campion, R. P.; Foxon, C. T.; Wunderlich, J.
2011-01-01
Our ab initio theory calculations predict a semiconducting band structure of I-Mn-V compounds. We demonstrate on LiMnAs that high-quality materials with group-I alkali metals in the crystal structure can be grown by molecular beam epitaxy. Optical measurements on the LiMnAs epilayers are consistent with the theoretical electronic structure. Our calculations also reproduce earlier reports of high antiferromagnetic ordering temperature and predict large, spin-orbit-coupling-induced magnetic anisotropy effects. We propose a strategy for employing antiferromagnetic semiconductors in high-temperature semiconductor spintronics.
Ablikim, Utuq; Bomme, Cédric; Xiong, Hui; Savelyev, Evgeny; Obaid, Razib; Kaderiya, Balram; Augustin, Sven; Schnorr, Kirsten; Dumitriu, Ileana; Osipov, Timur; Bilodeau, René; Kilcoyne, David; Kumarappan, Vinod; Rudenko, Artem; Berrah, Nora; Rolles, Daniel
2016-12-02
An experimental route to identify and separate geometric isomers by means of coincident Coulomb explosion imaging is presented, allowing isomer-resolved photoionization studies on isomerically mixed samples. We demonstrate the technique on cis/trans 1,2-dibromoethene (C 2 H 2 Br 2 ). The momentum correlation between the bromine ions in a three-body fragmentation process induced by bromine 3d inner-shell photoionization is used to identify the cis and trans structures of the isomers. The experimentally determined momentum correlations and the isomer-resolved fragment-ion kinetic energies are matched closely by a classical Coulomb explosion model.
Energy Technology Data Exchange (ETDEWEB)
Su, Yanqing [School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332-0340 (United States); Xu, Shuozhi, E-mail: shuozhixu@gatech.edu [GWW School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405 (United States)
2016-12-15
Void growth is usually considered one of the most critical phases leading to dynamic fracture of ductile materials. Investigating the detailed process of void growth at the nanoscale aids in understanding the damage mechanism of metals. While most atomistic simulations by far assume circular or spherical voids for simplicity, recent studies highlight the significance of the initial void ellipticity in mechanical response of voided metals. In this work, we perform large scale molecular dynamics simulations with millions of atoms to investigate the void growth in plastic deformation of thin films in face-centered cubic Cu. It is found that the initial ellipticity and the initial orientation angle of the void have substantial impacts on the dislocation nucleation, the void evolution, and the stress-strain response. In particular, the initial dislocation emission sites and the sequence of slip plane activation vary with the initial void geometry. For the void size evolution, three regimes are identified: (I) the porosity increases relatively slowly in the absence of dislocations, (II) the porosity grows much more rapidly after dislocations start to glide on different slip planes, and (III) the rate of porosity variation becomes much more slowly when dislocations are saturated in the model, and the void surface becomes irregular, non-smooth. In terms of the stress-strain response, the effects of the initial orientation angle are more pronounced when the initial void ellipticity is large; the influence of the initial void ellipticity is different for different initial orientation angles. The effects of the temperature, the strain rate, the loading direction, and the initial porosity in the void growth are also explored. Our results reveal the underlying mechanisms of initial void geometry-dependent plastic deformation of metallic thin films and shed light on informing more accurate theoretical models.
International Nuclear Information System (INIS)
Su, Yanqing; Xu, Shuozhi
2016-01-01
Void growth is usually considered one of the most critical phases leading to dynamic fracture of ductile materials. Investigating the detailed process of void growth at the nanoscale aids in understanding the damage mechanism of metals. While most atomistic simulations by far assume circular or spherical voids for simplicity, recent studies highlight the significance of the initial void ellipticity in mechanical response of voided metals. In this work, we perform large scale molecular dynamics simulations with millions of atoms to investigate the void growth in plastic deformation of thin films in face-centered cubic Cu. It is found that the initial ellipticity and the initial orientation angle of the void have substantial impacts on the dislocation nucleation, the void evolution, and the stress-strain response. In particular, the initial dislocation emission sites and the sequence of slip plane activation vary with the initial void geometry. For the void size evolution, three regimes are identified: (I) the porosity increases relatively slowly in the absence of dislocations, (II) the porosity grows much more rapidly after dislocations start to glide on different slip planes, and (III) the rate of porosity variation becomes much more slowly when dislocations are saturated in the model, and the void surface becomes irregular, non-smooth. In terms of the stress-strain response, the effects of the initial orientation angle are more pronounced when the initial void ellipticity is large; the influence of the initial void ellipticity is different for different initial orientation angles. The effects of the temperature, the strain rate, the loading direction, and the initial porosity in the void growth are also explored. Our results reveal the underlying mechanisms of initial void geometry-dependent plastic deformation of metallic thin films and shed light on informing more accurate theoretical models.
Czech Academy of Sciences Publication Activity Database
Rastogi, V.K.; Palafox, M. A.; Mittal, L.; Peica, N.; Keifer, W.; Lang, Kamil; Ojha, S.P.
2007-01-01
Roč. 38, č. 10 (2007), s. 1227-1241 ISSN 0377-0486 Institutional research plan: CEZ:AV0Z40320502 Keywords : FTIR and FT-Raman spectra * density functional computations * molecular geometry Subject RIV: CA - Inorganic Chemistry Impact factor: 3.514, year: 2007
Directory of Open Access Journals (Sweden)
Dawid Schellingerhout
Full Text Available BACKGROUND AND PURPOSE: The purpose of our study was to utilize a molecular imaging technology based on the retrograde axonal transport mechanism (neurography, to determine if oxaliplatin-induced neurotoxicity affects retrograde axonal transport in an animal model. MATERIALS AND METHODS: Mice (n = 8/group were injected with a cumulative dose of 30 mg/kg oxaliplatin (sufficient to induce neurotoxicity or dextrose control injections. Intramuscular injections of Tetanus Toxin C-fragment (TTc labeled with Alexa 790 fluorescent dye were done (15 ug/20 uL in the left calf muscles, and in vivo fluorescent imaging performed (0-60 min at baseline, and then weekly for 5 weeks, followed by 2-weekly imaging out to 9 weeks. Tissues were harvested for immunohistochemical analysis. RESULTS: With sham treatment, TTc transport causes fluorescent signal intensity over the thoracic spine to increase from 0 to 60 minutes after injection. On average, fluorescence signal increased 722%+/-117% (Mean+/-SD from 0 to 60 minutes. Oxaliplatin treated animals had comparable transport at baseline (787%+/-140%, but transport rapidly decreased through the course of the study, falling to 363%+/-88%, 269%+/-96%, 191%+/-58%, 121%+/-39%, 75%+/-21% with each successive week and stabilizing around 57% (+/-15% at 7 weeks. Statistically significant divergence occurred at approximately 3 weeks (p≤0.05, linear mixed-effects regression model. Quantitative immuno-fluorescence histology with a constant cutoff threshold showed reduced TTc in the spinal cord at 7 weeks for treated animals versus controls (5.2 Arbitrary Units +/-0.52 vs 7.1 AU +/-1.38, p0.56, T-test. CONCLUSION: We show-for the first time to our knowledge-that neurographic in vivo molecular imaging can demonstrate imaging changes in a model of oxaliplatin-induced neuropathy. Impaired retrograde neural transport is suggested to be an important part of the pathophysiology of oxaliplatin-induced neuropathy.
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...
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.
Continuous all-optical deceleration of molecular beams and demonstration with Rb atoms
Long, Xueping; Jayich, Andrew; Campbell, Wesley
2017-04-01
Ultracold samples of molecules are desirable for a variety of applications, such as many-body physics, precision measurement and quantum information science. However, the pursuit of ultracold molecules has achieved limited success: spontaneous emission into many different dark states makes it hard to optically decelerate molecules to trappable speed. We propose to address this problem with a general optical deceleration technique that exploits a pump-dump pulse pair from a mode-locked laser. A molecular beam is first excited by a counter-propagating ``pump'' pulse. The molecular beam is then driven back to the initial ground state by a co-propagating ``dump'' pulse via stimulated emission. The delay between the pump and dump pulse is set to be shorter than the excited state lifetimes in order to limit decays to dark states. We report progress benchmarking this stimulated force by accelerating a cold sample of neutral Rb atoms.
Li, Ying-hui; Reif, Jochen C; Ma, Yan-song; Hong, Hui-long; Liu, Zhang-xiong; Chang, Ru-zhen; Qiu, Li-juan
2015-10-23
The relative abundance of five dominant fatty acids (FAs) (palmitic, stearic, oleic, linoleic and linolenic acids) is a major factor determining seed quality in soybean. To clarify the currently poorly understood genetic architecture of FAs in soybean, targeted association analysis was conducted in 421 diverse accessions phenotyped in three environments and genotyped using 1536 pre-selected SNPs. The population of 421 soybean accessions displayed significant genetic variation for each FA. Analysis of the molecular data revealed three subpopulations, which reflected a trend depending on latitude of cultivation. A total of 37 significant (p seed quality of soybean with benefits for human health and for food processing.
Demonstration of molecular beam epitaxy and a semiconducting band structure for I-Mn-V compounds
Czech Academy of Sciences Publication Activity Database
Jungwirth, Tomáš; Novák, Vít; Martí, X.; Cukr, Miroslav; Máca, František; Shick, Alexander; Mašek, Jan; Horodyská, P.; Němec, P.; Holý, V.; Zemek, Josef; Kužel, Petr; Němec, I.; Gallagher, B. L.; Campion, R. P.; Foxon, C. T.; Wunderlich, Joerg
2011-01-01
Roč. 83, č. 3 (2011), , , "035321-1"-"035321-6" ISSN 1098-0121 R&D Projects: GA MŠk LC510; GA AV ČR KAN400100652; GA MŠk(CZ) 7E08087 EU Projects: European Commission(XE) 215368 - SemiSpinNet; European Commission(XE) 214499 - NAMASTE; European Commission(XE) 268066 - 0MSPIN Grant - others:AV ČR(CZ) AP0801 Program:Akademická prémie - Praemium Academiae Institutional research plan: CEZ:AV0Z10100520; CEZ:AV0Z10100521 Keywords : antiferromagnetic semiconductors * spintronics * molecular beam epitaxy Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.691, year: 2011
Soe, We-Hyo; Manzano, Carlos; Renaud, Nicolas; de Mendoza, Paula; De Sarkar, Abir; Ample, Francisco; Hliwa, Mohamed; Echavarren, Antonio M; Chandrasekhar, Natarajan; Joachim, Christian
2011-02-22
Quantum states of a trinaphthylene molecule were manipulated by putting its naphthyl branches in contact with single Au atoms. One Au atom carries 1-bit of classical information input that is converted into quantum information throughout the molecule. The Au-trinaphthylene electronic interactions give rise to measurable energy shifts of the molecular electronic states demonstrating a NOR logic gate functionality. The NOR truth table of the single molecule logic gate was characterized by means of scanning tunnelling spectroscopy.
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.
Demonstration of a mid-infrared NO molecular Faraday optical filter.
Wu, Kuijun; Feng, Yutao; Li, Juan; Yu, Guangbao; Liu, Linmei; Xiong, Yuanhui; Li, Faquan
2017-12-11
A molecular Faraday optical filter (MFOF) working in the mid-infrared region is realized for the first time. NO molecule was used as the working material of the MFOF for potential applications in atmospheric remote sensing and combustion diagnosis. We develop a complete theory to describe the performance of MFOF by taking both Zeeman absorption and Faraday rotation into account. We also record the Faraday rotation transmission (FRT) signal using a quantum cascade laser over the range of 1,820 cm -1 to 1,922 cm -1 and calibrate it by using a 101.6 mm long solid germanium etalon with a free spectral range of 0.012 cm -1 . Good agreement between the simulation results and experimental data is achieved. The NO-MFOF's transmission characteristics as a function of magnetic field and pressure are studied in detail. Both Comb-like FRT spectrum and single branch transmission spectrum are obtained by changing the magnetic field. The diversity of FRT spectrum expands the range of potential applications in infrared optical remote sensing. This filtering method can also be extended to the lines of other paramagnetic molecules.
Energy Technology Data Exchange (ETDEWEB)
BOWERS,RICHARD; CHANDLER,GORDON A.; HEBRON,DAVID E.; LEEPER,RAMON J.; MATUSLKA,WALTER; MOCK,RAYMOND CECIL; NASH,THOMAS J.; OLSON,CRAIG L.; PETERSON,BOB; PETERSON,DARRELL; RUGGLES,LAURENCE E.; SANFORD,THOMAS W. L.; SIMPSON,WALTER W.; STRUVE,KENNETH W.; VESEY,ROGER A.
1999-11-01
Hohlraums of full ignition scale (6-mm diameter by 7-mm length) have been heated by x-rays from a z-pinch magnet on Z to a variety of temperatures and pulse shapes which can be used to simulate the early phases of the National Ignition Facility (NIF) temperature drive. The pulse shape is varied by changing the on-axis target of the z pinch in a static-wall-hohlraum geometry. A 2-{micro}m-thick walled Cu cylindrical target of 8-mm diameter filled with 10 mg/cm{sup 3} CH, for example, produces foot-pulse conditions of {approx}85 eV for a duration of {approx}10 ns, while a solid cylindrical target of 5-mm diameter and 14-mg/cm{sup 3} CH generates first-step-pulse conditions of {approx}122 eV for a duration of a few ns. Alternatively, reducing the hohlraum size (to 4-mm diameter by 4-mm length) with the latter target has increased the peak temperature to {approx}150 eV, which is characteristic of a second-step-pulse temperature. In general, the temperature T of these x-ray driven hohlraums is in agreement with the Planckian relation T{approx}(P/A){sup 1/4}. P is the measured x-ray input power and A is the surface area of the hohlraum. Fully-integrated 2-D radiation-hydrodynamic simulations of the z pinch and subsequent hohlraum heating show plasma densities within the useful volume of the hohlraums to be on the order of air or less.
International Nuclear Information System (INIS)
Sandord, T.W.L.; Olson, R.E.; Chandler, G.A.; Hebron, D.E.; Mock, R.C.; Leeper, R.J.; Nash, T.J.; Ruggles, L.E.; Simpson, W.W.; Struve, K.W.; Vesey, R.A.; Bowers, R.L.; Matuska, W.; Peterson, D.L.; Peterson, R.R.
1999-01-01
Hohlraums of full ignition scale (6-mm diameter by 7-mm length) have been heated by x-rays from a z-pinch target on Z to a variety of temperatures and pulse shapes which can be used to simulate the early phases of the National Ignition Facility (NIF) temperature drive. The pulse shape is varied by changing the on-axis target of the z pinch in a static-wall-hohlraum geometry. A 2-microm-thick walled Cu cylindrical target of 8-mm diameter filled with 10 mg/cm 3 CH, for example, produces foot-pulse conditions of minus85 eV for a duration of approximately 10 ns, while a solid cylindrical target of 5-mm diameter and 14-mg/cm 3 CH generates first-step-pulse conditions of approximately 122 eV for a duration of a few ns. Alternatively, reducing the hohlraum size (to 4-mm diameter by 4-mm length) with the latter target has increased the peak temperature to approximately 150 eV, which is characteristic of a second-step-pulse temperature. In general, the temperature T of these x-ray driven hohlraums is in agreement with the Planckian relation (T-(P/A) 1/4 ). P is the measured x-ray input power and A is the surface area of the hohlraum. Fully-integrated 2-D radiation-hydrodynamic simulations of the z pinch and subsequent hohlraum heating show plasma densities within the useful volume of the hohlraums to be on the order of air or less
Energy Technology Data Exchange (ETDEWEB)
Sandord, T.W.L.; Olson, R.E.; Chandler, G.A.; Hebron, D.E.; Mock, R.C.; Leeper, R.J.; Nash, T.J.; Ruggles, L.E.; Simpson, W.W.; Struve, K.W.; Vesey, R.A.; Bowers, R.L.; Matuska, W.; Peterson, D.L.; Peterson, R.R.
1999-08-25
Hohlraums of full ignition scale (6-mm diameter by 7-mm length) have been heated by x-rays from a z-pinch target on Z to a variety of temperatures and pulse shapes which can be used to simulate the early phases of the National Ignition Facility (NIF) temperature drive. The pulse shape is varied by changing the on-axis target of the z pinch in a static-wall-hohlraum geometry. A 2-{micro}m-thick walled Cu cylindrical target of 8-mm diameter filled with 10 mg/cm{sup 3} CH, for example, produces foot-pulse conditions of {minus}85 eV for a duration of {approximately} 10 ns, while a solid cylindrical target of 5-mm diameter and 14-mg/cm{sup 3} CH generates first-step-pulse conditions of {approximately} 122 eV for a duration of a few ns. Alternatively, reducing the hohlraum size (to 4-mm diameter by 4-mm length) with the latter target has increased the peak temperature to {approximately} 150 eV, which is characteristic of a second-step-pulse temperature. In general, the temperature T of these x-ray driven hohlraums is in agreement with the Planckian relation (T-(P/A){sup 1/4}). P is the measured x-ray input power and A is the surface area of the hohlraum. Fully-integrated 2-D radiation-hydrodynamic simulations of the z pinch and subsequent hohlraum heating show plasma densities within the useful volume of the hohlraums to be on the order of air or less.
International Nuclear Information System (INIS)
Sanford, T.W.L.; Olson, R.E.; Mock, R.C.; Chandler, G.A.; Hebron, D.E.; Leeper, R.J.; Nash, T.J.; Ruggles, L.E.; Simpson, W.W.; Struve, K.W.; Vesey, R.A.; Bowers, R.L.; Matuska, W.; Peterson, D.L.; Peterson, R.R.
2000-01-01
Hohlraums of full ignition scale (6-mm diameter by 7-mm length) have been heated by x-rays from a z-pinch target on Z to a variety of temperatures and pulse shapes which can be used to simulate the early phases of the National Ignition Facility (NIF) temperature drive. The pulse shape is varied by changing the on-axis target of the z pinch in a static-wall-hohlraum geometry [Fusion Technol. 35, 260 (1999)]. A 2-μm-thick walled Cu cylindrical target of 8-mm diameter filled with 10 mg/cm 3 CH, for example, produces foot-pulse conditions of ∼85 eV for a duration of ∼10 ns, while a solid cylindrical target of 5-mm diameter and 14-mg/cm 3 CH generates first-step-pulse conditions of ∼122 eV for a duration of a few ns. Alternatively, reducing the hohlraum size (to 4-mm diameter by 4-mm length) with the latter target has increased the peak temperature to ∼150 eV, which is characteristic of a second-step-pulse temperature. In general, the temperature T of these x-ray driven hohlraums is in agreement with the Planckian relation T∼(P/A) 1/4 . P is the measured x-ray input power and A is the surface area of the hohlraum. Fully-integrated 2-D radiation hydrodynamic simulations of the z pinch and subsequent hohlraum heating show plasma densities within the useful volume of the hohlraums to be on the order of 10 -3 g/cm 3 or less. (authors)
International Nuclear Information System (INIS)
Sanford, Thomas W.L.; Bowers, Richard; Chandler, Gordon A.; Hebron, David E.; Leeper, Ramon J.; Matulska, W Alter; Mock, Raymond Cecil; Nash, Thomas J.; Olson, Craig L.; Peterson, Bob; Peterson, Darrell; Ruggles, Laurence E.; Simpson, Walter W.; Struve, Kenneth W.; Vesey, Roger A.
1999-01-01
Hohlraums of full ignition scale (6-mm diameter by 7-mm length) have been heated by x-rays from a z-pinch magnet on Z to a variety of temperatures and pulse shapes which can be used to simulate the early phases of the National Ignition Facility (NIF) temperature drive. The pulse shape is varied by changing the on-axis target of the z pinch in a static-wall-hohlraum geometry. A 2-microm-thick walled Cu cylindrical target of 8-mm diameter filled with 10 mg/cm 3 CH, for example, produces foot-pulse conditions of ∼85 eV for a duration of ∼10 ns, while a solid cylindrical target of 5-mm diameter and 14-mg/cm 3 CH generates first-step-pulse conditions of ∼122 eV for a duration of a few ns. Alternatively, reducing the hohlraum size (to 4-mm diameter by 4-mm length) with the latter target has increased the peak temperature to ∼150 eV, which is characteristic of a second-step-pulse temperature. In general, the temperature T of these x-ray driven hohlraums is in agreement with the Planckian relation T∼(P/A) 1/4 . P is the measured x-ray input power and A is the surface area of the hohlraum. Fully-integrated 2-D radiation-hydrodynamic simulations of the z pinch and subsequent hohlraum heating show plasma densities within the useful volume of the hohlraums to be on the order of air or less
International Nuclear Information System (INIS)
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A.; Plecháč, Petr
2015-01-01
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems
Energy Technology Data Exchange (ETDEWEB)
Kalligiannaki, Evangelia, E-mail: ekalligian@tem.uoc.gr [Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion (Greece); Harmandaris, Vagelis, E-mail: harman@uoc.gr [Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion (Greece); Institute of Applied and Computational Mathematics (IACM), Foundation for Research and Technology Hellas (FORTH), IACM/FORTH, GR-71110 Heraklion (Greece); Katsoulakis, Markos A., E-mail: markos@math.umass.edu [Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States); Plecháč, Petr, E-mail: plechac@math.udel.edu [Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716 (United States)
2015-08-28
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force and to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.
McAnally, Michael O.; Hlavacek, Nikolaus C.; Drucker, Stephen
2012-06-01
The spectroscopically derived inertial constants for acrolein (propenal) in its T_1(n,π*) state were used to test predictions from a variety of computational methods. One focus was on multiconfigurational methods, such as CASSCF and CASPT2, that are applicable to excited states. We also examined excited-state methods that utilize single reference configurations, including EOM-EE-CCSD and TD-PBE0. Finally, we applied unrestricted ground-state techniques, such as UCCSD(T) and the more economical UPBE0 method, to the T_1(n,π*) excited state under the constraint of C_s symmetry. The unrestricted ground-state methods are applicable because at a planar geometry, the T_1(n,π*) state of acrolein is the lowest-energy state of its spin multiplicity. Each of the above methods was used with a triple zeta quality basis set to optimize the T_1(n,π*) geometry. This procedure resulted in the following sets of inertial constants: Inertial constants (cm-1) of acrolein in its T_1(n,π*) state Method A B C Method A B C CASPT2(6,5) 1.667 0.1491 0.1368 UCCSD(T)^b 1.668 0.1480 0.1360 CASSCF(6,5) 1.667 0.1491 0.1369 UPBE0 1.699 0.1487 0.1367 EOM-EE-CCSD 1.675 0.1507 0.1383 TD-PBE0 1.719 0.1493 0.1374 Experiment^a 1.662 0.1485 0.1363 The two multiconfigurational methods produce the same inertial constants, and those constants agree closely with experiment. However the sets of computed bond lengths differ significantly for the two methods. In the CASSCF calculation, the lengthening of the C=O and C=C bonds and the shortening of the C--C bond are more pronounced than in CASPT2. O. S. Bokareva et al., Int. J. Quant. Chem. {108}, 2719 (2008).
International Nuclear Information System (INIS)
Clore, G.M.; Gronenborn, A.M.; Nilges, M.; Ryan, C.A.
1987-01-01
The solution conformation of potato carboxypeptidase inhibitor (CPI) has been investigated by 1 H NMR spectroscopy. The spectrum is assigned in a sequential manner by using two-dimensional NMR techniques to identify through-bond and through-space (<5 A) connectivities. A set of 309 approximate interproton distance restraints is derived from the two-dimensional nuclear Overhauser enhancement spectra and used as the basis of a three-dimensional structure determination by a combination of metric matrix distance geometry and restrained molecular dynamics calculations. A total of 11 converged distance geometry structures were computed and refined by using restrained molecular dynamics. The average atomic root mean square (rms) difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.3 A for residues 2-39 and 0.9 +/- 0.2 A for residues 5-37. The corresponding values for all atoms are 1.9 +/- 0.3 and 1.4 +/- 0.2 A, respectively. The computed structures are very close to the X-ray structure of CPI in its complex with carboxypeptidase, and the backbone atomic rms difference between the mean of the computed structures and the X-ray structure is only 1.2 A. Nevertheless, there are some real differences present which are evidenced by significant deviations between the experimental upper interproton distance limits and the corresponding interproton distances derived from the X-ray structure. These principally occur in two regions, residues 18-20 and residues 28-30, the latter comprising part of the region of secondary contact between CPI and carboxypeptidase in the X-ray structure
International Nuclear Information System (INIS)
Robinson, I.; Trautman, A.
1988-01-01
The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem
Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes
2014-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
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
International Nuclear Information System (INIS)
Slater, G.F.; Nelson, R.K.; Kile, B.M.; Reddy, C.M.
2006-01-01
Natural abundance, molecular-level C 14 analysis was combined with comprehensive gas chromatography (GC x GC) to investigate, in situ, the role of intrinsic biodegradation in the loss of petroleum hydrocarbons from the rocky, inter-tidal zone impacted by the Bouchard 120 oil spill. GC x GC analysis indicated accelerated losses of n-alkane components of the residual petroleum hydrocarbons between day 40 and day 50 after the spill. 14 C analysis of bacterial phospholipid fatty acids (PLFA) from the impacted zone on day 44 showed that the polyunsaturated fatty acids attributed to the photoautotrophic component of the microbial community had the same ( 14 C as the local dissolved inorganic carbon (DIG), indicating that this DIG was their carbon source. In contrast there was significant (C depletion in the saturated and mono-unsaturated PLFA indicating incorporation of petroleum carbon. This correlation between the observed accelerated n-alkane losses and microbial incorporation of (C-depleted carbon directly demonstrated, in situ, that intrinsic biodegradation was affecting the petroleum. Since the majority of organic contaminants originate from petroleum feed-stocks, in situ molecular-level 14 C analysis of microbial PLFA can provide insights into the occurrence and pathways of biodegradation of a wide range of organic contaminants. (Author)
Energy Technology Data Exchange (ETDEWEB)
Oie, Tetsuro [Univ. of Rochester, NY (United States); Univ. of Kansas, Lawrence, KS (United States). Dept. of Chemistry
1980-07-28
A purpose of the present studies is twofold: (1) development of an empirical potential function (EPF) and (2) application of it to the studies of photoreaction center chlorophyll a dimer. The reliable estimate of geometric structures and energies of large molecules by quantum mechanical methods is not possible at the present time. An alternative method is, therefore, needed for the studies of large molecular systems, and Chapter I is dedicated to the development of this tool, i.e., an empirical potential function, which could suffice this purpose. Because of a large number of variable chemical compositions and functional groups characteristically present in a large molecule, it is important to include a large number of structurally diverse molecules in the development of the EPF. In Chapter II, the EPF is applied to study the geometrical structure of a chlorophyll a (Chl a) dimer, which is believed to exist at the photoreaction center of green plants and is known to play an essential role in photosynthetic energy conversion. Although various models have been proposed for this dimer structure, there is still a great need for information concerning the detailed geometric structure of this dimer. Therefore, in this chapter the structural stabilities of various dimer models are examined by the EPF, and detailed and quantitative information on the structure and stability of these models is provided.
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Kemnitz, Arnfried
Der Grundgedanke der Analytischen Geometrie besteht darin, dass geometrische Untersuchungen mit rechnerischen Mitteln geführt werden. Geometrische Objekte werden dabei durch Gleichungen beschrieben und mit algebraischen Methoden untersucht.
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...
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
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,
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
Connes, Alain
1994-01-01
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat
Indian Academy of Sciences (India)
mathematicians are trained to use very precise language, and so find it hard to simplify and state .... thing. If you take a plane on which there are two such triangles which enjoy the above ... within this geometry to simplify things if needed.
Geometry -----------~--------------RESONANCE
Indian Academy of Sciences (India)
Parallel: A pair of lines in a plane is said to be parallel if they do not meet. Mathematicians were at war ... Subsequently, Poincare, Klein, Beltrami and others refined non-. Euclidean geometry. ... plane divides the plane into two half planes and.
Suresh, S; Gunasekaran, S; Srinivasan, S
2014-11-11
The solid phase FT-IR and FT-Raman spectra of 2-hydroxybenzoic acid (salicylic acid) have been recorded in the region 4000-400 and 4000-100 cm(-1) respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method at 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies are scaled and they are compared with experimentally obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method is employed to predict its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MEP) are also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis. Published by Elsevier B.V.
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...
International Nuclear Information System (INIS)
Strominger, A.
1990-01-01
A special manifold is an allowed target manifold for the vector multiplets of D=4, N=2 supergravity. These manifolds are of interest for string theory because the moduli spaces of Calabi-Yau threefolds and c=9, (2,2) conformal field theories are special. Previous work has given a local, coordinate-dependent characterization of special geometry. A global description of special geometries is given herein, and their properties are studied. A special manifold M of complex dimension n is characterized by the existence of a holomorphic Sp(2n+2,R)xGL(1,C) vector bundle over M with a nowhere-vanishing holomorphic section Ω. The Kaehler potential on M is the logarithm of the Sp(2n+2,R) invariant norm of Ω. (orig.)
Hannah, Daniel C; Gezelter, J Daniel; Schaller, Richard D; Schatz, George C
2015-06-23
We examine the role played by surface structure and passivation in thermal transport at semiconductor/organic interfaces. Such interfaces dominate thermal transport in semiconductor nanomaterials owing to material dimensions much smaller than the bulk phonon mean free path. Utilizing reverse nonequilibrium molecular dynamics simulations, we calculate the interfacial thermal conductance (G) between a hexane solvent and chemically passivated wurtzite CdSe surfaces. In particular, we examine the dependence of G on the CdSe slab thickness, the particular exposed crystal facet, and the extent of surface passivation. Our results indicate a nonmonotonic dependence of G on ligand-grafting density, with interfaces generally exhibiting higher thermal conductance for increasing surface coverage up to ∼0.08 ligands/Å(2) (75-100% of a monolayer, depending on the particular exposed facet) and decreasing for still higher coverages. By analyzing orientational ordering and solvent penetration into the ligand layer, we show that a balance of competing effects is responsible for this nonmonotonic dependence. Although the various unpassivated CdSe surfaces exhibit similar G values, the crystal structure of an exposed facet nevertheless plays an important role in determining the interfacial thermal conductance of passivated surfaces, as the density of binding sites on a surface determines the ligand-grafting densities that may ultimately be achieved. We demonstrate that surface passivation can increase G relative to a bare surface by roughly 1 order of magnitude and that, for a given extent of passivation, thermal conductance can vary by up to a factor of ∼2 between different surfaces, suggesting that appropriately tailored nanostructures may direct heat flow in an anisotropic fashion for interface-limited thermal transport.
International Nuclear Information System (INIS)
Allen, P.G.; Berg, J.M.; Chisholm-Brause, C.J.; Conradson, S.D.; Donohoe, R.J.; Morris, D.E.; Musgrave, J.A.; Tait, C.D.
1994-01-01
The US Department of Energy's former uranium production facility located at Fernald, OH (18 mi NW of Cincinnati) is the host site for an Integrated Demonstration for remediation of uranium-contaminated soils. A wide variety of source terms for uranium contamination have been identified reflecting the diversity of operations at the facility. Most of the uranium contamination is contained in the top ∼1/2 m of soil, but uranium has been found in perched waters indicating substantial migration. In support of the development of remediation technologies and risk assessment, we are conducting uranium speciation studies on untreated and treated soils using molecular spectroscopies. Untreated soils from five discrete sites have been analyzed. We have found that ∼80--90% of the uranium exists as hexavalent UO 2 2+ species even though many source terms consisted of tetravalent uranium species such as UO 2 . Much of the uranium exists as microcrystalline precipitates (secondary minerals). There is also clear evidence for variations in uranium species from the microscopic to the macroscopic scale. However, similarities in speciation at sites having different source terms suggest that soil and groundwater chemistry may be as important as source term in defining the uranium speciation in these soils. Characterization of treated soils has focused on materials from two sites that have undergone leaching using conventional extractants (e.g., carbonate, citrate) or novel chelators such as Tiron. Redox reagents have also been used to facilitate the leaching process. Three different classes of treated soils have been identified based on the speciation of uranium remaining in the soils. In general, the effective treatments decrease the total uranium while increasing the ratio of U(IV) to U(VI) species
Lagorce, David; Pencheva, Tania; Villoutreix, Bruno O; Miteva, Maria A
2009-11-13
Discovery of new bioactive molecules that could enter drug discovery programs or that could serve as chemical probes is a very complex and costly endeavor. Structure-based and ligand-based in silico screening approaches are nowadays extensively used to complement experimental screening approaches in order to increase the effectiveness of the process and facilitating the screening of thousands or millions of small molecules against a biomolecular target. Both in silico screening methods require as input a suitable chemical compound collection and most often the 3D structure of the small molecules has to be generated since compounds are usually delivered in 1D SMILES, CANSMILES or in 2D SDF formats. Here, we describe the new open source program DG-AMMOS which allows the generation of the 3D conformation of small molecules using Distance Geometry and their energy minimization via Automated Molecular Mechanics Optimization. The program is validated on the Astex dataset, the ChemBridge Diversity database and on a number of small molecules with known crystal structures extracted from the Cambridge Structural Database. A comparison with the free program Balloon and the well-known commercial program Omega generating the 3D of small molecules is carried out. The results show that the new free program DG-AMMOS is a very efficient 3D structure generator engine. DG-AMMOS provides fast, automated and reliable access to the generation of 3D conformation of small molecules and facilitates the preparation of a compound collection prior to high-throughput virtual screening computations. The validation of DG-AMMOS on several different datasets proves that generated structures are generally of equal quality or sometimes better than structures obtained by other tested methods.
Directory of Open Access Journals (Sweden)
Villoutreix Bruno O
2009-11-01
Full Text Available Abstract Background Discovery of new bioactive molecules that could enter drug discovery programs or that could serve as chemical probes is a very complex and costly endeavor. Structure-based and ligand-based in silico screening approaches are nowadays extensively used to complement experimental screening approaches in order to increase the effectiveness of the process and facilitating the screening of thousands or millions of small molecules against a biomolecular target. Both in silico screening methods require as input a suitable chemical compound collection and most often the 3D structure of the small molecules has to be generated since compounds are usually delivered in 1D SMILES, CANSMILES or in 2D SDF formats. Results Here, we describe the new open source program DG-AMMOS which allows the generation of the 3D conformation of small molecules using Distance Geometry and their energy minimization via Automated Molecular Mechanics Optimization. The program is validated on the Astex dataset, the ChemBridge Diversity database and on a number of small molecules with known crystal structures extracted from the Cambridge Structural Database. A comparison with the free program Balloon and the well-known commercial program Omega generating the 3D of small molecules is carried out. The results show that the new free program DG-AMMOS is a very efficient 3D structure generator engine. Conclusion DG-AMMOS provides fast, automated and reliable access to the generation of 3D conformation of small molecules and facilitates the preparation of a compound collection prior to high-throughput virtual screening computations. The validation of DG-AMMOS on several different datasets proves that generated structures are generally of equal quality or sometimes better than structures obtained by other tested methods.
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...
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
Directory of Open Access Journals (Sweden)
Francis J. May
2017-02-01
Full Text Available Exercise improves whole-body metabolic health through adaptations to various tissues, including adipose tissue, but the effects of exercise training on the lipidome of white adipose tissue (WAT and brown adipose tissue (BAT are unknown. Here, we utilize MS/MSALL shotgun lipidomics to determine the molecular signatures of exercise-induced adaptations to subcutaneous WAT (scWAT and BAT. Three weeks of exercise training decrease specific molecular species of phosphatidic acid (PA, phosphatidylcholines (PC, phosphatidylethanolamines (PE, and phosphatidylserines (PS in scWAT and increase specific molecular species of PC and PE in BAT. Exercise also decreases most triacylglycerols (TAGs in scWAT and BAT. In summary, exercise-induced changes to the scWAT and BAT lipidome are highly specific to certain molecular lipid species, indicating that changes in tissue lipid content reflect selective remodeling in scWAT and BAT of both phospholipids and glycerol lipids in response to exercise training, thus providing a comprehensive resource for future studies of lipid metabolism pathways.
Stein, R Will; Brown, Joseph W; Mooers, Arne Ø
2015-11-01
The phylogeny of Galliformes (landfowl) has been studied extensively; however, the associated chronologies have been criticized recently due to misplaced or misidentified fossil calibrations. As a consequence, it is unclear whether any crown-group lineages arose in the Cretaceous and survived the Cretaceous-Paleogene (K-Pg; 65.5 Ma) mass extinction. Using Bayesian phylogenetic inference on an alignment spanning 14,539 bp of mitochondrial and nuclear DNA sequence data, four fossil calibrations, and a combination of uncorrelated lognormally distributed relaxed-clock and strict-clock models, we inferred a time-calibrated molecular phylogeny for 225 of the 291 extant Galliform taxa. These analyses suggest that crown Galliformes diversified in the Cretaceous and that three-stem lineages survived the K-Pg mass extinction. Ideally, characterizing the tempo and mode of diversification involves a taxonomically complete phylogenetic hypothesis. We used simple constraint structures to incorporate 66 data-deficient taxa and inferred the first taxon-complete phylogenetic hypothesis for the Galliformes. Diversification analyses conducted on 10,000 timetrees sampled from the posterior distribution of candidate trees show that the evolutionary history of the Galliformes is best explained by a rate-shift model including 1-3 clade-specific increases in diversification rate. We further show that the tempo and mode of diversification in the Galliformes conforms to a three-pulse model, with three-stem lineages arising in the Cretaceous and inter and intrafamilial diversification occurring after the K-Pg mass extinction, in the Paleocene-Eocene (65.5-33.9 Ma) or in association with the Eocene-Oligocene transition (33.9 Ma). Copyright © 2015 Elsevier Inc. All rights reserved.
De Backer, M; Bonants, P; Pedley, K F; Maes, M; Roldan-Ruiz, I; Van Bockstaele, E; Heungens, K; van der Lee, T
2013-11-01
The obligate biotrophic pathogen Puccinia horiana is the causal agent of chrysanthemum white rust. Although P. horiana is a quarantine organism, it has been able to spread to most chrysanthemum-producing regions in the world since the 1960s; however, the transfer routes are largely obscure. An extremely low level of allelic diversity was observed in a geographically diverse set of eight isolates using complexity reduction of polymorphic sequences (CRoPS) technology. Only 184 of the 16,196 contigs (1.1%) showed one or more single-nucleotide polymorphisms (SNPs). Thirty-two SNPs and one simple-sequence repeat were translated into molecular markers and used to genotype 45 isolates originating from North and South America, Asia, and Europe. In most cases, phylogenetic clustering was related to geographic origin, indicating local establishment. The European isolates mostly grouped in two major populations that may relate to the two historic introductions previously reported. However, evidence of recent geographic transfer was also observed, including transfer events between Europe and South America and between Southeast Asia and Europe. In contrast with the presumed clonal propagation of this microcyclic rust, strong indications of marker recombination were observed, presumably as a result of anastomosis, karyogamy, and somatic meiosis. Recombination and transfer also explain the geographic dispersal of specific markers. A near-to-significant correlation between the genotypic data and previously obtained pathotype data was observed and one marker was associated with the most virulent pathotype group. In combination with a fast SNP detection method, the markers presented here will be helpful tools to further elucidate the transfer pathways and local survival of this pathogen.
Silva, Alessandro
1993-01-01
The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.
Eisenhart, Luther Pfahler
2005-01-01
This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.
International Nuclear Information System (INIS)
Gurevich, L.Eh.; Gliner, Eh.B.
1978-01-01
Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding
Goldberg, Caren S; Pilliod, David S; Arkle, Robert S; Waits, Lisette P
2011-01-01
Stream ecosystems harbor many secretive and imperiled species, and studies of vertebrates in these systems face the challenges of relatively low detection rates and high costs. Environmental DNA (eDNA) has recently been confirmed as a sensitive and efficient tool for documenting aquatic vertebrates in wetlands and in a large river and canal system. However, it was unclear whether this tool could be used to detect low-density vertebrates in fast-moving streams where shed cells may travel rapidly away from their source. To evaluate the potential utility of eDNA techniques in stream systems, we designed targeted primers to amplify a short, species-specific DNA fragment for two secretive stream amphibian species in the northwestern region of the United States (Rocky Mountain tailed frogs, Ascaphus montanus, and Idaho giant salamanders, Dicamptodon aterrimus). We tested three DNA extraction and five PCR protocols to determine whether we could detect eDNA of these species in filtered water samples from five streams with varying densities of these species in central Idaho, USA. We successfully amplified and sequenced the targeted DNA regions for both species from stream water filter samples. We detected Idaho giant salamanders in all samples and Rocky Mountain tailed frogs in four of five streams and found some indication that these species are more difficult to detect using eDNA in early spring than in early fall. While the sensitivity of this method across taxa remains to be determined, the use of eDNA could revolutionize surveys for rare and invasive stream species. With this study, the utility of eDNA techniques for detecting aquatic vertebrates has been demonstrated across the majority of freshwater systems, setting the stage for an innovative transformation in approaches for aquatic research.
Directory of Open Access Journals (Sweden)
Caren S Goldberg
Full Text Available Stream ecosystems harbor many secretive and imperiled species, and studies of vertebrates in these systems face the challenges of relatively low detection rates and high costs. Environmental DNA (eDNA has recently been confirmed as a sensitive and efficient tool for documenting aquatic vertebrates in wetlands and in a large river and canal system. However, it was unclear whether this tool could be used to detect low-density vertebrates in fast-moving streams where shed cells may travel rapidly away from their source. To evaluate the potential utility of eDNA techniques in stream systems, we designed targeted primers to amplify a short, species-specific DNA fragment for two secretive stream amphibian species in the northwestern region of the United States (Rocky Mountain tailed frogs, Ascaphus montanus, and Idaho giant salamanders, Dicamptodon aterrimus. We tested three DNA extraction and five PCR protocols to determine whether we could detect eDNA of these species in filtered water samples from five streams with varying densities of these species in central Idaho, USA. We successfully amplified and sequenced the targeted DNA regions for both species from stream water filter samples. We detected Idaho giant salamanders in all samples and Rocky Mountain tailed frogs in four of five streams and found some indication that these species are more difficult to detect using eDNA in early spring than in early fall. While the sensitivity of this method across taxa remains to be determined, the use of eDNA could revolutionize surveys for rare and invasive stream species. With this study, the utility of eDNA techniques for detecting aquatic vertebrates has been demonstrated across the majority of freshwater systems, setting the stage for an innovative transformation in approaches for aquatic research.
Mariappan, G.; Sundaraganesan, N.
2014-04-01
Vibrational assignments for the 7-amino-2-methylchromone (abbreviated as 7A2MC) molecule using a combination of experimental vibrational spectroscopic measurements and ab initio computational methods are reported. The optimized geometry, intermolecular hydrogen bonding, first order hyperpolarizability and harmonic vibrational wavenumbers of 7A2MC have been investigated with the help of B3LYP density functional theory method. The calculated molecular geometry parameters, the theoretically computed vibrational frequencies for monomer and dimer and relative peak intensities were compared with experimental data. DFT calculations using the B3LYP method and 6-31 + G(d,p) basis set were found to yield results that are very comparable to experimental IR and Raman spectra. Detailed vibrational assignments were performed with DFT calculations and the potential energy distribution (PED) obtained from the Vibrational Energy Distribution Analysis (VEDA) program. Natural Bond Orbital (NBO) study revealed the characteristics of the electronic delocalization of the molecular structure. 13C and 1H NMR spectra have been recorded and 13C and 1H nuclear magnetic resonance chemical shifts of the molecule have been calculated using the gauge independent atomic orbital (GIAO) method. Furthermore, All the possible calculated values are analyzed using correlation coefficients linear fitting equation and are shown strong correlation with the experimental data.
Gessler, Florian; Baumgarten, Peter; Bernstock, Joshua D; Harter, Patrick; Lescher, Stephanie; Senft, Christian; Seifert, Volker; Marquardt, Gerhard; Weise, Lutz
2017-06-01
The classification, treatment and prognosis of high-grade gliomas has been shown to correlate with the expression of molecular markers (e.g. MGMT promotor methylation and IDH1 mutations). Acquisition of tumor samples may be obtained via stereotactic biopsy or open craniotomy. Between the years 2009 and 2013, 22 patients initially diagnosed with HGGs via stereotactic biopsy, that ultimately underwent open craniotomy for resection of their tumor were prospectively included in an institutional glioma database. MGMT promotor analysis was performed using methylation-specific (MS)-PCR and IDH1R132H mutation analysis was performed using immunohistochemistry. Three patients (13.7%) exhibited IDH1R132H mutations in samples obtained via stereotactic biopsy. Tissue derived from stereotaxic biopsy was demonstrated to have MGMT promotor methylation in ten patients (45.5%), while a non-methylated MGMT promotor was demonstrated in ten patients (45.5%); inconclusive results were obtained for the remaining two patients (9%) within our cohort. The initial histologic grading, IDH1R132H mutation and MGMT promotor methylation results were confirmed using samples obtained during open craniotomy in all but one patient; here inconclusive MGMT promotor analysis was obtained in contrast to that which was obtained via stereotactic biopsy. Tumor samples acquired via stereotactic biopsy provide accurate information with regard to clinically relevant molecular markers that have been shown to impact patient care decisions. The profile of markers analyzed in our cohort was nearly concordant between those samples obtained via stereotactic biopsy or open craniotomy thereby suggesting that clinical decisions may be based on the molecular profile of the tumor samples obtained via stereotactic biopsy.
Directory of Open Access Journals (Sweden)
Denis Kole
2017-05-01
Full Text Available Basic fibroblast growth factor (FGF2 is a highly pleiotropic member of a large family of growth factors with a broad range of activities, including mitogenesis and angiogenesis (Ornitz et al., 1996; Zhang et al., 2006, and it is known to be essential for maintenance of balance between survival, proliferation, and self-renewal in human pluripotent stem cells (Eiselleova et al., 2009; Zoumaro-Djayoon et al., 2011. A single FGF2 transcript can be translated into five FGF2 protein isoforms, an 18 kDa low molecular weight (LMW isoform and four larger high molecular weight (HMW isoforms (Arese et al., 1999; Arnaud et al., 1999. As they are not generally secreted, high molecular weight (HMW FGF2 isoforms have predominantly been investigated intracellularly; only a very limited number of studies have investigated their activity as extracellular factors. Here we report over-expression, isolation, and biological activity of all recombinant human FGF2 isoforms. We show that HMW FGF2 isoforms can support self-renewal of human embryonic stem cells (hESCs in vitro. Exogenous supplementation with HMW FGF2 isoforms also activates the canonical FGFR/MAPK pathway and induces mitogenic activity in a manner similar to that of the 18 kDa FGF2 isoform. Though all HMW isoforms, when supplemented exogenously, are able to recapitulate LMW FGF2 activity to some degree, it appears that certain isoforms tend to do so more poorly, demonstrating a lesser functional response by several measures. A better understanding of isoform-specific FGF2 effects will lead to a better understanding of developmental and pathological FGF2 signaling.
Chen, Chunyan; Wang, Jie; Loch, Cheryl L; Ahn, Dongchan; Chen, Zhan
2004-02-04
In this paper, the feasibility of monitoring molecular structures at a moving polymer/liquid interface by sum frequency generation (SFG) vibrational spectroscopy has been demonstrated. N-(2-Aminoethyl)-3-aminopropyltrimethoxysilane (AATM, NH2(CH2)2NH(CH2)3Si(OCH3)3) has been brought into contact with a deuterated poly(methyl methacrylate) (d-PMMA) film, and the interfacial silane structure has been monitored using SFG. Upon initial contact, the SFG spectra can be detected, but as time progresses, the spectral intensity changes and finally disappears. Additional experiments indicate that these silane molecules can diffuse into the polymer film and the detected SFG signals are actually from the moving polymer/silane interface. Our results show that the molecular order of the polymer/silane interface exists during the entire diffusion process and is lost when the silane molecules traverse through the thickness of the d-PMMA film. The loss of the SFG signal is due to the formation of a new disordered substrate/silane interface, which contributes no detectable SFG signal. The kinetics of the diffusion of the silane into the polymer have been deduced from the time-dependent SFG signals detected from the AATM molecules as they diffuse through polymer films of different thickness.
Indian Academy of Sciences (India)
algebraic geometry but also in related fields like number theory. ... every vector bundle on the affine space is trivial. (equivalently ... les on a compact Riemann surface to unitary rep- ... tial geometry and topology and was generalised in.
International Nuclear Information System (INIS)
Sloane, Peter
2007-01-01
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
Energy Technology Data Exchange (ETDEWEB)
Sloane, Peter [Department of Mathematics, King' s College, University of London, Strand, London WC2R 2LS (United Kingdom)
2007-09-15
We adapt the spinorial geometry method introduced in [J. Gillard, U. Gran and G. Papadopoulos, 'The spinorial geometry of supersymmetric backgrounds,' Class. Quant. Grav. 22 (2005) 1033 [ (arXiv:hep-th/0410155)
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
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS
International Nuclear Information System (INIS)
BERG, J.S.; JOHNSTONE, C.; SUMMERS, D.
2001-01-01
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective
Arithmetic noncommutative geometry
Marcolli, Matilde
2005-01-01
Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...
Directory of Open Access Journals (Sweden)
Emilia Barra Ferreira
2009-12-01
Full Text Available Este trabalho descreve uma pesquisa realizada junto a professores de Matemática objetivando investigar a contribuição dos ambientes de geometria dinâmica em sua formação, no sentido de incentivá-los ao uso das demonstrações no ensino da Geometria. Considerando-se as demonstrações, pela própria natureza da Matemática, elemento fundamental na construção do conhecimento geométrico, a proposta foi que dificuldades, geralmente encontradas na necessária passagem do conhecimento de natureza empírica àquele de natureza formal, podem ser minimizadas ou superadas através de trabalho em ambientes que possibilitem o experimentar, visualizar, conjecturar, generalizar e demonstrar, como propõem os ambientes de geometria dinâmica. A análise feita baseouse em estudos de Piaget (1983, de Van Hiele (1959 e da Didática da Matemática (BROUSSEAU, 1986, DUVAl, 1995. Desenvolveu-se uma engenharia didática no ambiente proposto e os resultados sugerem que tal trabalho se constitui numa alternativa eficiente no processo de formação de professores no sentido de incentivá-los ao uso das demonstrações. Palavras-chave: Formação de Professores. Demonstrações. Geometria Dinâmica.This paper describes research conducted with mathematics teachers aiming to investigate the contribution of environments of dynamic geometry in their education, to encourage them to use demonstrations in the teaching of geometry. Considering demonstrations, which are by nature a key element in the construction of geometric knowledge, the proposal was that difficulties typically encountered in the necessary passage from empirical knowledge to formal knowledge, can be minimized or overcome through work in environments that allow experimentation, viewing, conjecturing, generalization and demonstration, as proposed by environments of dynamic geometry. The analysis was based on studies of Piaget (1983, Van Hiele (1959 and Didactic of Mathematics (BROUSSEAU, 1986, DUVAL
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.
International Nuclear Information System (INIS)
Buescher, R.
2005-01-01
Casimir interactions are interactions induced by quantum vacuum fluctuations and thermal fluctuations of the electromagnetic field. Using a path integral quantization for the gauge field, an effective Gaussian action will be derived which is the starting point to compute Casimir forces between macroscopic objects analytically and numerically. No assumptions about the independence of the material and shape dependent contributions to the interaction are made. We study the limit of flat surfaces in further detail and obtain a concise derivation of Lifshitz' theory of molecular forces. For the case of ideally conducting boundaries, the Gaussian action will be calculated explicitly. Both limiting cases are also discussed within the framework of a scalar field quantization approach, which is applicable for translationally invariant geometries. We develop a non-perturbative approach to calculate the Casimir interaction from the Gaussian action for periodically deformed and ideally conducting objects numerically. The obtained results reveal two different scaling regimes for the Casimir force as a function of the distance between the objects, their deformation wavelength and -amplitude. The results confirm that the interaction is non-additive, especially in the presence of strong geometric deformations. Furthermore, the numerical approach is extended to calculate lateral Casimir forces. The results are consistent with the results of the proximity-force approximation for large deformation wavelengths. A qualitatively different behaviour between the normal and lateral force is revealed. We also establish a relation between the boundary induced change of the of the density of states for the scalar Helmholtz equation and the Casimir interaction using the path integral method. For statically deformed boundaries, this relation can be expressed as a novel trace formula, which is formally similar to the so-called Krein-Friedel-Lloyd formula. While the latter formula describes the
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
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
Developments in special geometry
International Nuclear Information System (INIS)
Mohaupt, Thomas; Vaughan, Owen
2012-01-01
We review the special geometry of N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we discuss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
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.
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.
Geometry of multihadron production
International Nuclear Information System (INIS)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
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.
Methods of information geometry
Amari, Shun-Ichi
2000-01-01
Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...
International Nuclear Information System (INIS)
Grotz, Andreas
2011-01-01
In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.
Granular flows in constrained geometries
Murthy, Tejas; Viswanathan, Koushik
Confined geometries are widespread in granular processing applications. The deformation and flow fields in such a geometry, with non-trivial boundary conditions, determine the resultant mechanical properties of the material (local porosity, density, residual stresses etc.). We present experimental studies of deformation and plastic flow of a prototypical granular medium in different nontrivial geometries- flat-punch compression, Couette-shear flow and a rigid body sliding past a granular half-space. These geometries represent simplified scaled-down versions of common industrial configurations such as compaction and dredging. The corresponding granular flows show a rich variety of flow features, representing the entire gamut of material types, from elastic solids (beam buckling) to fluids (vortex-formation, boundary layers) and even plastically deforming metals (dead material zone, pile-up). The effect of changing particle-level properties (e.g., shape, size, density) on the observed flows is also explicitly demonstrated. Non-smooth contact dynamics particle simulations are shown to reproduce some of the observed flow features quantitatively. These results showcase some central challenges facing continuum-scale constitutive theories for dynamic granular flows.
Molecular geometry in the ultraviolet absorption spectra
International Nuclear Information System (INIS)
Albuquerque, S.F. de; Monteiro, L.S.; Adamis, L.M.B.; Baltar, M.C.P.; Silva, R.M. da
1977-01-01
The ultraviolet absorption spectra may be sensibly affected by steric effects. These effects can cause a lot of difficulties and unexpected changes in spectrum. The most general source of such difficulties is steric inhibition of resonance. In addition to this, ultraviolet epectra may be markedly changed by steric factors which change the positions of dipoles in the molecule with respect to each other and by the interaction of nonconjugated chromophores suitably located in space. We have studied in detail each of these effects presenting a lot of usual and importants examples in Organic Chemistry. Others relevants subjects were not considerated in this present work [pt
HYBRIDIZATION AND MOLECULAR GEOMETRY: A NUMBER GAME
African Journals Online (AJOL)
Temechegn
This article is not emphasizing the theory behind the hybridization, but only on how to ... The new orbitals have the same total electron capacity .... the quantum mechanics and from a theory of paramagnetic susceptibility to the structure.
Geometry on the space of geometries
International Nuclear Information System (INIS)
Christodoulakis, T.; Zanelli, J.
1988-06-01
We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs
Machine learning spatial geometry from entanglement features
You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang
2018-02-01
Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT2 point).
Complex and symplectic geometry
Medori, Costantino; Tomassini, Adriano
2017-01-01
This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.
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
Roe, John
2003-01-01
Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This point of view is effective because it is often true that the relevant geometric properties of metric spaces are determined by their coarse geometry. Two examples of important uses of coarse geometry are Gromov's beautiful notion of a hyperbolic group and Mostow's proof of his famous rigidity theorem. The first few chapters of the book provide a general perspective on coarse structures. Even when only metric coarse structures are in view, the abstract framework brings the same simplification as does the passage from epsilons and deltas to open sets when speaking of continuity. The middle section reviews notions of negative curvature and rigidity. Modern interest in large scale geometry derives in large part from Mostow's rigidity theorem and from Gromov's subsequent 'large scale' rendition of the crucial properties of n...
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...
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.
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...
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.
Tabachnikov, Serge
2005-01-01
Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...
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...
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
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
Ceresole, Anna; Gnecchi, Alessandra; Marrani, Alessio
2013-01-01
We analyze some properties of the four dimensional supergravity theories which originate from five dimensions upon reduction. They generalize to N>2 extended supersymmetries the d-geometries with cubic prepotentials, familiar from N=2 special K\\"ahler geometry. We emphasize the role of a suitable parametrization of the scalar fields and the corresponding triangular symplectic basis. We also consider applications to the first order flow equations for non-BPS extremal black holes.
International Nuclear Information System (INIS)
Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J
2014-01-01
CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.
Software Geometry in Simulations
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
Introduction to combinatorial geometry
International Nuclear Information System (INIS)
Gabriel, T.A.; Emmett, M.B.
1985-01-01
The combinatorial geometry package as used in many three-dimensional multimedia Monte Carlo radiation transport codes, such as HETC, MORSE, and EGS, is becoming the preferred way to describe simple and complicated systems. Just about any system can be modeled using the package with relatively few input statements. This can be contrasted against the older style geometry packages in which the required input statements could be large even for relatively simple systems. However, with advancements come some difficulties. The users of combinatorial geometry must be able to visualize more, and, in some instances, all of the system at a time. Errors can be introduced into the modeling which, though slight, and at times hard to detect, can have devastating effects on the calculated results. As with all modeling packages, the best way to learn the combinatorial geometry is to use it, first on a simple system then on more complicated systems. The basic technique for the description of the geometry consists of defining the location and shape of the various zones in terms of the intersections and unions of geometric bodies. The geometric bodies which are generally included in most combinatorial geometry packages are: (1) box, (2) right parallelepiped, (3) sphere, (4) right circular cylinder, (5) right elliptic cylinder, (6) ellipsoid, (7) truncated right cone, (8) right angle wedge, and (9) arbitrary polyhedron. The data necessary to describe each of these bodies are given. As can be easily noted, there are some subsets included for simplicity
Brorsen, Kurt R; Yang, Yang; Hammes-Schiffer, Sharon
2017-08-03
Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent density functional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF - . The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK a 's, optimized geometries, and reaction paths.
International Nuclear Information System (INIS)
Mobley, P.L.; Gonzalez, N.E.
1991-01-01
Studies were conducted to determine if soman, a cholinesterase inhibitor, could activate the protein kinase C system in the rat neocortex. Using microwave radiation for rapid tissue fixation, it was demonstrated that treatment with soman increased 32 P incorporation into an acidic 80,000 molecular weight, heat-stable protein in vivo. Based on relative molecular weight and isoelectric point this protein appears to be identical to a protein identified as a substrate for protein kinase C. Additionally, a protein of the same molecular weight and isoelectric point could be phosphorylated in tissue slices prepared from the neocortex by cholinergic dependent mechanisms. Also, treatment with soman decreased protein kinase C in the soluble fraction of this brain region; however, no corresponding increase was observed in the particulate fraction. These results suggest that soman can activate protein kinase C in vivo, and demonstrate the utility of using microwave tissue fixation to study protein phosphorylation events in vivo
Energy Technology Data Exchange (ETDEWEB)
Mobley, P.L.; Gonzalez, N.E. (Univ. of Texas Health Science Center, San Antonio (United States))
1991-01-01
Studies were conducted to determine if soman, a cholinesterase inhibitor, could activate the protein kinase C system in the rat neocortex. Using microwave radiation for rapid tissue fixation, it was demonstrated that treatment with soman increased {sup 32}P incorporation into an acidic 80,000 molecular weight, heat-stable protein in vivo. Based on relative molecular weight and isoelectric point this protein appears to be identical to a protein identified as a substrate for protein kinase C. Additionally, a protein of the same molecular weight and isoelectric point could be phosphorylated in tissue slices prepared from the neocortex by cholinergic dependent mechanisms. Also, treatment with soman decreased protein kinase C in the soluble fraction of this brain region; however, no corresponding increase was observed in the particulate fraction. These results suggest that soman can activate protein kinase C in vivo, and demonstrate the utility of using microwave tissue fixation to study protein phosphorylation events in vivo.
Global aspects of complex geometry
Catanese, Fabrizio; Huckleberry, Alan T
2006-01-01
Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry.
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...
International Nuclear Information System (INIS)
Jonsson, Rickard; Westman, Hans
2006-01-01
We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz M A and Lasota J-P 1997 Class. Quantum Grav. A 14 23-30). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson R 2006 Class. Quantum Grav. 23 1)) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity
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...
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 as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
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.
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...
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...
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
Fleischer, Holger; Wann, Derek A; Hinchley, Sarah L; Borisenko, Konstantin B; Lewis, James R; Mawhorter, Richard J; Robertson, Heather E; Rankin, David W H
2005-10-07
The molecular structures of Se(SCH(3))(2) and Te(SCH(3))(2) were investigated using gas-phase electron diffraction (GED) and ab initio and DFT geometry optimisations. While parameters involving H atoms were refined using flexible restraints according to the SARACEN method, parameters that depended only on heavy atoms could be refined without restraints. The GED-determined geometric parameters (r(h1)) are: rSe-S 219.1(1), rS-C 183.2(1), rC-H 109.6(4) pm; angleS-Se-S 102.9(3), angleSe-S-C 100.6(2), angleS-C-H (mean) 107.4(5), phiS-Se-S-C 87.9(20), phiSe-S-C-H 178.8(19) degrees for Se(SCH(3))(2), and rTe-S 238.1(2), rS-C 184.1(3), rC-H 110.0(6) pm; angleS-Te-S 98.9(6), angleTe-S-C 99.7(4), angleS-C-H (mean) 109.2(9), phiS-Te-S-C 73.0(48), phiTe-S-C-H 180.1(19) degrees for Te(SCH(3))(2). Ab initio and DFT calculations were performed at the HF, MP2 and B3LYP levels, employing either full-electron basis sets [3-21G(d) or 6-31G(d)] or an effective core potential with a valence basis set [LanL2DZ(d)]. The best fit to the GED structures was achieved at the MP2 level. Differences between GED and MP2 results for rS-C and angleS-Te-S were explained by the thermal population of excited vibrational states under the experimental conditions. All theoretical models agreed that each compound exists as two stable conformers, one in which the methyl groups are on the same side (g(+)g(-) conformer) and one in which they are on different sides (g(+)g(+) conformer) of the S-Y-S plane (Y = Se, Te). The conformational composition under the experimental conditions could not be resolved from the GED data. Despite GED R-factors and ab initio and DFT energies favouring the g(+)g(+) conformer, it is likely that both conformers are present, for Se(SCH(3))(2) as well as for Te(SCH(3))(2).
Geometry of anisotropic CO outflows
International Nuclear Information System (INIS)
Liseau, R.; Sandell, G.; Helsinki Univ., Observatory, Finland)
1986-01-01
A simple geometrical model for the space motions of the bipolar high-velocity CO outflows in regions of recent, active star formation is proposed. It is assumed that the velocity field of the neutral gas component can be represented by large-scale uniform motions. From observations of the spatial distribution and from the characteristics of the line shape of the high-velocity molecular gas emission the geometry of the line-emitting regions can be inferred, i.e., the direction in space and the collimating angle of the flow. The model has been applied to regions where a check on presently obtained results is provided by independent optical determinations of the motions of Herbig-Haro objects associated with the CO flows. These two methods are in good agreement and, furthermore, the results obtained provide convincingly strong evidence for the physical association of CO outflows and Herbig-Haro objects. This also supports the common view that a young stellar central source is responsible for the active phenomena observed in its environmental neighborhood. It is noteworthy that within the framework of the model the determination of the flow geometry of the high-velocity gas from CO measurements is independent of the distance to the source and, furthermore, can be done at relatively low spatial resolution. 32 references
Alam, Mohammad Shafiul; Ley, Benedikt; Nima, Maisha Khair; Johora, Fatema Tuj; Hossain, Mohammad Enayet; Thriemer, Kamala; Auburn, Sarah; Marfurt, Jutta; Price, Ric N; Khan, Wasif A
2017-08-15
Artemisinin resistance is present in the Greater Mekong region and poses a significant threat for current anti-malarial treatment guidelines in Bangladesh. The aim of this molecular study was to assess the current status of drug resistance in the Chittagong Hill Tracts of Bangladesh near the Myanmar border. Samples were obtained from patients enrolled into a Clinical Trial (NCT02389374) conducted in Alikadam, Bandarban between August 2014 and January 2015. Plasmodium falciparum infections were confirmed by PCR and all P. falciparum positive isolates genotyped for the pfcrt K76T and pfmdr1 N86Y markers. The propeller region of the kelch 13 (k13) gene was sequenced from isolates from patients with delayed parasite clearance. In total, 130 P. falciparum isolates were available for analysis. The pfcrt mutation K76T, associated with chloroquine resistance was found in 81.5% (106/130) of cases and the pfmdr1 mutation N86Y in 13.9% (18/130) cases. No single nucleotide polymorphisms were observed in the k13 propeller region. This study provides molecular evidence for the ongoing presence of chloroquine resistant P. falciparum in Bangladesh, but no evidence of mutations in the k13 propeller domain associated with artemisinin resistance. Monitoring for artemisinin susceptibility in Bangladesh is needed to ensure early detection and containment emerging anti-malarial resistance.
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.
Multiplicity in difference geometry
Tomasic, Ivan
2011-01-01
We prove a first principle of preservation of multiplicity in difference geometry, paving the way for the development of a more general intersection theory. In particular, the fibres of a \\sigma-finite morphism between difference curves are all of the same size, when counted with correct multiplicities.
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.
International Nuclear Information System (INIS)
Konopleva, N.P.
2009-01-01
The basic ideas of description methods of physical fields and elementary particle interactions are discussed. One of such ideas is the conception of space-time geometry. In this connection experimental measurement methods are analyzed. It is shown that measure procedures are the origin of geometrical axioms. The connection between space symmetry properties and the conservation laws is considered
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…
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
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...
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.
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.
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.
Coxeter, HSM
1965-01-01
This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
International Nuclear Information System (INIS)
Ezin, J.P.
1988-08-01
The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs
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 ...
Gilbert, George L.
1983-01-01
An apparatus is described in which effects of pressure, volume, and temperature changes on a gas can be observed simultaneously. Includes use of the apparatus in demonstrating Boyle's, Gay-Lussac's, and Charles' Laws, attractive forces, Dalton's Law of Partial pressures, and in illustrating measurable vapor pressures of liquids and some solids.…
Gilbert, George L., Ed.
1987-01-01
Describes two demonstrations to illustrate characteristics of substances. Outlines a method to detect the changes in pH levels during the electrolysis of water. Uses water pistols, one filled with methane gas and the other filled with water, to illustrate the differences in these two substances. (TW)
Suphioglu, C; Mawdsley, D; Schäppi, G; Gruehn, S; de Leon, M; Rolland, J M; O'Hehir, R E
1999-12-03
A novel isoform of a major rye grass pollen allergen Lol p 5 was isolated from a cDNA expression library. The new isoform, Lol p 5C, shares 95% amino acid sequence identity with Lol p 5A. Both isoforms demonstrated shared antigenic activity but different allergenic activities. Recombinant Lol p 5C demonstrated 100% IgE reactivity in 22 rye grass pollen sensitive patients. In comparison, recombinant Lol p 5A showed IgE reactivity in less than 64% of the patients. Therefore, Lol p 5C represents a novel and highly IgE-reactive isoform allergen of rye grass pollen.
Directory of Open Access Journals (Sweden)
Rizwana Parveen Rani
2017-05-01
Full Text Available Probiotic bacteria are beneficial to the health of poultry animals, thus are used as alternative candidates for antibiotics used as growth promoters (AGPs. However, they also reduce the body weight gain due to innate bile salt hydrolase (BSH activity. Hence, the addition of a suitable BSH inhibitor along with the probiotic feed can decrease the BSH activity. In this study, a BSH gene (981 bp encoding 326-amino acids was identified from the genome of Lactobacillus gasseri FR4 (LgBSH. The LgBSH-encoding gene was cloned and purified using an Escherichia coli BL21 (DE3 expression system, and its molecular weight (37 kDa was confirmed by SDS–PAGE and a Western blot analysis. LgBSH exhibited greater hydrolysis toward glyco-conjugated bile salts compared to tauro-conjugated bile salts. LgBSH displayed optimal activity at 52°C at a pH of 5.5, and activity was further increased by several reducing agents (DTT, surfactants (Triton X-100 and Tween 80, and organic solvents (isopropanol, butanol, and acetone. Riboflavin and penicillin V, respectively, inhibited LgBSH activity by 98.31 and 97.84%. A homology model of LgBSH was predicted using EfBSH (4WL3 as a template. Molecular docking analysis revealed that the glycocholic acid had lowest binding energy of -8.46 kcal/mol; on the other hand, inhibitors, i.e., riboflavin and penicillin V, had relatively higher binding energies of -6.25 and -7.38 kcal/mol, respectively. Our results suggest that L. gasseri FR4 along with riboflavin might be a potential alternative to AGPs for poultry animals.
International Nuclear Information System (INIS)
Dokukin, M E; Sokolov, I; Guz, N V; Woodworth, C D
2015-01-01
Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation. (paper)
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.
Transformational plane geometry
Umble, Ronald N
2014-01-01
Axioms of Euclidean Plane Geometry The Existence and Incidence Postulates The Distance and Ruler Postulates The Plane Separation Postulate The Protractor Postulate The Side-Angle-Side Postulate and the Euclidean Parallel Postulate Theorems of Euclidean Plane Geometry The Exterior Angle Theorem Triangle Congruence Theorems The Alternate Interior Angles Theorem and the Angle Sum Theorem Similar Triangles Introduction to Transformations, Isometries, and Similarities Transformations Isometries and SimilaritiesAppendix: Proof of Surjectivity Translations, Rotations, and Reflections Translations Rotations Reflections Appendix: Geometer's Sketchpad Commands Required by Exploratory Activities Compositions of Translations, Rotations, and Reflections The Three Points Theorem Rotations as Compositions of Two Reflections Translations as Compositions of Two Halfturns or Two Reflections The Angle Addition Theorem Glide Reflections Classification of Isometries The Fundamental Theorem and Congruence Classification of Isometr...
Multilevel geometry optimization
Rodgers, Jocelyn M.; Fast, Patton L.; Truhlar, Donald G.
2000-02-01
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol.
Multilevel geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Rodgers, Jocelyn M. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Fast, Patton L. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States); Truhlar, Donald G. [Department of Chemistry and Supercomputer Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431 (United States)
2000-02-15
Geometry optimization has been carried out for three test molecules using six multilevel electronic structure methods, in particular Gaussian-2, Gaussian-3, multicoefficient G2, multicoefficient G3, and two multicoefficient correlation methods based on correlation-consistent basis sets. In the Gaussian-2 and Gaussian-3 methods, various levels are added and subtracted with unit coefficients, whereas the multicoefficient Gaussian-x methods involve noninteger parameters as coefficients. The multilevel optimizations drop the average error in the geometry (averaged over the 18 cases) by a factor of about two when compared to the single most expensive component of a given multilevel calculation, and in all 18 cases the accuracy of the atomization energy for the three test molecules improves; with an average improvement of 16.7 kcal/mol. (c) 2000 American Institute of Physics.
Indovina, Paola; Collini, Maddalena; Chirico, Giuseppe; Santini, Maria Teresa
2007-02-20
Hypoxia through HRE (hypoxia-responsive element) activity in MG-63 human osteosarcoma cells grown in monolayer and as very small, three-dimensional tumor spheroids was investigated using molecular imaging techniques. MG-63 cells were stably transfected with a vector constructed with multiple copies of the HRE sequence of the human vascular endothelial growth factor (VEGF) gene and with the enhanced green fluorescent protein (EGFP) coding sequence. During hypoxia when HIF-1alpha (hypoxia-inducible factor-1alpha) is stabilized, the binding of HIF-1 to the HRE sequences of the vector allows the transcription of EGFP and the appearance of fluorescence. Transfected monolayer cells were characterized by flow cytometric analysis in response to various hypoxic conditions and HIF-1alpha expression in these cells was assessed by Western blotting. Two-photon excitation (TPE) microscopy was then used to examine both MG-63-transfected monolayer cells and spheroids at 2 and 5 days of growth in normoxic conditions. Monolayer cells reveal almost no fluorescence, whereas even very small spheroids (HRE activation. This activation of the HRE sequences, which control a wide variety of genes, suggests that monolayer cells and spheroids of the MG-63 cell line have different genes activated and thus diverse functional activities.
Purcell, Maureen; Thompson, Rachel L.; Evered, Joy; Kerwin, John; Meyers, Ted R.; Stewart, Bruce; Winton, James
2018-01-01
This research was initiated in conjunction with a systematic, multiagency surveillance effort in the United States (U.S.) in response to reported findings of infectious salmon anaemia virus (ISAV) RNA in British Columbia, Canada. In the systematic surveillance study reported in a companion paper, tissues from various salmonids taken from Washington and Alaska were surveyed for ISAV RNA using the U.S.-approved diagnostic method, and samples were released for use in this present study only after testing negative. Here, we tested a subset of these samples for ISAV RNA with three additional published molecular assays, as well as for RNA from salmonid alphavirus (SAV), piscine myocarditis virus (PMCV) and piscine orthoreovirus (PRV). All samples (n = 2,252; 121 stock cohorts) tested negative for RNA from ISAV, PMCV, and SAV. In contrast, there were 25 stock cohorts from Washington and Alaska that had one or more individuals test positive for PRV RNA; prevalence within stocks varied and ranged from 2% to 73%. The overall prevalence of PRV RNA-positive individuals across the study was 3.4% (77 of 2,252 fish tested). Findings of PRV RNA were most common in coho (Oncorhynchus kisutch Walbaum) and Chinook (O. tshawytscha Walbaum) salmon.
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.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
International Nuclear Information System (INIS)
Lepora, N.; Kibble, T.
1999-01-01
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the scalar sector, and a squashed metric associated with the gauge sector. Physically, the interplay between these metrics gives rise to many of the non-perturbative features of Weinberg-Salam theory. (author)
International Nuclear Information System (INIS)
Hull, C.M.
1993-01-01
The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∝ -gravity is analysed in detail. While the gauge group for gravity in d dimensions is the diffeomorphism group of the space-time, the gauge group for a certain W-gravity theory (which is W ∝ -gravity in the case d=2) is the group of symplectic diffeomorphisms of the cotangent bundle of the space-time. Gauge transformations for W-gravity gauge fields are given by requiring the invariance of a generalised line element. Densities exist and can be constructed from the line element (generalising √detg μν ) only if d=1 or d=2, so that only for d=1,2 can actions be constructed. These two cases and the corresponding W-gravity actions are considered in detail. In d=2, the gauge group is effectively only a subgroup of the symplectic diffeomorphisms group. Some of the constraints that arise for d=2 are similar to equations arising in the study of self-dual four-dimensional geometries and can be analysed using twistor methods, allowing contact to be made with other formulations of W-gravity. While the twistor transform for self-dual spaces with one Killing vector reduces to a Legendre transform, that for two Killing vectors gives a generalisation of the Legendre transform. (orig.)
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...
CBM RICH geometry optimization
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Tariq; Hoehne, Claudia [II. Physikalisches Institut, Giessen Univ. (Germany); Collaboration: CBM-Collaboration
2016-07-01
The Compressed Baryonic Matter (CBM) experiment at the future FAIR complex will investigate the phase diagram of strongly interacting matter at high baryon density and moderate temperatures in A+A collisions from 2-11 AGeV (SIS100) beam energy. The main electron identification detector in the CBM experiment will be a RICH detector with a CO{sub 2} gaseous-radiator, focusing spherical glass mirrors, and MAPMT photo-detectors being placed on a PMT-plane. The RICH detector is located directly behind the CBM dipole magnet. As the final magnet geometry is now available, some changes in the RICH geometry become necessary. In order to guarantee a magnetic field of 1 mT at maximum in the PMT plane for effective operation of the MAPMTs, two measures have to be taken: The PMT plane is moved outwards of the stray field by tilting the mirrors by 10 degrees and shielding boxes have been designed. In this contribution the results of the geometry optimization procedure are presented.
Introducing geometry concept based on history of Islamic geometry
Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.
2018-01-01
Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.
Two lectures on D-geometry and noncommutative geometry
International Nuclear Information System (INIS)
Douglas, M.R.
1999-01-01
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)
An improved injector bunching geometry for ATLAS
Indian Academy of Sciences (India)
This geometry improves the handling of space charge for high-current beams, signiﬁcantly increases the capture fraction into the primary rf bucket and reduces the capture fraction of the unwanted parasitic rf bucket. Total capture and transport through the PII has been demonstrated as high as 80% of the injected dc beam ...
Prediction of protein loop geometries in solution
Rapp, Chaya S.; Strauss, Temima; Nederveen, Aart; Fuentes, Gloria
2007-01-01
The ability to determine the structure of a protein in solution is a critical tool for structural biology, as proteins in their native state are found in aqueous environments. Using a physical chemistry based prediction protocol, we demonstrate the ability to reproduce protein loop geometries in
International Nuclear Information System (INIS)
Hook, D W
2008-01-01
A geometric framework for quantum mechanics arose during the mid 1970s when authors such as Cantoni explored the notion of generalized transition probabilities, and Kibble promoted the idea that the space of pure quantum states provides a natural quantum mechanical analogue for classical phase space. This central idea can be seen easily since the projection of Schroedinger's equation from a Hilbert space into the space of pure spaces is a set of Hamilton's equations. Over the intervening years considerable work has been carried out by a variety of authors and a mature description of quantum mechanics in geometric terms has emerged with many applications. This current offering would seem ideally placed to review the last thirty years of progress and relate this to the most recent work in quantum entanglement. Bengtsson and Zyczkowski's beautifully illustrated volume, Geometry of Quantum States (referred to as GQS from now on) attempts to cover considerable ground in its 466 pages. Its topics range from colour theory in Chapter 1 to quantum entanglement in Chapter 15-to say that this is a whirlwind tour is, perhaps, no understatement. The use of the work 'introduction' in the subtitle of GQS, might suggest to the reader that this work be viewed as a textbook and I think that this interpretation would be incorrect. The authors have chosen to present a survey of different topics with the specific aim to introduce entanglement in geometric terms-the book is not intended as a pedagogical introduction to the geometric approach to quantum mechanics. Each of the fifteen chapters is a short, and mostly self-contained, essay on a particular aspect or application of geometry in the context of quantum mechanics with entanglement being addressed specifically in the final chapter. The chapters fall into three classifications: those concerned with the mathematical background, those which discuss quantum theory and the foundational aspects of the geometric framework, and
Functional integration over geometries
International Nuclear Information System (INIS)
Mottola, E.
1995-01-01
The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted
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.
Torsional heterotic geometries
International Nuclear Information System (INIS)
Becker, Katrin; Sethi, Savdeep
2009-01-01
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.
Geometrie verstehen: statisch - kinematisch
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
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
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
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
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
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
Graded geometry and Poisson reduction
Cattaneo, A S; Zambon, M
2009-01-01
The main result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in [2]. Further, we provide an alternative algebraic proof for the main result. ©2009 American Institute of Physics
Cloaking of 2D particle geometries in a surface medium
Energy Technology Data Exchange (ETDEWEB)
Alexopoulos, A., E-mail: Aris.Alexopoulos@dsto.defence.gov.au [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia); Yau, K.S.B. [Electronic Warfare and Radar Division, Defence Science and Technology Organisation (DSTO), PO Box 1500, Edinburgh 5111 (Australia)
2013-06-17
We theoretically examine the cloaking condition for two-dimensional particles with varying geometry embedded inside a surface medium. General solutions are obtained for multi-layer particle configurations with either all positive or partially negative constitutive parameters respectively. Cloaking of particle geometries that are large relative to the incident wavelength is demonstrated. Theoretical predictions are compared to full-wave numerical simulations for arrays of particles consisting of different geometries.
Strontium clusters: electronic and geometry shell effects
DEFF Research Database (Denmark)
Lyalin, Andrey G.; Solov'yov, Ilia; Solov'yov, Andrey V.
2008-01-01
charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, and spectra of the density of electronic states (DOS). It is demonstrated that the size-evolution of structural and electronic properties of strontium clusters...... is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters. It is shown that the excessive charge essentially affects the optimized geometry...
Noncommutative geometry and twisted conformal symmetry
International Nuclear Information System (INIS)
Matlock, Peter
2005-01-01
The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra
Pearson's Functions to Describe FSW Weld Geometry
International Nuclear Information System (INIS)
Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.
2011-01-01
Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.
The estimation of collision probabilities in complicated geometries
International Nuclear Information System (INIS)
Roth, M.J.
1969-04-01
This paper demonstrates how collision probabilities in complicated geometries may be estimated. It is assumed that the reactor core may be divided into a number of cells each with simple geometry so that a collision probability matrix can be calculated for each cell by standard methods. It is then shown how these may be joined together. (author)
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.
Critique of information geometry
International Nuclear Information System (INIS)
Skilling, John
2014-01-01
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples
International Nuclear Information System (INIS)
Correa, Diego H.; Silva, Guillermo A.
2008-01-01
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents
Emergent geometry of membranes
Energy Technology Data Exchange (ETDEWEB)
Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)
2015-11-13
In work http://dx.doi.org/10.1103/PhysRevD.86.086001, a surface embedded in flat ℝ{sup 3} is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary noncommutative membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in ℝ{sup 3}. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
Geometry through history Euclidean, hyperbolic, and projective geometries
Dillon, Meighan I
2018-01-01
Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...
Goodson-Espy, Tracy; Lynch-Davis, Kathleen; Schram, Pamela; Quickenton, Art
2010-01-01
This paper describes the genesis and purpose of our geometry methods course, focusing on a geometry-teaching technology we created using NVIDIA[R] Chameleon demonstration. This article presents examples from a sequence of lessons centered about a 3D computer graphics demonstration of the chameleon and its geometry. In addition, we present data…
Interplay of electronic and geometry shell effects in properties of neutral and charged Sr clusters
DEFF Research Database (Denmark)
Lyalin, Andrey; Solov'yov, Ilia; Solov'yov, Andrey V.
2007-01-01
that the size evolution of structural and electronic properties of strontium clusters is governed by an interplay of the electronic and geometry shell closures. Influence of the electronic shell effects on structural rearrangements can lead to violation of the icosahedral growth motif of strontium clusters......The optimized structure and electronic properties of neutral, singly, and doubly charged strontium clusters have been investigated using ab initio theoretical methods based on density-functional theory. We have systematically calculated the optimized geometries of neutral, singly, and doubly...... charged strontium clusters consisting of up to 14 atoms, average bonding distances, electronic shell closures, binding energies per atom, the gap between the highest occupied and the lowest unoccupied molecular orbitals, and spectra of the density of electronic states (DOS). It is demonstrated...
On organizing principles of discrete differential geometry. Geometry of spheres
International Nuclear Information System (INIS)
Bobenko, Alexander I; Suris, Yury B
2007-01-01
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.
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
Lee, Jaewon; Singh, Ranbir; Sin, Dong Hun; Kim, Heung Gyu; Song, Kyu Chan; Cho, Kilwon
2016-01-06
A new 3D nonfullerene small-molecule acceptor is reported. The 3D interlocking geometry of the small-molecule acceptor enables uniform molecular conformation and strong intermolecular connectivity, facilitating favorable nanoscale phase separation and electron charge transfer. By employing both a novel polymer donor and a nonfullerene small-molecule acceptor in the solution-processed organic solar cells, a high-power conversion efficiency of close to 6% is demonstrated. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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...
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
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
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.
Nonperturbative quantum geometries
International Nuclear Information System (INIS)
Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara
1988-01-01
Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)
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.
GPS: Geometry, Probability, and Statistics
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
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....
Kaehler geometry and SUSY mechanics
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen
2001-01-01
We present two examples of SUSY mechanics related with Kaehler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kaehler manifold. The relation of these models with antisymplectic geometry is discussed
A prediction for bubbling geometries
Okuda, Takuya
2007-01-01
We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory. Their vacuum expectation values are computed in the parameter region that admits smooth bubbling geometry duals. The results are a prediction for the supergravity action evaluated on the bubbling geometries for Wilson loops.
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...
Optical geometry across the horizon
International Nuclear Information System (INIS)
Jonsson, Rickard
2006-01-01
In a recent paper (Jonsson and Westman 2006 Class. Quantum Grav. 23 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to (a finite four-volume) of any spherically symmetric spacetime. In particular we apply the formalism, using a non-static reference congruence, to do optical geometry across the horizon of a static black hole. While the resulting geometry in principle is time dependent, we can choose the reference congruence in such a manner that an embedding of the geometry always looks the same. Relative to the embedded geometry the reference points are then moving. We discuss the motion of photons, inertial forces and gyroscope precession in this framework
Classification of radar echoes using fractal geometry
International Nuclear Information System (INIS)
Azzaz, Nafissa; Haddad, Boualem
2017-01-01
Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.
Differential geometry in string models
International Nuclear Information System (INIS)
Alvarez, O.
1986-01-01
In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold
Stochastic geometry in PRIZMA code
International Nuclear Information System (INIS)
Malyshkin, G. N.; Kashaeva, E. A.; Mukhamadiev, R. F.
2007-01-01
The paper describes a method used to simulate radiation transport through random media - randomly placed grains in a matrix material. The method models the medium consequently from one grain crossed by particle trajectory to another. Like in the Limited Chord Length Sampling (LCLS) method, particles in grains are tracked in the actual grain geometry, but unlike LCLS, the medium is modeled using only Matrix Chord Length Sampling (MCLS) from the exponential distribution and it is not necessary to know the grain chord length distribution. This helped us extend the method to media with randomly oriented arbitrarily shaped convex grains. Other extensions include multicomponent media - grains of several sorts, and polydisperse media - grains of different sizes. Sort and size distributions of crossed grains were obtained and an algorithm was developed for sampling grain orientations and positions. Special consideration was given to medium modeling at the boundary of the stochastic region. The method was implemented in the universal 3D Monte Carlo code PRIZMA. The paper provides calculated results for a model problem where we determine volume fractions of modeled components crossed by particle trajectories. It also demonstrates the use of biased sampling techniques implemented in PRIZMA for solving a problem of deep penetration in model random media. Described are calculations for the spectral response of a capacitor dose detector whose anode was modeled with account for its stochastic structure. (authors)
Complex analysis and CR geometry
Zampieri, Giuseppe
2008-01-01
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the \\bar\\partial-Neumann problem, it has rapidly acquired a life of its own and has became an important topic in differential geometry and the study of non-linear partial differential equations. A full understanding of modern CR geometry requires knowledge of various topics such as real/complex differential and symplectic geometry, foliation theory, the geometric theory of PDE's, and microlocal analysis. Nowadays, the subject of CR geometry is very rich in results, and the amount of material required to reach competence is daunting to graduate students who wish to learn it. However, the present book does not aim at introducing all the topics of current interest in CR geometry. Instead, an attempt is made to be friendly to the novice by moving, in a fairly relaxed way, f...
The geometry description markup language
International Nuclear Information System (INIS)
Chytracek, R.
2001-01-01
Currently, a lot of effort is being put on designing complex detectors. A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier. A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment. However, no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files, source code (C/C++/FORTRAN), to XML and database solutions. The XML (Extensible Markup Language) has proven to provide an interesting approach for describing detector geometries, with several different but incompatible XML-based solutions existing. Therefore, interoperability and geometry data exchange among different frameworks is not possible at present. The author introduces a markup language for geometry descriptions. Its aim is to define a common approach for sharing and exchanging of geometry description data. Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML
Photoionization and molecular structure
International Nuclear Information System (INIS)
Palma, A.
1983-01-01
A presentation is here given of the theoretical work on photoionization and molecular structure carried out by the author and coworkers. The implications of the photoionization process on the molecular geometry are emphasized. In particular, the ionization effect on deep orbitals is considered and it is shown that, contrary to traditional thinking, these orbitals have relevant effects on the molecular geometry. The problem of calculating photoionization relative intensities for the full spectrum is also considered, and the results of the present model are compared with experimental and other theoretical results. (author)
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
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
Differential geometry curves, surfaces, manifolds
Kohnel, Wolfgang
2002-01-01
This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. Special topics that are explored include Frenet frames, ruled surfaces, minimal surfaces and the Gauss-Bonnet theorem. The second part is an introduction to the geometry of general manifolds, with particular emphasis on connections and curvature. The final two chapters are insightful examinations of the special cases of spaces of constant curvature and Einstein manifolds. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra.
Stages as models of scene geometry.
Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark
2010-09-01
Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.
Demonstration of Cauchy: Understanding Algebraic
Directory of Open Access Journals (Sweden)
T.L. Costa
2012-11-01
Full Text Available ABSTRACT: In this study we present some considerations about the End of Course Work undergraduate Full Degree in Mathematics / UFMT, drafted in 2011, and by taking title "A story about Cauchy and Euler's theorem on polyhedra" that gave birth to our research project Master of Education, begun in 2012, on the approaches of Euler's theorem on polyhedra in mathematics textbooks. At work in 2011 presented some considerations about the history of Euler's theorem for polyhedra which focus the demonstration presented by Cauchy (1789-1857, who tries to generalize it, relying on assumptions not observable in Euclidean geometry. Therefore, we seek the accessible literature on the history of mathematics; relate some aspects of the demonstration Cauchy with historical events on the development of mathematics in the nineteenth century, which allowed the acceptance of such a demonstration by mathematicians of his time.Keywords: History of Mathematics. Euler's Theorem on Polyhedra. Demonstration of Cauchy.
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, ...
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...
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.
Symplectic geometry and Fourier analysis
Wallach, Nolan R
2018-01-01
Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. Includes Appendix on Quantum Mechanics by Robert Hermann. 1977 edition.
Topology and geometry for physicists
Nash, Charles
1983-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Spectral dimension of quantum geometries
International Nuclear Information System (INIS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2014-01-01
The spectral dimension is an indicator of geometry and topology of spacetime and a tool to compare the description of quantum geometry in various approaches to quantum gravity. This is possible because it can be defined not only on smooth geometries but also on discrete (e.g., simplicial) ones. In this paper, we consider the spectral dimension of quantum states of spatial geometry defined on combinatorial complexes endowed with additional algebraic data: the kinematical quantum states of loop quantum gravity (LQG). Preliminarily, the effects of topology and discreteness of classical discrete geometries are studied in a systematic manner. We look for states reproducing the spectral dimension of a classical space in the appropriate regime. We also test the hypothesis that in LQG, as in other approaches, there is a scale dependence of the spectral dimension, which runs from the topological dimension at large scales to a smaller one at short distances. While our results do not give any strong support to this hypothesis, we can however pinpoint when the topological dimension is reproduced by LQG quantum states. Overall, by exploring the interplay of combinatorial, topological and geometrical effects, and by considering various kinds of quantum states such as coherent states and their superpositions, we find that the spectral dimension of discrete quantum geometries is more sensitive to the underlying combinatorial structures than to the details of the additional data associated with them. (paper)
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Energy Technology Data Exchange (ETDEWEB)
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
International Nuclear Information System (INIS)
Pfeifer, Christian
2013-11-01
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Sheikhi, Masoome; Shahab, Siyamak; Khaleghian, Mehrnoosh; Hajikolaee, Fatemeh Haji; Balakhanava, Iryna; Alnajjar, Radwan
2018-05-01
In the present work the adsorption properties of the molecule Resveratrol (RSV) (trans-3,5,4‧-Trihydroxystilbene) on CNT(8,0-10) nanotube was investigated by Density Functional Theory (DFT) in the gaseous phase for the first time. The non-bonded interaction effects of compounds RSV and CNT(8,0-10) nanotube on the electronic properties, chemical shift tensors and natural charge were determined and discussed. The electronic spectra of the RSV and the complex CNT(8,0-10)/RSV in the gaseous phase were calculated by Time Dependent Density Functional Theory (TD-DFT) for investigation of the maximum wavelength value of the RSV before and after the non-bonded interaction with the CNT(8,0-10) nanotube and molecular orbitals involved in the formation of absorption spectrum of the complex RSV at maximum wavelength.
Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry.
Yamada, N; Nishikawa, T
2010-06-21
In this study, an evolutionary algorithm (EA), which consists of genetic and immune algorithms, is introduced to design the optical geometry of a nonimaging Fresnel lens; this lens generates the uniform flux concentration required for a photovoltaic cell. Herein, a design procedure that incorporates a ray-tracing technique in the EA is described, and the validity of the design is demonstrated. The results show that the EA automatically generated a unique geometry of the Fresnel lens; the use of this geometry resulted in better uniform flux concentration with high optical efficiency.
From combinatorial optimization to real algebraic geometry and back
Directory of Open Access Journals (Sweden)
Janez Povh
2014-12-01
Full Text Available In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub-eld of real algebraic geometry.
Biofilm formation in geometries with different surface curvature and oxygen availability
International Nuclear Information System (INIS)
Chang, Ya-Wen; Fragkopoulos, Alexandros A; Kim, Harold D; Fernández-Nieves, Alberto; Marquez, Samantha M; Angelini, Thomas E
2015-01-01
Bacteria in the natural environment exist as interface-associated colonies known as biofilms . Complex mechanisms are often involved in biofilm formation and development. Despite the understanding of the molecular mechanisms involved in biofilm formation, it remains unclear how physical effects in standing cultures influence biofilm development. The topology of the solid interface has been suggested as one of the physical cues influencing bacteria-surface interactions and biofilm development. Using the model organism Bacillus subtilis, we study the transformation of swimming bacteria in liquid culture into robust biofilms in a range of confinement geometries (planar, spherical and toroidal) and interfaces (air/water, silicone/water, and silicone elastomer/water). We find that B. subtilis form submerged biofilms at both solid and liquid interfaces in addition to air-water pellicles. When confined, bacteria grow on curved surfaces of both positive and negative Gaussian curvature. However, the confinement geometry does affect the resulting biofilm roughness and relative coverage. We also find that the biofilm location is governed by oxygen availability as well as by gravitational effects; these compete with each other in some situations. Overall, our results demonstrate that confinement geometry is an effective way to control oxygen availability and subsequently biofilm growth. (paper)
Amin, Elizabeth A; Truhlar, Donald G
2008-01-01
We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0
Variable geometry Darrieus wind machine
Pytlinski, J. T.; Serrano, D.
1983-08-01
A variable geometry Darrieus wind machine is proposed. The lower attachment of the blades to the rotor can move freely up and down the axle allowing the blades of change shape during rotation. Experimental data for a 17 m. diameter Darrieus rotor and a theoretical model for multiple streamtube performance prediction were used to develop a computer simulation program for studying parameters that affect the machine's performance. This new variable geometry concept is described and interrelated with multiple streamtube theory through aerodynamic parameters. The computer simulation study shows that governor behavior of a Darrieus turbine can not be attained by a standard turbine operating within normally occurring rotational velocity limits. A second generation variable geometry Darrieus wind turbine which uses a telescopic blade is proposed as a potential improvement on the studied concept.
Flux compactifications and generalized geometries
International Nuclear Information System (INIS)
Grana, Mariana
2006-01-01
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T 6 /(Z 3 x Z 3 ) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry
Flux compactifications and generalized geometries
Energy Technology Data Exchange (ETDEWEB)
Grana, Mariana [Service de Physique Theorique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex (France)
2006-11-07
Following the lectures given at CERN Winter School 2006, we present a pedagogical overview of flux compactifications and generalized geometries, concentrating on closed string fluxes in type II theories. We start by reviewing the supersymmetric flux configurations with maximally symmetric four-dimensional spaces. We then discuss the no-go theorems (and their evasion) for compactifications with fluxes. We analyse the resulting four-dimensional effective theories for Calabi-Yau and Calabi-Yau orientifold compactifications, concentrating on the flux-induced superpotentials. We discuss the generic mechanism of moduli stabilization and illustrate with two examples: the conifold in IIB and a T{sup 6} /(Z{sub 3} x Z{sub 3}) torus in IIA. We finish by studying the effective action and flux vacua for generalized geometries in the context of generalized complex geometry.
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...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Dayside merging and cusp geometry
International Nuclear Information System (INIS)
Crooker, N.U.
1979-01-01
Geometrical considerations are presented to show that dayside magnetic merging when constrained to act only where the fields are antiparallel results in lines of merging that converge at the polar cusps. An important consequence of this geometry is that no accelerated flows are predicted across the dayside magnetopause. Acceleration owing to merging acts in opposition to the magnetosheath flow at the merging point and produces the variably directed, slower-than-magnetosheath flows observed in the entry layer. Another consequence of the merging geometry is that much of the time closed field lines constitute the subsolar region of the magnetopause. The manner in which the polar cap convection patterns predicted by the proposed geometry change as the interplanetary field is rotated through 360 0 provides a unifying description of how the observed single circular vortex and the crescent-shaped double vortex patterns mutually evolve under the influence of a single operating principle
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
KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI
Directory of Open Access Journals (Sweden)
Irkham Ulil Albab
2014-10-01
Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews
Graphical debugging of combinational geometry
International Nuclear Information System (INIS)
Burns, T.J.; Smith, M.S.
1992-01-01
A graphical debugger for combinatorial geometry being developed at Oak Ridge National Laboratory is described. The prototype debugger consists of two parts: a FORTRAN-based ''view'' generator and a Microsoft Windows application for displaying the geometry. Options and features of both modules are discussed. Examples illustrating the various options available are presented. The potential for utilizing the images produced using the debugger as a visualization tool for the output of the radiation transport codes is discussed as is the future direction of the development
Lectures on Algebraic Geometry I
Harder, Gunter
2012-01-01
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern metho
Combinatorial geometry in the plane
Hadwiger, Hugo; Klee, Victor
2014-01-01
Geared toward advanced undergraduates familiar with analysis and college geometry, this concise book discusses theorems on topics restricted to the plane such as convexity, coverings, and graphs. In addition to helping students cultivate rigorous thought, the text encourages the development of mathematical intuition and clarifies the nature of mathematical research.The two-part treatment begins with specific topics including integral distances, covering problems, point set geometry and convexity, simple paradoxes involving point sets, and pure combinatorics, among other subjects. The second pa
Modern differential geometry for physicists
Isham, C J
1989-01-01
These notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by the first-year theoretical physics PhD students, or by students attending the one-year MSc course "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen with an eye to the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday [Univ. of California, Berkeley, CA (United States)
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Spatial geometry and special relativity
DEFF Research Database (Denmark)
Kneubil, Fabiana Botelho
2016-01-01
In this work, it is shown the interplay of relative and absolute entities, which are present in both spatial geometry and special relativity. In order to strengthen the understanding of special relativity, we discuss firstly an instance of geometry and the existence of both frame......-dependent and frame-independent entities. We depart from a subject well known by students, which is the three-dimensional geometric space in order to compare, afterwards, with the treatment of four-dimensional space in the special relativity. The differences and similarities between these two subjects are also...
Stochastic geometry and its applications
Chiu, Sung Nok; Kendall, Wilfrid S; Mecke, Joseph
2013-01-01
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital a
Introduction to topology and geometry
Stahl, Saul
2014-01-01
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." -CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparallele
Algebraic geometry and theta functions
Coble, Arthur B
1929-01-01
This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and
Geometry, topology, and string theory
International Nuclear Information System (INIS)
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated
Krenn, V; Hensel, F; Kim, H J; Souto Carneiro, M M; Starostik, P; Ristow, G; König, A; Vollmers, H P; Müller-Hermelink, H K
1999-11-01
In osteoarthritis (OA), the synovial tissue exhibits a nonfollicular inflammatory infiltration with a characteristic arrangement of lymphocytes and plasma cells. These arrangements are either small perivascular aggregates with plasma cells surrounding the lymphocytes or small groups of plasma cells, located in the vicinity of small blood vessels. These patterns suggest that B lymphocytes directly differentiate into plasma cells. To understand the B-cell response in OA, we analyzed the V(H) genes from B cells of synovial tissue of nine OA patients (average age, 71.5+/-10.5 years; six female and three male). V(H) gene repertoires were determined from RNA prepared from tissue cryosections and from DNA of single isolated B lymphocytes and plasma cells. The inflammatory infiltrate was analyzed immunohistochemically by detecting CD20, Ki-M4 (follicular dendritic cells), CD4, IgG, IgM, IgA, Ki-67, and by simultaneous demonstration of the plasma-cell-specific antigen CD138 (syndecan-1) and factor VIII. The molecular data demonstrate B cells with a high number of somatic mutations (average, 16.5 to 19.8), and high ratios of replacement to silent mutations in the small lymphocytic/plasmacellular aggregates of OA. In the tissue cryosections, the values of the sigmaR/sigmaS at the complementarity determining regions were 5.3 and 2.0 in the framework regions. For both the isolated B lymphocytes and plasma cells, the value of this ratio in the complementarity determining regions was 3.5. In the framework regions, the values of this ratio were 2.0 for the isolated B cells and 1.8 for the plasma cells. B lymphocytes and plasma cells exhibited a distribution not described thus far. Two patterns of B-cell distribution could be observed: (a) Centrally located CD20+ B and CD4+ and CD8+ T lymphocytes were surrounded directly by IgG (predominantly) or IgA and IgM plasma cells. No proliferating Ki-67-positive cells and no follicular dendritic cells (germinal centers) could be detected in
The Idea of Order at Geometry Class.
Rishel, Thomas
The idea of order in geometry is explored using the experience of assignments given to undergraduates in a college geometry course "From Space to Geometry." Discussed are the definition of geometry, and earth measurement using architecture, art, and common experience. This discussion concludes with a consideration of the question of whether…
Teaching Spatial Geometry in a Virtual World
DEFF Research Database (Denmark)
Förster, Klaus-Tycho
2017-01-01
Spatial geometry is one of the fundamental mathematical building blocks of any engineering education. However, it is overshadowed by planar geometry in the curriculum between playful early primary education and later analytical geometry, leaving a multi-year gap where spatial geometry is absent...
Proximal Femoral Geometry and the Risk of Fractures: Literature Review
Directory of Open Access Journals (Sweden)
N.V. Grygorieva
2016-02-01
Full Text Available This article presents the literature review of the impact of the upper third of the femur geometry (hip axis length, femoral neck angle, inter-trochanteric length, horizontal offset, thickness of the cortical bone, etc. on the risk of fractures. The article demonstrates the capabilities of techniques for measurement of hip geometry, namely conventional X-ray of pelvic bones, dual-energy X-ray absorptiometry, computed tomography. Possible correlation is shown between some genetic markers and features of the geometry of the upper third of the femur. Also, there are presented the results of own researches of age and sex characteristics of proximal hip geometry parameters in patients without fractures, as well as in patients of older age groups with internal and extraarticular femoral fractures.
Analogical Reasoning in Geometry Education
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Normal forms in Poisson geometry
Marcut, I.T.
2013-01-01
The structure of Poisson manifolds is highly nontrivial even locally. The first important result in this direction is Conn's linearization theorem around fixed points. One of the main results of this thesis (Theorem 2) is a normal form theorem in Poisson geometry, which is the Poisson-geometric
Exploring Bundling Theory with Geometry
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Stochastic Modelling of River Geometry
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Schaarup-Jensen, K.
1996-01-01
Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....
Matter in toy dynamical geometries
Konopka, T.J.
2009-01-01
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus important to understand to what extent and to what effect
Ca??adas, Mar??a C.; Molina, Marta; Gallardo, Sandra; Mart??nez-Santaolalla, Manuel J.; Pe??as, Mar??a
2010-01-01
In this work we present an activity for High School students in which various mathematical concepts of plane and spatial geometry are involved. The final objective of the proposed tasks is constructing a particular polyhedron, the cube, by using a modality of origami called modular origami.
General Relativity: Geometry Meets Physics
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Learners engaging with transformation geometry
African Journals Online (AJOL)
participants engaged in investigative semi-structured interviews with the resear- chers. ... Keywords: analysis; conversions; transformation geometry; transformations; treatments .... semiotic systems of representation is not only to designate mathematical objects or to com- municate but also to ... Research design. We believe ...
Multivariable calculus and differential geometry
Walschap, Gerard
2015-01-01
This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem.
College geometry a unified development
Kay, David C
2011-01-01
""The book is a comprehensive textbook on basic geometry. … Key features of the book include numerous figures and many problems, more than half of which come with hints or even complete solutions. Frequent historical comments add to making the reading a pleasant one.""-Michael Joswig, Zentralblatt MATH 1273
Mahaffey, Michael L.
One of a series of experimental units for children at the preschool level, this booklet deals with geometric concepts. A unit on volume and a unit on linear measurement are covered; for each unit a discussion of mathematical objectives, a list of materials needed, and a sequence of learning activities are provided. Directions are specified for the…
DEFF Research Database (Denmark)
Byg din egen boomerang, kast den, se den flyve, forstå hvorfor og hvordan den vender tilbage, og grib den. Det handler om opdriften på vingerne når du flyver, men det handler også og allermest om den mærkværdige gyroskop-effekt, du bruger til at holde balancen, når du kører på cykel. Vi vil bruge...
Drawert, Brian; Engblom, Stefan; Hellander, Andreas
2012-06-22
Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at
Fujita, Takatoshi; Mochizuki, Yuji
2018-04-19
We developed the fragment-based method for calculating nonlocal excitations in large molecular systems. This method is based on the multilayer fragment molecular orbital method and the configuration interaction single (CIS) wave function using localized molecular orbitals. The excited-state wave function for the whole system is described as a superposition of configuration state functions (CSFs) for intrafragment excitations and for interfragment charge-transfer excitations. The formulation and calculations of singlet excited-state Hamiltonian matrix elements in the fragment CSFs are presented in detail. The efficient approximation schemes for calculating the matrix elements are also presented. The computational efficiency and the accuracy were evaluated using the molecular dimers and molecular aggregates. We confirmed that absolute errors of 50 meV (relative to the conventional calculations) are achievable for the molecular systems in their equilibrium geometries. The perturbative electron correlation correction to the CIS excitation energies is also demonstrated. The present theory can compute a large number of excited states in large molecular systems; in addition, it allows for the systematic derivation of a model exciton Hamiltonian. These features are useful for studying excited-state dynamics in condensed molecular systems based on the ab initio electronic structure theory.
Discrete differential geometry. Consistency as integrability
Bobenko, Alexander I.; Suris, Yuri B.
2005-01-01
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...
Numerically robust geometry engine for compound solid geometries
International Nuclear Information System (INIS)
Vlachoudis, V.; Sinuela-Pastor, D.
2013-01-01
Monte Carlo programs heavily rely on a fast and numerically robust solid geometry engines. However the success of solid modeling, depends on facilities for specifying and editing parameterized models through a user-friendly graphical front-end. Such a user interface has to be fast enough in order to be interactive for 2D and/or 3D displays, but at the same time numerically robust in order to display possible modeling errors at real time that could be critical for the simulation. The graphical user interface Flair for FLUKA currently employs such an engine where special emphasis has been given on being fast and numerically robust. The numerically robustness is achieved by a novel method of estimating the floating precision of the operations, which dynamically adapts all the decision operations accordingly. Moreover a predictive caching mechanism is ensuring that logical errors in the geometry description are found online, without compromising the processing time by checking all regions. (authors)
Armen, Roger S; Chen, Jianhan; Brooks, Charles L
2009-10-13
Incorporating receptor flexibility into molecular docking should improve results for flexible proteins. However, the incorporation of explicit all-atom flexibility with molecular dynamics for the entire protein chain may also introduce significant error and "noise" that could decrease docking accuracy and deteriorate the ability of a scoring function to rank native-like poses. We address this apparent paradox by comparing the success of several flexible receptor models in cross-docking and multiple receptor ensemble docking for p38α mitogen-activated protein (MAP) kinase. Explicit all-atom receptor flexibility has been incorporated into a CHARMM-based molecular docking method (CDOCKER) using both molecular dynamics (MD) and torsion angle molecular dynamics (TAMD) for the refinement of predicted protein-ligand binding geometries. These flexible receptor models have been evaluated, and the accuracy and efficiency of TAMD sampling is directly compared to MD sampling. Several flexible receptor models are compared, encompassing flexible side chains, flexible loops, multiple flexible backbone segments, and treatment of the entire chain as flexible. We find that although including side chain and some backbone flexibility is required for improved docking accuracy as expected, docking accuracy also diminishes as additional and unnecessary receptor flexibility is included into the conformational search space. Ensemble docking results demonstrate that including protein flexibility leads to to improved agreement with binding data for 227 active compounds. This comparison also demonstrates that a flexible receptor model enriches high affinity compound identification without significantly increasing the number of false positives from low affinity compounds.
Code subspaces for LLM geometries
Berenstein, David; Miller, Alexandra
2018-03-01
We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.
Euclidean distance geometry an introduction
Liberti, Leo
2017-01-01
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
The geometry of celestial mechanics
Geiges, Hansjörg
2016-01-01
Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Grassmannian geometry of scattering amplitudes
Arkani-Hamed, Nima; Cachazo, Freddy; Goncharov, Alexander; Postnikov, Alexander; Trnka, Jaroslav
2016-01-01
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the...
Foliation theory in algebraic geometry
McKernan, James; Pereira, Jorge
2016-01-01
Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classificati...
Groups and Geometries : Siena Conference
Kantor, William; Lunardon, Guglielmo; Pasini, Antonio; Tamburini, Maria
1998-01-01
On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of f...
Needle decompositions in Riemannian geometry
Klartag, Bo'az
2017-01-01
The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.
Systematics of IIB spinorial geometry
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2005-01-01
We reduce the classification of all supersymmetric backgrounds of IIB supergravity to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This extends the work of [hep-th/0503046] to IIB supergravity. We give the expressions of the Killing spinor equations on all five types of spinors. In this way, the Killing spinor equations become a linear system for the fluxes, geometry and spacetime derivatives of...
Geometry Dependence of Stellarator Turbulence
International Nuclear Information System (INIS)
Mynick, H.E.; Xanthopoulos, P.; Boozer, A.H.
2009-01-01
Using the nonlinear gyrokinetic code package GENE/GIST, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry-dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the 2D structure of the microturbulence over that surface, and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrodinger-like equation governing linear drift modes
Superbanana orbits in stellarator geometries
International Nuclear Information System (INIS)
Derr, J.A.; Shohet, J.L.
1979-04-01
The presence of superbanana orbit types localized to either the interior or the exterior of stellarators and torsatrons is numerically investigated for 3.5 MeV alpha particles. The absence of the interior superbanana in both geometries is found to be due to non-conservation of the action. Exterior superbananas are found in the stellarator only, as a consequence of the existence of closed helical magnetic wells. No superbananas of either type are found in the torsatron
Turtle geometry the Python way
Battle, S.
2014-01-01
An introduction to coding using Python’s on-screen ‘turtle’ that can be commanded with a few simple instructions including forward, backward, left and right. The turtle leaves a trace that can be used to draw geometric figures. This workshop is aimed at beginners of all ages. The aim is to learn a smattering of programming and a little bit of geometry in a fun way.
Topics in modern differential geometry
Verstraelen, Leopold
2017-01-01
A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.
Computational geometry for reactor applications
International Nuclear Information System (INIS)
Brown, F.B.; Bischoff, F.G.
1988-01-01
Monte Carlo codes for simulating particle transport involve three basic computational sections: a geometry package for locating particles and computing distances to regional boundaries, a physics package for analyzing interactions between particles and problem materials, and an editing package for determining event statistics and overall results. This paper describes the computational geometry methods in RACER, a vectorized Monte Carlo code used for reactor physics analysis, so that comparisons may be made with techniques used in other codes. The principal applications for RACER are eigenvalue calculations and power distributions associated with reactor core physics analysis. Successive batches of neutrons are run until convergence and acceptable confidence intervals are obtained, with typical problems involving >10 6 histories. As such, the development of computational geometry methods has emphasized two basic needs: a flexible but compact geometric representation that permits accurate modeling of reactor core details and efficient geometric computation to permit very large numbers of histories to be run. The current geometric capabilities meet these needs effectively, supporting a variety of very large and demanding applications
Number theory III Diophantine geometry
1991-01-01
From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...
Riemannian geometry and geometric analysis
Jost, Jürgen
2017-01-01
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...
Donaldson invariants in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)
Aspects of differential geometry II
Gilkey, Peter
2015-01-01
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...
Algebraic Geometry and Number Theory Summer School
Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk
2017-01-01
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.
Geometry success in 20 minutes a day
LLC, LearningExpress
2014-01-01
Whether you're new to geometry or just looking for a refresher, Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day: Covers all vital geometry skills, from the basic building blocks of geometry to ratio, proportion, and similarity to trigonometry and beyond Provides hundreds of practice exercises in test format Applies geometr
Computational modeling of geometry dependent phonon transport in silicon nanostructures
Cheney, Drew A.
Recent experiments have demonstrated that thermal properties of semiconductor nanostructures depend on nanostructure boundary geometry. Phonons are quantized mechanical vibrations that are the dominant carrier of heat in semiconductor materials and their aggregate behavior determine a nanostructure's thermal performance. Phonon-geometry scattering processes as well as waveguiding effects which result from coherent phonon interference are responsible for the shape dependence of thermal transport in these systems. Nanoscale phonon-geometry interactions provide a mechanism by which nanostructure geometry may be used to create materials with targeted thermal properties. However, the ability to manipulate material thermal properties via controlling nanostructure geometry is contingent upon first obtaining increased theoretical understanding of fundamental geometry induced phonon scattering processes and having robust analytical and computational models capable of exploring the nanostructure design space, simulating the phonon scattering events, and linking the behavior of individual phonon modes to overall thermal behavior. The overall goal of this research is to predict and analyze the effect of nanostructure geometry on thermal transport. To this end, a harmonic lattice-dynamics based atomistic computational modeling tool was created to calculate phonon spectra and modal phonon transmission coefficients in geometrically irregular nanostructures. The computational tool is used to evaluate the accuracy and regimes of applicability of alternative computational techniques based upon continuum elastic wave theory. The model is also used to investigate phonon transmission and thermal conductance in diameter modulated silicon nanowires. Motivated by the complexity of the transmission results, a simplified model based upon long wavelength beam theory was derived and helps explain geometry induced phonon scattering of low frequency nanowire phonon modes.
Network geometry with flavor: From complexity to quantum geometry
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
Prediction of melt geometry in laser cutting
Energy Technology Data Exchange (ETDEWEB)
Tani, Giovanni; Tomesani, Luca; Campana, Giampaolo
2003-03-15
In this paper, an analytical model for the evaluation of the melt film geometry in laser cutting of steels is developed. Using as basis, a previous model for kerf geometry estimation developed by the authors, with both reactive and non-reactive process gases, the film thickness and velocity were determined as a function of the kerf depth in the cutting plate. Two criteria were then adopted to predict the quality of the laser cutting operation: the first is based on a minimum acceptable value of the ejection speed of the melt from the bottom of the kerf, the second on the occlusion of the kerf itself due to an excess of molten material in the boundary layer at the kerf width. These criteria determined a feasibility region in the domain of the process and material variables, such as cutting speed, assistant gas pressure, laser beam power and material characteristics. These factors may be successfully used to build a process-planning tool for parameters optimisation and setting, in order to achieve a satisfactory process quality. The model response is in excellent agreement with the feasibility regions reported from experimental data by various authors and demonstrates a relationship between the occurrence of dross adhesion and the two different mechanisms predicted for such a phenomenon were: unsatisfactory ejection speed of the melt film from the bottom of the kerf and occlusion of the kerf.
Geometry and self-righting of turtles.
Domokos, Gábor; Várkonyi, Péter L
2008-01-07
Terrestrial animals with rigid shells face imminent danger when turned upside down. A rich variety of righting strategies of beetle and turtle species have been described, but the exact role of the shell's geometry in righting is so far unknown. These strategies are often based on active mechanisms, e.g. most beetles self-right via motion of their legs or wings; flat, aquatic turtles use their muscular neck to flip back. On the other hand, highly domed, terrestrial turtles with short limbs and necks have virtually no active control: here shape itself may serve as a fundamental tool. Based on field data gathered on a broad spectrum of aquatic and terrestrial turtle species we develop a geometric model of the shell. Inspired by recent mathematical results, we demonstrate that a simple mechanical classification of the model is closely linked to the animals' righting strategy. Specifically, we show that the exact geometry of highly domed terrestrial species is close to optimal for self-righting, and the shell's shape is the predominant factor of their ability to flip back. Our study illustrates how evolution solved a far-from-trivial geometrical problem and equipped some turtles with monostatic shells: beautiful forms, which rarely appear in nature otherwise.
Hand-Geometry Recognition Based on Contour Parameters
Veldhuis, Raymond N.J.; Bazen, A.M.; Booij, W.D.T.; Hendrikse, A.J.; Jain, A.K.; Ratha, N.K.
This paper demonstrates the feasibility of a new method of hand-geometry recognition based on parameters derived from the contour of the hand. The contour is completely determined by the black-and-white image of the hand and can be derived from it by means of simple image-processing techniques. It
A Whirlwind Tour of Computational Geometry.
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
Optimizing solar-cell grid geometry
Crossley, A. P.
1969-01-01
Trade-off analysis and mathematical expressions calculate optimum grid geometry in terms of various cell parameters. Determination of the grid geometry provides proper balance between grid resistance and cell output to optimize the energy conversion process.
International Nuclear Information System (INIS)
Gervais, J.L.
1993-01-01
By analyzing the extrinsic geometry of two dimensional surfaces chirally embedded in C P n (the C P n W-surface), we give exact treatments in various aspects of the classical W-geometry in the conformal gauge: First, the basis of tangent and normal vectors are defined at regular points of the surface, such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the (conformal) A n -Toda Lax pair. Since the latter is known to be intrinsically related with the W symmetries, this gives the geometrical meaning of the A n W-Algebra. Second, W-surfaces are put in one-to-one correspondence with solutions of the conformally-reduced WZNW model, which is such that the Toda fields give the Cartan part in the Gauss decomposition of its solutions. Third, the additional variables of the Toda hierarchy are used as coordinates of C P n . This allows us to show that W-transformations may be extended as particular diffeomorphisms of this target-space. Higher-dimensional generalizations of the WZNW equations are derived and related with the Zakharov-Shabat equations of the Toda hierarchy. Fourth, singular points are studied from a global viewpoint, using our earlier observation that W-surfaces may be regarded as instantons. The global indices of the W-geometry, which are written in terms of the Toda fields, are shown to be the instanton numbers for associated mappings of W-surfaces into the Grassmannians. The relation with the singularities of W-surface is derived by combining the Toda equations with the Gauss-Bonnet theorem. (orig.)
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Magnetoelectrostatic thruster physical geometry tests
Ramsey, W. D.
1981-01-01
Inert gas tests are conducted with several magnetoelectrostatic containment discharge chamber geometries. The configurations tested include three discharge chamber lengths; three boundary magnet patterns; two different flux density magnet materials; hemispherical and conical shaped thrusters having different surface-to-volume ratios; and two and three grid ion optics. Argon mass utilizations of 60 to 79% are attained at 210 to 280 eV/ion in different test configurations. Short hemi thruster configurations are found to produce 70 to 92% xenon mass utilization at 185 to 220 eV/ion.
Programming system for analytic geometry
International Nuclear Information System (INIS)
Raymond, Jacques
1970-01-01
After having outlined the characteristics of computing centres which do not comply with engineering tasks, notably the time required by all different tasks to be performed when developing a software (assembly, compilation, link edition, loading, run), and identified constraints specific to engineering, the author identifies the characteristics a programming system should have to suit engineering tasks. He discussed existing conversational systems and their programming language, and their main drawbacks. Then, he presents a system which aims at facilitating programming and addressing problems of analytic geometry and trigonometry
The geometry of special relativity
International Nuclear Information System (INIS)
Parizet, Jean
2008-01-01
This book for students in mathematics or physics shows the interest of geometry to understand special relativity as a consequence of invariance of Maxwell equations and of constancy of the speed of light. Space-time is actually provided with a geometrical structure and a physical interpretation: at each observer are associated his own time and his own physical space in which occur events he is concerned with. This leads to a natural approach to special relativity. The Lorentz group and its algebra are then studied by using matrices and the Pauli algebra. Quaternions are also addressed
Moduli spaces in algebraic geometry
International Nuclear Information System (INIS)
Goettsche, L.
2000-01-01
This volume of the new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics contains the lecture notes of the School on Algebraic Geometry which took place at the Abdus Salam International Centre for Theoretical Physics from 26 July to 13 August 1999. The school consisted of 2 weeks of lecture courses and one week of conference. The topic of the school was moduli spaces. More specifically the lectures were divided into three subtopics: principal bundles on Riemann surfaces, moduli spaces of vector bundles and sheaves on projective varieties, and moduli spaces of curves
Worldsheet geometries of ambitwistor string
Energy Technology Data Exchange (ETDEWEB)
Ohmori, Kantaro [Department of Physics, the University of Tokyo,Hongo, Bunkyo-ku, Tokyo 133-0022 (Japan)
2015-06-12
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Porous media geometry and transports
Adler, Pierre
1992-01-01
The goal of ""Porous Media: Geometry and Transports"" is to provide the basis of a rational and modern approach to porous media. This book emphasizes several geometrical structures (spatially periodic, fractal, and random to reconstructed) and the three major single-phase transports (diffusion, convection, and Taylor dispersion).""Porous Media"" serves various purposes. For students it introduces basic information on structure and transports. Engineers will find this book useful as a readily accessible assemblage of al the major experimental results pertaining to single-phase tr
Geometry of physical dispersion relations
International Nuclear Information System (INIS)
Raetzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-01-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Projective geometry and projective metrics
Busemann, Herbert
2005-01-01
The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio
Tropical geometry of statistical models.
Pachter, Lior; Sturmfels, Bernd
2004-11-16
This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
Clustering in Hilbert simplex geometry
Nielsen, Frank
2017-04-03
Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.
An invitation to noncommutative geometry
Marcolli, Matilde
2008-01-01
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke
Trends and developments in computational geometry
Berg, de M.
1997-01-01
This paper discusses some trends and achievements in computational geometry during the past five years, with emphasis on problems related to computer graphics. Furthermore, a direction of research in computational geometry is discussed that could help in bringing the fields of computational geometry
Global affine differential geometry of hypersurfaces
Li, An-Min; Zhao, Guosong; Hu, Zejun
2015-01-01
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry- as differential geometry in general- has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.
"WGL," a Web Laboratory for Geometry
Quaresma, Pedro; Santos, Vanda; Maric, Milena
2018-01-01
The role of information and communication technologies (ICT) in education is nowadays well recognised. The "Web Geometry Laboratory," is an e-learning, collaborative and adaptive, Web environment for geometry, integrating a well known dynamic geometry system. In a collaborative session, teachers and students, engaged in solving…
Towards Fast Tracking of the Keyhole Geometry
Brock, C.; Hohenstein, R.; Schmidt, M.
We describe a sensor principle permitting the fast online measurement of the position of the optical process emissions in deep penetration laser welding. Experiments show a strong correlation between the position of the vapour plume and the keyhole geometry, demonstrated here by varying the penetration depth of the weld. In order to achieve an absolute position measurement, the sensor was calibrated using a light source with well defined characteristics. The setup for the calibration measurements and the corresponding data evaluation methods are discussed. The precision of the calibration with a green LED is 6 μm in lateral and 55 μm in axial direction, for a working distance of 200 mm.
DEFF Research Database (Denmark)
Jennum, Karsten Stein
This thesis includes the synthesis and characterisation of organic compounds designed for molecular electronics. The synthesised organic molecules are mainly based on two motifs, the obigo(phenyleneethynylenes) (OPE)s and tetrathiafulvalene (TTF) as shown below. These two scaffolds (OPE and TTF......) are chemically merged together to form cruciform-like structures that are an essential part of the thesis. The cruciform molecules were subjected to molecular conductance measurements to explore their capability towards single-crystal field-effect transistors (Part 1), molecular wires, and single electron......, however, was obtained by a study of a single molecular transistor. The investigated OPE5-TTF compound was captured in a three-terminal experiment, whereby manipulation of the molecule’s electronic spin was possible in different charge states. Thus, we demonstrated how the cruciform molecules could...
Computational geometry algorithms and applications
de Berg, Mark; Overmars, Mark; Schwarzkopf, Otfried
1997-01-01
Computational geometry emerged from the field of algorithms design and anal ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can ...
Tearing modes in toroidal geometry
International Nuclear Information System (INIS)
Connor, J.W.; Cowley, S.C.; Hastie, R.J.; Hender, T.C.; Hood, A.; Martin, T.J.
1988-01-01
The separation of the cylindrical tearing mode stability problem into a resistive resonant layer calculation and an external marginal ideal magnetohydrodynamic (MHD) calculation (Δ' calculation) is generalized to axisymmetric toroidal geometry. The general structure of this separation is analyzed and the marginal ideal MHD information (the toroidal generalization of Δ') required to discuss stability is isolated. This can then, in principle, be combined with relevant resonant layer calculations to determine tearing mode growth rates in realistic situations. Two examples are given: the first is an analytic treatment of toroidally coupled (m = 1, n = 1) and (m = 2, n = 1) tearing modes in a large aspect ratio torus; the second, a numerical treatment of the toroidal coupling of three tearing modes through finite pressure effects in a large aspect ratio torus. In addition, the use of a coupling integral approach for determining the stability of coupled tearing modes is discussed. Finally, the possibility of using initial value resistive MHD codes in realistic toroidal geometry to determine the necessary information from the ideal MHD marginal solution is discussed
Foundations of arithmetic differential geometry
Buium, Alexandru
2017-01-01
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Geometry of isotropic convex bodies
Brazitikos, Silouanos; Valettas, Petros; Vritsiou, Beatrice-Helen
2014-01-01
The study of high-dimensional convex bodies from a geometric and analytic point of view, with an emphasis on the dependence of various parameters on the dimension stands at the intersection of classical convex geometry and the local theory of Banach spaces. It is also closely linked to many other fields, such as probability theory, partial differential equations, Riemannian geometry, harmonic analysis and combinatorics. It is now understood that the convexity assumption forces most of the volume of a high-dimensional convex body to be concentrated in some canonical way and the main question is whether, under some natural normalization, the answer to many fundamental questions should be independent of the dimension. The aim of this book is to introduce a number of well-known questions regarding the distribution of volume in high-dimensional convex bodies, which are exactly of this nature: among them are the slicing problem, the thin shell conjecture and the Kannan-Lov�sz-Simonovits conjecture. This book prov...
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Canonical differential geometry of string backgrounds
International Nuclear Information System (INIS)
Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2006-01-01
String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes
Estrada, T; Zhang, B; Cicotti, P; Armen, R S; Taufer, M
2012-07-01
We present a scalable and accurate method for classifying protein-ligand binding geometries in molecular docking. Our method is a three-step process: the first step encodes the geometry of a three-dimensional (3D) ligand conformation into a single 3D point in the space; the second step builds an octree by assigning an octant identifier to every single point in the space under consideration; and the third step performs an octree-based clustering on the reduced conformation space and identifies the most dense octant. We adapt our method for MapReduce and implement it in Hadoop. The load-balancing, fault-tolerance, and scalability in MapReduce allow screening of very large conformation spaces not approachable with traditional clustering methods. We analyze results for docking trials for 23 protein-ligand complexes for HIV protease, 21 protein-ligand complexes for Trypsin, and 12 protein-ligand complexes for P38alpha kinase. We also analyze cross docking trials for 24 ligands, each docking into 24 protein conformations of the HIV protease, and receptor ensemble docking trials for 24 ligands, each docking in a pool of HIV protease receptors. Our method demonstrates significant improvement over energy-only scoring for the accurate identification of native ligand geometries in all these docking assessments. The advantages of our clustering approach make it attractive for complex applications in real-world drug design efforts. We demonstrate that our method is particularly useful for clustering docking results using a minimal ensemble of representative protein conformational states (receptor ensemble docking), which is now a common strategy to address protein flexibility in molecular docking. Copyright © 2012 Elsevier Ltd. All rights reserved.
F-Theory - From Geometry to Physics and Back
CERN. Geneva
2017-01-01
Compactifications of string theory have the potential to form a bridge between what we believe is a consistent quantum theory of gravity in 10 spacetime dimensions and observed physics in four dimensions. At the same time, beautiful results from mathematics, especially algebraic geometry, are directly linked to some of the key concepts in modern particle and quantum field theory. This theory colloquium will illustrate some of these ideas in the context of F-theory, which provides a non-perturbative formulation of a class of string compactifications in their geometric regime. Recent applications of F-theory range from very concrete suggestions to address known challenges in physics beyond the Standard Model to the 'physicalization of geometry' to the construction and investigations of strongly coupled quantum field theories in various dimensions. After reviewing examples of such applications we will conclude by demonstrating the close links between geometry and physics in F-theory via some new results on the r...
Perception of global facial geometry is modulated through experience
Directory of Open Access Journals (Sweden)
Meike Ramon
2015-03-01
Full Text Available Identification of personally familiar faces is highly efficient across various viewing conditions. While the presence of robust facial representations stored in memory is considered to aid this process, the mechanisms underlying invariant identification remain unclear. Two experiments tested the hypothesis that facial representations stored in memory are associated with differential perceptual processing of the overall facial geometry. Subjects who were personally familiar or unfamiliar with the identities presented discriminated between stimuli whose overall facial geometry had been manipulated to maintain or alter the original facial configuration (see Barton, Zhao & Keenan, 2003. The results demonstrate that familiarity gives rise to more efficient processing of global facial geometry, and are interpreted in terms of increased holistic processing of facial information that is maintained across viewing distances.
Webb, Jason C.; Lauret, Jerome; Perevoztchikov, Victor
2012-12-01
Increasingly detailed descriptions of complex detector geometries are required for the simulation and analysis of today's high-energy and nuclear physics experiments. As new tools for the representation of geometry models become available during the course of an experiment, a fundamental challenge arises: how best to migrate from legacy geometry codes developed over many runs to the new technologies, such as the ROOT/TGeo [1] framework, without losing touch with years of development, tuning and validation. One approach, which has been discussed within the community for a number of years, is to represent the geometry model in a higher-level language independent of the concrete implementation of the geometry. The STAR experiment has used this approach to successfully migrate its legacy GEANT 3-era geometry to an Abstract geometry Modelling Language (AgML), which allows us to create both native GEANT 3 and ROOT/TGeo implementations. The language is supported by parsers and a C++ class library which enables the automated conversion of the original source code to AgML, supports export back to the original AgSTAR[5] representation, and creates the concrete ROOT/TGeo geometry implementation used by our track reconstruction software. In this paper we present our approach, design and experience and will demonstrate physical consistency between the original AgSTAR and new AgML geometry representations.
Power deposition in a cylindrical geometry using B-10 coatings
International Nuclear Information System (INIS)
Chung, A.K.; Prelas, M.A.
1983-01-01
The transport of charged particles produced by 10 B (n, α) Li and 235 U (n, νn) ff nuclear reactions in a two region cylindrical geometry is predicted. We employed a mean-range straight-flight approximation to calculate the power deposition by the charged particles in a gaseous medium. Our model demonstrated some features in a cylindrical experiment which were suspected but not proven. In the common slab model used by Guyot et al 1 and Romero 2 , the spatial distribution of power deposition is much flatter than it would be in a cylindrical model. A steeper gradient in the power deposition is expected in a cylindrical geometry than in a slab geometry. We also found that for a standard thickness of Boron-10 coating (1.73 μm) used in NPLs, the expected efficiency of a cylindrical geometry (7.5%) is much lower than the 12% efficiency predicted by the slab model. Indeed the use of slab geometry in modeling current NPL experimental devices is not accurate
Hopf algebras in noncommutative geometry
International Nuclear Information System (INIS)
Varilly, Joseph C.
2001-10-01
We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)
Integrable systems, geometry, and topology
Terng, Chuu-Lian
2006-01-01
The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and their relations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu, and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of ...
Tarski Geometry Axioms. Part III
Directory of Open Access Journals (Sweden)
Coghetto Roland
2017-12-01
Full Text Available In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters. Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations the propositions (“Satz” are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2.
Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Introduction to global variational geometry
Krupka, Demeter
2015-01-01
The book is devoted to recent research in the global variational theory on smooth manifolds. Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. Emphasis is placed on the foundations of the theory of variational functionals on fibered manifolds - relevant geometric structures for variational principles in geometry, physical field theory and higher-order fibered mechanics. The book chapters include: - foundations of jet bundles and analysis of differential forms and vector fields on jet bundles, - the theory of higher-order integral variational functionals for sections of a fibred space, the (global) first variational formula in infinitesimal and integral forms- extremal conditions and the discussion of Noether symmetries and generalizations,- the inverse problems of the calculus of variations of Helmholtz type- variational se...
Some Progress in Conformal Geometry
Directory of Open Access Journals (Sweden)
Sun-Yung A. Chang
2007-12-01
Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, S.J.; Shafi, Q.
2003-09-01
We show how the seesaw mechanism for neutrino masses can be realized within a five dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M P1 .exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed. (orig.)
Seesaw mechanism in warped geometry
International Nuclear Information System (INIS)
Huber, Stephan J.; Shafi, Qaisar
2004-01-01
We show how the seesaw mechanism for neutrino masses can be realized within a five-dimensional (5D) warped geometry framework. Intermediate scale standard model (SM) singlet neutrino masses, needed to explain the atmospheric and solar neutrino oscillations, are shown to be proportional to M Pl exp((2c-1)πkR), where c denotes the coefficient of the 5D Dirac mass term for the singlet neutrino which also has a Planck scale Majorana mass localized on the Planck-brane, and kR∼11 in order to resolve the gauge hierarchy problem. The case with a bulk 5D Majorana mass term for the singlet neutrino is briefly discussed
Conformal geometry and quasiregular mappings
Vuorinen, Matti
1988-01-01
This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook an...
Quantization of the Schwarzschild geometry
International Nuclear Information System (INIS)
Melas, Evangelos
2013-01-01
The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on the wave function. Based on their integrability conditions, only one of the three existing symmetries can be consistently imposed, while the unique Casimir invariant, being the product of the remaining two symmetries, is calculated as the only possible second condition on the wave function. This quadratic integral of motion is identified with the reparametrization generator, as an implication of the uniqueness of the dynamical evolution, by fixing a suitable parametrization of the r-lapse function. In this parametrization, the determinant of the supermetric plays the role of the mesure. The combined Wheeler – DeWitt and linear conditional symmetry equations are analytically solved. The solutions obtained depend on the product of the two ''scale factors''.
Butterfly wing color: A photonic crystal demonstration
Proietti Zaccaria, Remo
2016-01-01
We have theoretically modeled the optical behavior of a natural occurring photonic crystal, as defined by the geometrical characteristics of the Teinopalpus Imperialis butterfly. In particular, following a genetic algorithm approach, we demonstrate how its wings follow a triclinic crystal geometry with a tetrahedron unit base. By performing both photonic band analysis and transmission/reflection simulations, we are able to explain the characteristic colors emerging by the butterfly wings, thus confirming their crystal form.
Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry
2014-01-01
Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...
Convection in Slab and Spheroidal Geometries
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Microfluidic step-emulsification in axisymmetric geometry.
Chakraborty, I; Ricouvier, J; Yazhgur, P; Tabeling, P; Leshansky, A M
2017-10-25
Biphasic step-emulsification (Z. Li et al., Lab Chip, 2015, 15, 1023) is a promising microfluidic technique for high-throughput production of μm and sub-μm highly monodisperse droplets. The step-emulsifier consists of a shallow (Hele-Shaw) microchannel operating with two co-flowing immiscible liquids and an abrupt expansion (i.e., step) to a deep and wide reservoir. Under certain conditions the confined stream of the disperse phase, engulfed by the co-flowing continuous phase, breaks into small highly monodisperse droplets at the step. Theoretical investigation of the corresponding hydrodynamics is complicated due to the complex geometry of the planar device, calling for numerical approaches. However, direct numerical simulations of the three dimensional surface-tension-dominated biphasic flows in confined geometries are computationally expensive. In the present paper we study a model problem of axisymmetric step-emulsification. This setup consists of a stable core-annular biphasic flow in a cylindrical capillary tube connected co-axially to a reservoir tube of a larger diameter through a sudden expansion mimicking the edge of the planar step-emulsifier. We demonstrate that the axisymmetric setup exhibits similar regimes of droplet generation to the planar device. A detailed parametric study of the underlying hydrodynamics is feasible via inexpensive (two dimensional) simulations owing to the axial symmetry. The phase diagram quantifying the different regimes of droplet generation in terms of governing dimensionless parameters is presented. We show that in qualitative agreement with experiments in planar devices, the size of the droplets generated in the step-emulsification regime is independent of the capillary number and almost insensitive to the viscosity ratio. These findings confirm that the step-emulsification regime is solely controlled by surface tension. The numerical predictions are in excellent agreement with in-house experiments with the axisymmetric
Biodiesel Mass Transit Demonstration
2010-04-01
The Biodiesel Mass Transit Demonstration report is intended for mass transit decision makers and fleet managers considering biodiesel use. This is the final report for the demonstration project implemented by the National Biodiesel Board under a gran...
Authoring Effective Demonstrations
National Research Council Canada - National Science Library
Fu, Dan; Jensen, Randy; Salas, Eduardo; Rosen, Michael A; Ramachandran, Sowmya; Upshaw, Christin L; Hinkelman, Elizabeth; Lampton, Don
2007-01-01
... or human role-players for each training event. We report our ongoing efforts to (1) research the nature and purpose of demonstration, articulating guidelines for effective demonstration within a training context, and (2...
Comparing Demonstratives in Kwa
African Journals Online (AJOL)
This paper is a comparative study of demonstrative forms in three K wa languages, ... relative distance from the deictic centre, such as English this and that, here and there. ... Mostly, the referents of demonstratives are 'activated' or at least.
Polarized Light Corridor Demonstrations.
Davies, G. R.
1990-01-01
Eleven demonstrations of light polarization are presented. Each includes a brief description of the apparatus and the effect demonstrated. Illustrated are strain patterns, reflection, scattering, the Faraday Effect, interference, double refraction, the polarizing microscope, and optical activity. (CW)
Connections between algebra, combinatorics, and geometry
Sather-Wagstaff, Sean
2014-01-01
Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...
Second International workshop Geometry and Symbolic Computation
Walczak, Paweł; Geometry and its Applications
2014-01-01
This volume has been divided into two parts: Geometry and Applications. The geometry portion of the book relates primarily to geometric flows, laminations, integral formulae, geometry of vector fields on Lie groups, and osculation; the articles in the applications portion concern some particular problems of the theory of dynamical systems, including mathematical problems of liquid flows and a study of cycles for non-dynamical systems. This Work is based on the second international workshop entitled "Geometry and Symbolic Computations," held on May 15-18, 2013 at the University of Haifa and is dedicated to modeling (using symbolic calculations) in differential geometry and its applications in fields such as computer science, tomography, and mechanics. It is intended to create a forum for students and researchers in pure and applied geometry to promote discussion of modern state-of-the-art in geometric modeling using symbolic programs such as Maple™ and Mathematica®, as well as presentation of new results. ...
Strategy Guideline: Demonstration Home
Energy Technology Data Exchange (ETDEWEB)
Savage, C.; Hunt, A.
2012-12-01
This guideline will provide a general overview of the different kinds of demonstration home projects, a basic understanding of the different roles and responsibilities involved in the successful completion of a demonstration home, and an introduction into some of the lessons learned from actual demonstration home projects. Also, this guideline will specifically look at the communication methods employed during demonstration home projects. And lastly, we will focus on how to best create a communication plan for including an energy efficient message in a demonstration home project and carry that message to successful completion.
Strategy Guideline. Demonstration Home
Energy Technology Data Exchange (ETDEWEB)
Hunt, A.; Savage, C.
2012-12-01
This guideline will provide a general overview of the different kinds of demonstration home projects, a basic understanding of the different roles and responsibilities involved in the successful completion of a demonstration home, and an introduction into some of the lessons learned from actual demonstration home projects. Also, this guideline will specifically look at the communication methods employed during demonstration home projects. And lastly, we will focus on how to best create a communication plan for including an energy efficient message in a demonstration home project and carry that message to successful completion.
Ahmadi, Elaheh; Koksaldi, Onur S.; Zheng, Xun; Mates, Tom; Oshima, Yuichi; Mishra, Umesh K.; Speck, James S.
2017-07-01
β-(Al x Ga1- x )2O3/β-Ga2O3 heterostructures were grown via plasma-assisted molecular beam epitaxy. The β-(Al x Ga1- x )2O3 barrier was partially doped by Ge to achieve a two-dimensional electron gas (2DEG) in Ga2O3. The formation of the 2DEG was confirmed by capacitance-voltage measurements. The impact of Ga-polishing on both the surface morphology and the reduction of the unintentionally incorporated Si at the growth interface was investigated using atomic force microscopy and secondary-ion mass spectrometry. Modulation doped field-effect transistors were fabricated. A maximum current density of 20 mA/mm with a pinch-off voltage of -6 V was achieved on a sample with a 2DEG sheet charge density of 1.2 × 1013 cm-2.
A vector space approach to geometry
Hausner, Melvin
2010-01-01
The effects of geometry and linear algebra on each other receive close attention in this examination of geometry's correlation with other branches of math and science. In-depth discussions include a review of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. 1965 edition.
Classical geometry Euclidean, transformational, inversive, and projective
Leonard, I E; Liu, A C F; Tokarsky, G W
2014-01-01
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p
Introduction to non-Euclidean geometry
Wolfe, Harold E
2012-01-01
One of the first college-level texts for elementary courses in non-Euclidean geometry, this concise, readable volume is geared toward students familiar with calculus. A full treatment of the historical background explores the centuries-long efforts to prove Euclid's parallel postulate and their triumphant conclusion. Numerous original exercises form an integral part of the book.Topics include hyperbolic plane geometry and hyperbolic plane trigonometry, applications of calculus to the solutions of some problems in hyperbolic geometry, elliptic plane geometry and trigonometry, and the consistenc
Disformal transformation in Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Applications of Affine and Weyl geometry
García-Río, Eduardo; Nikcevic, Stana
2013-01-01
Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia
Special Geometry and Automorphic Forms
Berglund, P; Wyllard, N; Berglund, Per; Henningson, Mans; Wyllard, Niclas
1997-01-01
We consider special geometry of the vector multiplet moduli space in compactifications of the heterotic string on $K3 \\times T^2$ or the type IIA string on $K3$-fibered Calabi-Yau threefolds. In particular, we construct a modified dilaton that is invariant under $SO(2, n; Z)$ T-duality transformations at the non-perturbative level and regular everywhere on the moduli space. The invariant dilaton, together with a set of other coordinates that transform covariantly under $SO(2, n; Z)$, parameterize the moduli space. The construction involves a meromorphic automorphic function of $SO(2, n; Z)$, that also depends on the invariant dilaton. In the weak coupling limit, the divisor of this automorphic form is an integer linear combination of the rational quadratic divisors where the gauge symmetry is enhanced classically. We also show how the non-perturbative prepotential can be expressed in terms of meromorphic automorphic forms, by expanding a T-duality invariant quantity both in terms of the standard special coord...
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Latent geometry of bipartite networks
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
The geometry of population genetics
Akin, Ethan
1979-01-01
The differential equations which model the action of selection and recombination are nonlinear equations which are impossible to It is even difficult to describe in general the solve explicitly. Recently, Shahshahani began using qualitative behavior of solutions. differential geometry to study these equations [28]. with this mono graph I hope to show that his ideas illuminate many aspects of pop ulation genetics. Among these are his proof and clarification of Fisher's Fundamental Theorem of Natural Selection and Kimura's Maximum Principle and also the effect of recombination on entropy. We also discover the relationship between two classic measures of 2 genetic distance: the x measure and the arc-cosine measure. There are two large applications. The first is a precise definition of the biological concept of degree of epistasis which applies to general (i.e. frequency dependent) forms of selection. The second is the unexpected appearance of cycling. We show that cycles can occur in the two-locus-two-allele...
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Animating Geometry Discussions with Flexigons.
McClintock, Ruth
1994-01-01
Presents activities with 10- and 4-straw flexigons, an object created by stringing together lengths of plastic drinking straws with nylon fishing line. Discusses several geometric theorems that can be demonstrated with flexigons. (MKR)
Manufacturing Demonstration Facility (MDF)
Federal Laboratory Consortium — The U.S. Department of Energy Manufacturing Demonstration Facility (MDF) at Oak Ridge National Laboratory (ORNL) provides a collaborative, shared infrastructure to...
Micromagnetic recording model of writer geometry effects at skew
Plumer, M. L.; Bozeman, S.; van Ek, J.; Michel, R. P.
2006-04-01
The effects of the pole-tip geometry at the air-bearing surface on perpendicular recording at a skew angle are examined through modeling and spin-stand test data. Head fields generated by the finite element method were used to record transitions within our previously described micromagnetic recording model. Write-field contours for a variety of square, rectangular, and trapezoidal pole shapes were evaluated to determine the impact of geometry on field contours. Comparing results for recorded track width, transition width, and media signal to noise ratio at 0° and 15° skew demonstrate the benefits of trapezoidal and reduced aspect-ratio pole shapes. Consistency between these modeled results and test data is demonstrated.
Variable Geometry and Multicycle Engines
1977-03-01
Methane Ethyl Methyl Ammonia Hydrogen JP Fuel Methane Alcohol Alcohol Nominal composition CH 1 94 CH4 C2 H5 O01 CH 3 O NH3 112 Molecular weight -120...collage et en crololire A une 4l6vation des Amission. d oxydes La !;N2CMA a d~fini dons dos 4tudem A long term* une chazibro A "A6coulement a~rodynaaique...dana le conduit de m~lange ; ean ordonnný’e sont port~s lea indices dmiasion d~ oxyde d’azote mesur~s en int~grant lea valeurs de concen- trations
Alternating copolymers and alternative device geometries for organic photovoltaics.
Inganäs, Olle; Zhang, Fengling; Andersson, Mats R
2012-01-01
The efficiency of conversion of light to electrical energy with the help of conjugated polymers and molecules is rapidly improving. The optical absorption properties of these materials can be designed, and implemented via molecular engineering. Full coverage of the solar spectrum is thus feasible. Narrow absorption spectra allow construction of tandem solar cells. The poor transport properties of these materials require thin devices, which limits optical absorption. Alternative device geometries for these flexible materials compensate for the optical absorption by light trapping, and allow tandem cells.
Electrostatic stability of electron-positron plasmas in dipole geometry
Mishchenko, Alexey; Plunk, Gabriel; Helander, Per
2017-01-01
The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the zero-Debye-length case, the stability diagram is found to exhibit singular behavior. However, when the Debye length is non-zero, a fluid mode appears, which resolves the observed singularity, and also demonstrates that both the temperature and density gradients c...
Quantum groups: Geometry and applications
International Nuclear Information System (INIS)
Chu, C.S.
1996-01-01
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge
The geometry of elementary particles
International Nuclear Information System (INIS)
Lov, T.R.
1987-01-01
A new model of elementary particles based on the geometry of Quantum deSitter space QdS = SU (3,2)/(SU(3,1) x U(1)) is introduced and studied. QdS is a complexification of quantization of anti-de Sitter space, AdS = SO(3,2)/SO(3,1), which in recent years had played a pivotal role in supergravity. The nontrival principle fiber bundle has total space SU(3,2), fiber SU(3,1) x U(1) and base QdS. In this setting, the standard recipes for Yang-Mills fields don't work. These require connections and the associated covariant derivatives. Here it is shown that the Lie derivatives, not the covariant derivatives are important in quantization. In this setting, the no-go theorems are not valid. This new quantum mechanics leads to a model of elementary particles as vertical vector fields in the bundle with interaction via the Lie bracket. There are five physical interactions modelled by the bracket interaction. The quantum numbers are identified as the roots of su(3,2) and are preserved under the bracket interaction. The model explains conservation of charge, baryon number, lepton number, parity and the heirarchy problem. Since the bracket is the curvature of a homogeneous space, particles are then the curvature of QdS. This model for particles is consistent with the requirements of General Relativity. Furthermore, since the curvature tensor is built from the quantized wave functions, the curvature tensor is quantized and this is quantum theory of gravity
Geometry and physics of branes
International Nuclear Information System (INIS)
Gal'tsov, D V
2003-01-01
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two-dimensional conformal field
Description of SSG Geometry - phase 1
DEFF Research Database (Denmark)
Margheritini, Lucia; Kofoed, Jens Peter
The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work.......The purpose of the study is to define the optimized geometry for the SSG in Svaheia, Norway and to provide the responsible for the turbines with useful information to their work....
Increasing insightful thinking in analytic geometry
Timmer, Mark; Verhoef, Neeltje Cornelia
Elsewhere in this issue Ferdinand Verhulst described the discussion of the interaction of analysis and geometry in the 19th century. In modern times such discussions come up again and again. As of 2014, synthetic geometry will not be part of the Dutch 'vwo - mathematics B' programme anymore.
Symposium on Differential Geometry and Differential Equations
Berger, Marcel; Bryant, Robert
1987-01-01
The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.
Curvature tensor copies in affine geometry
International Nuclear Information System (INIS)
Srivastava, P.P.
1981-01-01
The sets of space-time and spin-connections which give rise to the same curvature tensor are constructed. The corresponding geometries are compared. Results are illustrated by an explicit calculation and comment on the copies in Einstein-Cartan and Weyl-Cartan geometries. (Author) [pt
Fractal geometry of high temperature superconductors
International Nuclear Information System (INIS)
Mosolov, A.B.
1989-01-01
Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials
Quantification of variability in bedform geometry
van der Mark, C.F.; Blom, Astrid; Hulscher, Suzanne J.M.H.
2008-01-01
We analyze the variability in bedform geometry in laboratory and field studies. Even under controlled steady flow conditions in laboratory flumes, bedforms are irregular in size, shape, and spacing, also in case of well-sorted sediment. Our purpose is to quantify the variability in bedform geometry.
Random geometry and Yang-Mills theory
International Nuclear Information System (INIS)
Froehlich, J.
1981-01-01
The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)
The Geometry of the Universe: Part 2
Francis, Stephanie
2009-01-01
Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…
Poisson geometry from a Dirac perspective
Meinrenken, Eckhard
2018-03-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
An approach for management of geometry data
Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.
1980-01-01
The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.
Transformasi Geometri Rotasi Berbantuan Software Geogebra
Directory of Open Access Journals (Sweden)
Muhamad Hanafi
2018-02-01
Full Text Available Penelitian ini bertujuan untuk membantu visualisasi dan menemukan konsep pada Transformasi geometri Rotasi di titik Pusat dengan menggunakan software GeoGebra. Penelitian ini mengulas tentang Koordinat Kartesius dan Polar, dan selanjutntya Transformasi geometri Rotasi di titik Pusat .
Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi
2014-01-01
The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...
The design of geometry teaching: learning from the geometry textbooks of Godfrey and Siddons
Fujita, Taro; Jones, Keith
2002-01-01
Deciding how to teach geometry remains a demanding task with one of major arguments being about how to combine the intuitive and deductive aspects of geometry into an effective teaching design. In order to try to obtain an insight into tackling this issue, this paper reports an analysis of innovative geometry textbooks which were published in the early part of the 20th Century, a time when significant efforts were being made to improve the teaching and learning of geometry. The analysis sugge...
Physical meaning of the optical reference geometry
International Nuclear Information System (INIS)
Abramowicz, M.A.
1990-09-01
I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS
Energy Technology Data Exchange (ETDEWEB)
Singer, Isadore M.
2008-03-04
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Final Report: Geometry And Elementary Particle Physics
International Nuclear Information System (INIS)
Singer, Isadore M.
2008-01-01
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
Special metrics and group actions in geometry
Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi
2017-01-01
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.
Stationary bubbles and their tunneling channels toward trivial geometry
Energy Technology Data Exchange (ETDEWEB)
Chen, Pisin; Yeom, Dong-han [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China); Domènech, Guillem; Sasaki, Misao, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: guillem.domenech@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp, E-mail: innocent.yeom@gmail.com [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2016-04-01
In the path integral approach, one has to sum over all histories that start from the same initial condition in order to obtain the final condition as a superposition of histories. Applying this into black hole dynamics, we consider stable and unstable stationary bubbles as a reasonable and regular initial condition. We find examples where the bubble can either form a black hole or tunnel toward a trivial geometry, i.e., with no singularity nor event horizon. We investigate the dynamics and tunneling channels of true vacuum bubbles for various tensions. In particular, in line with the idea of superposition of geometries, we build a classically stable stationary thin-shell solution in a Minkowski background where its fate is probabilistically given by non-perturbative effects. Since there exists a tunneling channel toward a trivial geometry in the entire path integral, the entire information is encoded in the wave function. This demonstrates that the unitarity is preserved and there is no loss of information when viewed from the entire wave function of the universe, whereas a semi-classical observer, who can see only a definitive geometry, would find an effective loss of information. This may provide a resolution to the information loss dilemma.
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry
Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe
2012-01-01
This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…
Quantum Entanglement and Projective Ring Geometry
Directory of Open Access Journals (Sweden)
Michel Planat
2006-08-01
Full Text Available The paper explores the basic geometrical properties of the observables characterizing two-qubit systems by employing a novel projective ring geometric approach. After introducing the basic facts about quantum complementarity and maximal quantum entanglement in such systems, we demonstrate that the 15 × 15 multiplication table of the associated four-dimensional matrices exhibits a so-far-unnoticed geometrical structure that can be regarded as three pencils of lines in the projective plane of order two. In one of the pencils, which we call the kernel, the observables on two lines share a base of Bell states. In the complement of the kernel, the eight vertices/observables are joined by twelve lines which form the edges of a cube. A substantial part of the paper is devoted to showing that the nature of this geometry has much to do with the structure of the projective lines defined over the rings that are the direct product of n copies of the Galois field GF(2, with n = 2, 3 and 4.
Innovative technology demonstration
International Nuclear Information System (INIS)
Anderson, D.B.; Luttrell, S.P.; Hartley, J.N.; Hinchee, R.
1992-04-01
The Innovative Technology Demonstration (ITD) program at Tinker Air Force Base (TAFB), Oklahoma City, Oklahoma, will demonstrate the overall utility and effectiveness of innovative technologies for site characterization, monitoring, and remediation of selected contaminated test sites. The current demonstration test sites include a CERCLA site on the NPL list, located under a building (Building 3001) that houses a large active industrial complex used for rebuilding military aircraft, and a site beneath and surrounding an abandoned underground tank vault used for storage of jet fuels and solvents. The site under Building 3001 (the NW Test Site) is contaminated with TCE and Cr +6 ; the site with the fuel storage vault (the SW Tanks Site) is contaminated with fuels, BTEX and TCE. These sites and others have been identified for cleanup under the Air Force's Installation Restoration Program (IRP). This document describes the demonstrations that have been conducted or are planned for the TAFB
Laser Communications Relay Demonstration
National Aeronautics and Space Administration — LCRD is a minimum two year flight demonstration in geosynchronous Earth orbit to advance optical communications technology toward infusion into Deep Space and Near...
Spacecraft Fire Safety Demonstration
National Aeronautics and Space Administration — The objective of the Spacecraft Fire Safety Demonstration project is to develop and conduct large-scale fire safety experiments on an International Space Station...
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some "the elementary particles of arithmetic" as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called "the elementary particles of physics" too. This study considers the problem of closely packing similar circles/spheres in 2D/3D space. This is in effect a discretization process of space and the allowable number in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This "number/physical" stability idea applies to bigger collections made from smaller (prime units leading to larger stable prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show convincingly that the growth of prime numbers and that of the masses of
Primes, Geometry and Condensed Matter
Directory of Open Access Journals (Sweden)
Al Rabeh R. H.
2009-07-01
Full Text Available Fascination with primes dates back to the Greeks and before. Primes are named by some “the elementary particles of arithmetic” as every nonprime integer is made of a unique set of primes. In this article we point to new connections between primes, geometry and physics which show that primes could be called “the elementary particles of physics” too. This study considers the problem of closely packing similar circles / spheres in 2D / 3D space. This is in effect a discretization process of space and the allowable num- ber in a pack is found to lead to some unexpected cases of prime configurations which is independent of the size of the constituents. We next suggest that a non-prime can be considered geometrically as a symmetric collection that is separable (factorable into similar parts- six is two threes or three twos for example. A collection that has no such symmetry is a prime. As a result, a physical prime aggregate is more difficult to split symmetrically resulting in an inherent stability. This “number / physical” stability idea applies to bigger collections made from smaller (prime units leading to larger sta- ble prime structures in a limitless scaling up process. The distribution of primes among numbers can be understood better using the packing ideas described here and we further suggest that differing numbers (and values of distinct prime factors making a nonprime collection is an important factor in determining the probability and method of possible and subsequent disintegration. Disintegration is bound by energy conservation and is closely related to symmetry by Noether theorems. Thinking of condensed matter as the packing of identical elements, we examine plots of the masses of chemical elements of the periodic table, and also those of the elementary particles of physics, and show that prime packing rules seem to play a role in the make up of matter. The plots show con- vincingly that the growth of prime numbers and that
Education Payload Operation - Demonstrations
Keil, Matthew
2009-01-01
Education Payload Operation - Demonstrations (EPO-Demos) are recorded video education demonstrations performed on the International Space Station (ISS) by crewmembers using hardware already onboard the ISS. EPO-Demos are videotaped, edited, and used to enhance existing NASA education resources and programs for educators and students in grades K-12. EPO-Demos are designed to support the NASA mission to inspire the next generation of explorers.
Buried Waste Integrated Demonstration
International Nuclear Information System (INIS)
1994-03-01
The Buried Waste Integrated Demonstration (BWID) supports the applied research, development, demonstration, and evaluation of a suite of advanced technologies that offer promising solutions to the problems associated with the remediation of buried waste. BWID addresses the difficult remediation problems associated with DOE complex-wide buried waste, particularly transuranic (TRU) contaminated buried waste. BWID has implemented a systems approach to the development and demonstration of technologies that will characterize, retrieve, treat, and dispose of DOE buried wastes. This approach encompasses the entire remediation process from characterization to post-monitoring. The development and demonstration of the technology is predicated on how a technology fits into the total remediation process. To address all of these technological issues, BWID has enlisted scientific expertise of individuals and groups from within the DOE Complex, as well as experts from universities and private industry. The BWID mission is to support development and demonstration of a suite of technologies that, when integrated with commercially-available technologies, forms a comprehensive, remediation system for the effective and efficient remediation of buried waste throughout the DOE Complex. BWID will evaluate and validate demonstrated technologies and transfer this information and equipment to private industry to support the Office of Environmental Restoration (ER), Office of Waste Management (WM), and Office of Facility Transition (FT) remediation planning and implementation activities
Geometry and physics of branes
Energy Technology Data Exchange (ETDEWEB)
Gal' tsov, D V
2003-03-21
The book brings together the contents of lecture courses delivered at the school 'Geometry and Physics of Branes' which took place at the Center 'Alessandro Volta' (Como, Italy) in the spring of 2001. The purpose of the school was to provide an introduction to some lines of research, related to the notion of branes in superstring theory, which are in the focus of attention both in the physical and mathematical communities. The book is structured into three parts: the first contains an elementary introduction to branes, the second is devoted to physical aspects (conformal field theory on open and unoriented surfaces and topics in string tachyon dynamics), and the last contains some more formal mathematical developments. An introduction to branes is given in a remarkably lucid contribution by A Lerda. It opens with a construction of p-brane solutions in classical IIA and IIB supergravities with particular emphasis on the 'fundamental string' solution, the NS5-brane and the D3-brane. Then, the quantum description of D-branes is discussed in terms of boundary states of the closed superstring, which is an alternative to the more common description in terms of open strings with Dirichlet boundary conditions in the transverse to the brane directions. When a constant gauge field is present in the D-brane worldvolume, the boundary states are coherent states of the string oscillators depending on the field strength tensor. The couplings of the brane to the bulk fields - the graviton, the dilaton, and the Kalb-Ramond fields - are then extracted and shown to be precisely the ones that are produced by the Dirac-Born-Infeld action governing the low-energy dynamics of the D-brane derived using the open strings formalism. It is also shown that in the classical limit, the boundary states correctly reproduce the parameters of the corresponding classical solutions. The second part of the book starts with a contribution by Y S Stanev devoted to the two
Hafizzal, Y.; Nurulhuda, A.; Izman, S.; Khadir, AZA
2017-08-01
POM-copolymer bond breaking leads to change depending with respect to processing methodology and material geometries. This paper present the oversights effect on the material integrity due to different geometries and processing methodology. Thermo-analytical methods with reference were used to examine the degradation of thermomechanical while Thermogravimetric Analysis (TGA) was used to judge the thermal stability of sample from its major decomposition temperature. Differential Scanning Calorimetry (DSC) investigation performed to identify the thermal behaviour and thermal properties of materials. The result shown that plastic gear geometries with injection molding at higher tonnage machine more stable thermally rather than resin geometries. Injection plastic gear geometries at low tonnage machine faced major decomposition temperatures at 313.61°C, 305.76 °C and 307.91 °C while higher tonnage processing method are fully decomposed at 890°C, significantly higher compared to low tonnage condition and resin geometries specimen at 398°C. Chemical composition of plastic gear geometries with injection molding at higher and lower tonnage are compare based on their moisture and Volatile Organic Compound (VOC) content, polymeric material content and the absence of filler. Results of higher moisture and Volatile Organic Compound (VOC) content are report in resin geometries (0.120%) compared to higher tonnage of injection plastic gear geometries which is 1.264%. The higher tonnage of injection plastic gear geometry are less sensitive to thermo-mechanical degradation due to polymer chain length and molecular weight of material properties such as tensile strength, flexural strength, fatigue strength and creep resistance.
Quantification of Porcine Vocal Fold Geometry.
Stevens, Kimberly A; Thomson, Scott L; Jetté, Marie E; Thibeault, Susan L
2016-07-01
The aim of this study was to quantify porcine vocal fold medial surface geometry and three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds. The medial surface geometries of five excised porcine larynges were quantified and reported. Five porcine larynges were imaged in a micro-CT scanner, frozen, and rescanned. Segmentations and three-dimensional reconstructions were used to quantify and characterize geometric features. Comparisons were made with geometry data previously obtained using canine and human vocal folds as well as geometries of selected synthetic vocal fold models. Freezing induced an overall expansion of approximately 5% in the transverse plane and comparable levels of nonuniform distortion in sagittal and coronal planes. The medial surface of the porcine vocal folds was found to compare reasonably well with other geometries, although the compared geometries exhibited a notable discrepancy with one set of published human female vocal fold geometry. Porcine vocal folds are qualitatively geometrically similar to data available for canine and human vocal folds, as well as commonly used models. Freezing of tissue in the larynx causes distortion of around 5%. The data can provide direction in estimating uncertainty due to bulk distortion of tissue caused by freezing, as well as quantitative geometric data that can be directly used in developing vocal fold models. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.
Discrete quantum geometries and their effective dimension
International Nuclear Information System (INIS)
Thuerigen, Johannes
2015-01-01
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
International Nuclear Information System (INIS)
Chuang, Wu-yen
2007-01-01
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism
Geometric Transitions, Topological Strings, and Generalized Complex Geometry
Energy Technology Data Exchange (ETDEWEB)
Chuang, Wu-yen; /SLAC /Stanford U., Phys. Dept.
2007-06-29
Mirror symmetry is one of the most beautiful symmetries in string theory. It helps us very effectively gain insights into non-perturbative worldsheet instanton effects. It was also shown that the study of mirror symmetry for Calabi-Yau flux compactification leads us to the territory of ''Non-Kaehlerity''. In this thesis we demonstrate how to construct a new class of symplectic non-Kaehler and complex non-Kaehler string theory vacua via generalized geometric transitions. The class admits a mirror pairing by construction. From a variety of sources, including super-gravity analysis and KK reduction on SU(3) structure manifolds, we conclude that string theory connects Calabi-Yau spaces to both complex non-Kaehler and symplectic non-Kaehler manifolds and the resulting manifolds lie in generalized complex geometry. We go on to study the topological twisted models on a class of generalized complex geometry, bi-Hermitian geometry, which is the most general target space for (2, 2) world-sheet theory with non-trivial H flux turned on. We show that the usual Kaehler A and B models are generalized in a natural way. Since the gauged supergravity is the low energy effective theory for the compactifications on generalized geometries, we study the fate of flux-induced isometry gauging in N = 2 IIA and heterotic strings under non-perturbative instanton effects. Interestingly, we find we have protection mechanisms preventing the corrections to the hyper moduli spaces. Besides generalized geometries, we also discuss the possibility of new NS-NS fluxes in a new doubled formalism.
DEFF Research Database (Denmark)
Koch, Christian; Bertelsen, Niels Haldor
2014-01-01
Demonstration projects are often used in the building sector to provide a basis for using new processes and/or products. The climate change agenda implies that construction is not only required to deliver value for the customer, cost reductions and efficiency but also sustainable buildings....... This paper reports on an early demonstration project, the Building of a passive house dormitory in the Central Region of Denmark in 2006-2009. The project was supposed to deliver value, lean design, prefabrication, quality in sustainability, certification according to German standards for passive houses......, and micro combined heat and power using hydrogen. Using sociological and business economic theories of innovation, the paper discusses how early movers of innovation tend to obtain only partial success when demonstrating their products and often feel obstructed by minor details. The empirical work...
Solar renovation demonstration projects
Energy Technology Data Exchange (ETDEWEB)
Bruun Joergensen, O [ed.
1998-10-01
In the framework of the IEA SHC Programme, a Task on building renovation was initiated, `Task 20, Solar Energy in Building Renovation`. In a part of the task, Subtask C `Design of Solar Renovation Projects`, different solar renovation demonstration projects were developed. The objective of Subtask C was to demonstrate the application of advanced solar renovation concepts on real buildings. This report documents 16 different solar renovation demonstration projects including the design processes of the projects. The projects include the renovation of houses, schools, laboratories, and factories. Several solar techniques were used: building integrated solar collectors, glazed balconies, ventilated solar walls, transparent insulation, second skin facades, daylight elements and photovoltaic systems. These techniques are used in several simple as well as more complex system designs. (au)
Biodenitrification demonstration test report
International Nuclear Information System (INIS)
Benear, A.K.; Murray, S.J.; Lahoda, E.J.; Leslie, J.W.; Patton, J.B.; Menako, C.R.
1987-08-01
A two-column biodenitrification (BDN) facility was constructed at the Feed Materials Production Center (FMPC) in 1985 and 1986 to test the feasibility of biological treatment for industrial nitrate-bearing waste water generated at FMPC. This demonstration facility comprises one-half of the proposed four-column production facility. A demonstration test was conducted over a four month period in 1987. The results indicate the proposed BDN production facility can process FMPC industrial wastewater in a continuous manner while maintaining an effluent that will consistently meet the proposed NPDES limits for combined nitrate nitrogen (NO 3 -N) and nitrite nitrogen (NO 2 -N). The proposed NPDES limits are 62 kg/day average and 124 kg/day maximum. These limits were proportioned to determine that the two-column demonstration facility should meet the limits of 31 kg/day average and 62 kg/day maximum
Distributed picture compilation demonstration
Alexander, Richard; Anderson, John; Leal, Jeff; Mullin, David; Nicholson, David; Watson, Graham
2004-08-01
A physical demonstration of distributed surveillance and tracking is described. The demonstration environment is an outdoor car park overlooked by a system of four rooftop cameras. The cameras extract moving objects from the scene, and these objects are tracked in a decentralized way, over a real communication network, using the information form of the standard Kalman filter. Each node therefore has timely access to the complete global picture and because there is no single point of failure in the system, it is robust. The demonstration system and its main components are described here, with an emphasis on some of the lessons we have learned as a result of applying a corpus of distributed data fusion theory and algorithms in practice. Initial results are presented and future plans to scale up the network are also outlined.
Photovoltaic demonstration projects
Energy Technology Data Exchange (ETDEWEB)
Gillett, W B; Hacker, R J; Kaut, W [eds.
1991-01-01
This book, the proceedings of the fourth PV-Contractors' Meeting organized by the Commission of the European Communities, Directorate-General for Energy, held at Brussels on 21 and 22 November 1989, provides an overview of the photovoltaic demonstration projects which have been supported in the framework of the Energy Demonstration Program since 1983. It includes reports by each of the contractors who submitted proposals in 1983, 1984, 1985 and 1986, describing progress with their projects. Summaries of the discussions held at the meeting, which included contractors whose projects were submitted in 1987, are also presented. The different technologies which are being demonstrated concern the modules, the cabling of the array, structure design, storage strategy and power conditioning. The various applications include desalination, communications, dairy farms, water pumping, and warning systems. Papers have been processed separately for inclusion on the data base.
Electric vehicle demonstration
Energy Technology Data Exchange (ETDEWEB)
Ouellet, M. [National Centre for Advanced Transportation, Saint-Jerome, PQ (Canada)
2010-07-01
The desirable characteristics of Canadian projects that demonstrate vehicle use in real-world operation and the appropriate mechanism to collect and disseminate the monitoring data were discussed in this presentation. The scope of the project was on passenger cars and light duty trucks operating in plug-in electric vehicle (PHEV) or battery electric vehicle modes. The presentation also discussed the funding, stakeholders involved, Canadian travel pattern analysis, regulatory framework, current and recent electric vehicle demonstration projects, and project guidelines. It was concluded that some demonstration project activities may have been duplicated as communication between the proponents was insufficient. It was recommended that data monitoring using automatic data logging with minimum reliance on logbooks and other user entry should be emphasized. figs.
A Gyrovector Space Approach to Hyperbolic Geometry
Ungar, Abraham
2009-01-01
The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. T
SABRINA, Geometry Plot Program for MCNP
International Nuclear Information System (INIS)
SEIDL, Marcus
2003-01-01
1 - Description of program or function: SABRINA is an interactive, three-dimensional, geometry-modeling code system, primarily for use with CCC-200/MCNP. SABRINA's capabilities include creation, visualization, and verification of three-dimensional geometries specified by either surface- or body-base combinatorial geometry; display of particle tracks are calculated by MCNP; and volume fraction generation. 2 - Method of solution: Rendering is performed by ray tracing or an edge and intersection algorithm. Volume fraction calculations are made by ray tracing. 3 - Restrictions on the complexity of the problem: A graphics display with X Window capability is required
Information geometry near randomness and near independence
Arwini, Khadiga A
2008-01-01
This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.
Introduction into integral geometry and stereology
DEFF Research Database (Denmark)
Kiderlen, Markus
Statistics and Random Fields and is a self-containing introduction into integral geometry and its applications in stereology. The most important integral geometric tools for stereological applications are kinematic formulas and results of Blaschke-Petkantschin type. Therefore, Crofton's formula......This text is the extended version of two talks held at the Summer Academy Stochastic Geometry, Spatial Statistics and Random Fields in the Soellerhaus, Germany, in September 2009. It forms (with slight modifications) a chapter of the Springer lecture notes Lectures on Stochastic Geometry, Spatial...
Differential geometry and topology of curves
Animov, Yu
2001-01-01
Differential geometry is an actively developing area of modern mathematics. This volume presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n-dimensional Euclidean space. The author investigates problems for special classes of curves and gives the working method used to obtain the conditions for closed polygonal curves. The proof of the Bakel-Werner theorem in conditions of boundedness for curves with periodic curvature and torsion is also presented. This volume also highlights the contributions made by great geometers. past and present, to differential geometry and the topology of curves.
Digital and discrete geometry theory and algorithms
Chen, Li
2014-01-01
This book provides comprehensive coverage of the modern methods for geometric problems in the computing sciences. It also covers concurrent topics in data sciences including geometric processing, manifold learning, Google search, cloud data, and R-tree for wireless networks and BigData.The author investigates digital geometry and its related constructive methods in discrete geometry, offering detailed methods and algorithms. The book is divided into five sections: basic geometry; digital curves, surfaces and manifolds; discretely represented objects; geometric computation and processing; and a
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
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
Innovative technology demonstrations
International Nuclear Information System (INIS)
Anderson, D.B.; Luttrell, S.P.; Hartley, J.N.
1992-08-01
Environmental Management Operations (EMO) is conducting an Innovative Technology Demonstration Program for Tinker Air Force Base (TAFB). Several innovative technologies are being demonstrated to address specific problems associated with remediating two contaminated test sites at the base. Cone penetrometer testing (CPT) is a form of testing that can rapidly characterize a site. This technology was selected to evaluate its applicability in the tight clay soils and consolidated sandstone sediments found at TAFB. Directionally drilled horizontal wells was selected as a method that may be effective in accessing contamination beneath Building 3001 without disrupting the mission of the building, and in enhancing the extraction of contamination both in ground water and in soil. A soil gas extraction (SGE) demonstration, also known as soil vapor extraction, will evaluate the effectiveness of SGE in remediating fuels and TCE contamination contained in the tight clay soil formations surrounding the abandoned underground fuel storage vault located at the SW Tanks Site. In situ sensors have recently received much acclaim as a technology that can be effective in remediating hazardous waste sites. Sensors can be useful for determining real-time, in situ contaminant concentrations during the remediation process for performance monitoring and in providing feedback for controlling the remediation process. Following the SGE demonstration, the SGE system and SW Tanks test site will be modified to demonstrate bioremediation as an effective means of degrading the remaining contaminants in situ. The bioremediation demonstration will evaluate a bioventing process in which the naturally occurring consortium of soil bacteria will be stimulated to aerobically degrade soil contaminants, including fuel and TCE, in situ
Innovative technology demonstrations
International Nuclear Information System (INIS)
Anderson, D.B.; Hartley, J.N.; Luttrell, S.P.
1992-04-01
Currently, several innovative technologies are being demonstrated at Tinker Air Force Base (TAFB) to address specific problems associated with remediating two contaminated test sites at the base. Cone penetrometer testing (CPT) is a form of testing that can rapidly characterize a site. This technology was selected to evaluate its applicability in the tight clay soils and consolidated sandstone sediments found at TAFB. Directionally drilled horizontal wells have been successfully installed at the US Department of Energy's (DOE) Savannah River Site to test new methods of in situ remediation of soils and ground water. This emerging technology was selected as a method that may be effective in accessing contamination beneath Building 3001 without disrupting the mission of the building, and in enhancing the extraction of contamination both in ground water and in soil. A soil gas extraction (SGE) demonstration, also known as soil vapor extraction, will evaluate the effectiveness of SGE in remediating fuels and TCE contamination contained in the tight clay soil formations surrounding the abandoned underground fuel storage vault located at the SW Tanks Site. In situ sensors have recently received much acclaim as a technology that can be effective in remediating hazardous waste sites. Sensors can be useful for determining real-time, in situ contaminant concentrations during the remediation process for performance monitoring and in providing feedback for controlling the remediation process. A demonstration of two in situ sensor systems capable of providing real-time data on contamination levels will be conducted and evaluated concurrently with the SGE demonstration activities. Following the SGE demonstration, the SGE system and SW Tanks test site will be modified to demonstrate bioremediation as an effective means of degrading the remaining contaminants in situ
Hadagali, Prasannaah; Peters, James R; Balasubramanian, Sriram
2018-03-12
Personalized Finite Element (FE) models and hexahedral elements are preferred for biomechanical investigations. Feature-based multi-block methods are used to develop anatomically accurate personalized FE models with hexahedral mesh. It is tedious to manually construct multi-blocks for large number of geometries on an individual basis to develop personalized FE models. Mesh-morphing method mitigates the aforementioned tediousness in meshing personalized geometries every time, but leads to element warping and loss of geometrical data. Such issues increase in magnitude when normative spine FE model is morphed to scoliosis-affected spinal geometry. The only way to bypass the issue of hex-mesh distortion or loss of geometry as a result of morphing is to rely on manually constructing the multi-blocks for scoliosis-affected spine geometry of each individual, which is time intensive. A method to semi-automate the construction of multi-blocks on the geometry of scoliosis vertebrae from the existing multi-blocks of normative vertebrae is demonstrated in this paper. High-quality hexahedral elements were generated on the scoliosis vertebrae from the morphed multi-blocks of normative vertebrae. Time taken was 3 months to construct the multi-blocks for normative spine and less than a day for scoliosis. Efforts taken to construct multi-blocks on personalized scoliosis spinal geometries are significantly reduced by morphing existing multi-blocks.
Gigashot Optical Laser Demonstrator
Energy Technology Data Exchange (ETDEWEB)
Deri, R. J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-13
The Gigashot Optical Laser Demonstrator (GOLD) project has demonstrated a novel optical amplifier for high energy pulsed lasers operating at high repetition rates. The amplifier stores enough pump energy to support >10 J of laser output, and employs conduction cooling for thermal management to avoid the need for expensive and bulky high-pressure helium subsystems. A prototype amplifier was fabricated, pumped with diode light at 885 nm, and characterized. Experimental results show that the amplifier provides sufficient small-signal gain and sufficiently low wavefront and birefringence impairments to prove useful in laser systems, at repetition rates up to 60 Hz.
Photovoltaic demonstration projects 2
Energy Technology Data Exchange (ETDEWEB)
Gillett, W B; Hacker, R J [Halcrow (William) and Partners, Swindon (UK); Kaut, W [eds.
1989-01-01
This book, the proceedings of the third Photovoltaic Contractors' Meeting organised by the Commission of the European Communities, Directorate-General for Energy provides an overview of the photovoltaic demonstration projects which have been supported by the Energy Directorate of the Commission of the European Communities since 1983. It includes reports by each of the contractors who submitted proposals in 1983, 1984 and 1985, describing progress with their projects. The different technologies which are being demonstrated concern the modules, the cabling of the array, structure design, storage strategy and power conditioning. The various applications include powering of houses, villages, recreation centres, water desalination, communications, dairy farms, water pumping and warning systems. (author).
Energy Technology Data Exchange (ETDEWEB)
Kanematsu, Yusuke; Tachikawa, Masanori [Quantum Chemistry Division, Yokohama City University, Seto 22-2, Kanazawa-ku, Yokohama 236-0027 (Japan)
2014-11-14
Multicomponent quantum mechanical (MC-QM) calculation has been extended with ONIOM (our own N-layered integrated molecular orbital + molecular mechanics) scheme [ONIOM(MC-QM:MM)] to take account of both the nuclear quantum effect and the surrounding environment effect. The authors have demonstrated the first implementation and application of ONIOM(MC-QM:MM) method for the analysis of the geometry and the isotope shift in hydrogen-bonding center of photoactive yellow protein. ONIOM(MC-QM:MM) calculation for a model with deprotonated Arg52 reproduced the elongation of O–H bond of Glu46 observed by neutron diffraction crystallography. Among the unique isotope shifts in different conditions, the model with protonated Arg52 with solvent effect reasonably provided the best agreement with the corresponding experimental values from liquid NMR measurement. Our results implied the availability of ONIOM(MC-QM:MM) to distinguish the local environment around hydrogen bonds in a biomolecule.
Nemykin, Victor N; Hadt, Ryan G; Belosludov, Rodion V; Mizuseki, Hiroshi; Kawazoe, Yoshiyuki
2007-12-20
A time-dependent density functional theory (TDDFT) approach coupled with 14 different exchange-correlation functionals was used for the prediction of vertical excitation energies in zinc phthalocyanine (PcZn). In general, the TDDFT approach provides a more accurate description of both visible and ultraviolet regions of the UV-vis and magnetic circular dichroism (MCD) spectra of PcZn in comparison to the more popular semiempirical ZINDO/S and PM3 methods. It was found that the calculated vertical excitation energies of PcZn correlate with the amount of Hartree-Fock exchange involved in the exchange-correlation functional. The correlation was explained on the basis of the calculated difference in energy between occupied and unoccupied molecular orbitals. The influence of PcZn geometry, optimized using different exchange-correlation functionals, on the calculated vertical excitation energies in PcZn was found to be relatively small. The influence of solvents on the calculated vertical excitation energies in PcZn was considered for the first time using a polarized continuum model TDDFT (PCM-TDDFT) method and was found to be relatively small in excellent agreement with the experimental data. For all tested TDDFT and PCM-TDDFT cases, an assignment of the Q-band as an almost pure a1u (HOMO)-->eg (LUMO) transition, initially suggested by Gouterman, was confirmed. Pure exchange-correlation functionals indicate the presence of six 1Eu states in the B-band region of the UV-vis spectrum of PcZn, while hybrid exchange-correlation functionals predict only five 1Eu states for the same energy envelope. The first two symmetry-forbidden n-->pi* transitions were predicted in the Q0-2 region and in the low-energy tail of the B-band, while the first two symmetry-allowed n-->pi* transitions were found within the B-band energy envelope when pure exchange-correlation functionals were used for TDDFT calculations. The presence of a symmetry-forbidden but vibronically allowed n
Inseparable Phone Books Demonstration
Balta, Nuri; Çetin, Ali
2017-01-01
This study is aimed at first introducing a well-known discrepant event; inseparable phone books and second, turning it into an experiment for high school or middle school students. This discrepant event could be used especially to indicate how friction force can be effective in producing an unexpected result. Demonstration, discussion, explanation…
Smith, A.J.E.; Bree, R.J.P. van; Calkoen, C.J.; Dekker, R.J.; Otten, M.P.G.; Rossum, W.L. van
2001-01-01
PHARUS is a polarimetric phased array C-band Synthetic Aperture Radar (SAR), designed and built for airborne use. Advanced SAR (ASAR) data in image and alternating polarization mode have been simulated with PHARUS to demonstrate the use of Envisat for a number of typical SAR applications that are
Holko, David A.
1982-01-01
Presents a complete computer program demonstrating the relationship between volume/pressure for Boyle's Law, volume/temperature for Charles' Law, and volume/moles of gas for Avagadro's Law. The programing reinforces students' application of gas laws and equates a simulated moving piston to theoretical values derived using the ideal gas law.…
Brecher, Kenneth
2006-12-01
Project LITE (Light Inquiry Through Experiments) is a materials, software, and curriculum development project. It focuses on light, optics, color and visual perception. According to two recent surveys of college astronomy faculty members, these are among the topics most often included in the large introductory astronomy courses. The project has aimed largely at the design and implementation of hands-on experiences for students. However, it has also included the development of lecture demonstrations that employ novel light sources and materials. In this presentation, we will show some of our new lecture demonstrations concerning geometrical and physical optics, fluorescence, phosphorescence and polarization. We have developed over 200 Flash and Java applets that can be used either by teachers in lecture settings or by students at home. They are all posted on the web at http://lite.bu.edu. For either purpose they can be downloaded directly to the user's computer or run off line. In lecture demonstrations, some of these applets can be used to control the light emitted by video projectors to produce physical effects in materials (e.g. fluorescence). Other applets can be used, for example, to demonstrate that the human percept of color does not have a simple relationship with the physical frequency of the stimulating source of light. Project LITE is supported by Grant #DUE-0125992 from the NSF Division of Undergraduate Education.
A Magnetic Circuit Demonstration.
Vanderkooy, John; Lowe, June
1995-01-01
Presents a demonstration designed to illustrate Faraday's, Ampere's, and Lenz's laws and to reinforce the concepts through the analysis of a two-loop magnetic circuit. Can be made dramatic and challenging for sophisticated students but is suitable for an introductory course in electricity and magnetism. (JRH)
Torsional Newton–Cartan geometry from Galilean gauge theory
International Nuclear Information System (INIS)
Banerjee, Rabin; Mukherjee, Pradip
2016-01-01
Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton–Cartan (NC) geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphism (Son and Wingate 2006 Ann. Phys. 321 197–224; Banerjee et al 2015 Phys. Rev. D 91 084021) is focussed from a new angle. The expression of the torsionful connection is worked out, which is in complete parallel with the relativistic theory. Also, smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the NC spacetime is provided where the first-order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression. (paper)
Introduction to Louis Michel's lattice geometry through group action
Zhilinskii, Boris
2015-01-01
Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Different basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative ...
Towards linearization of atmospheric radiative transfer in spherical geometry
International Nuclear Information System (INIS)
Walter, Holger H.; Landgraf, Jochen
2005-01-01
We present a general approach for the linearization of radiative transfer in a spherical planetary atmosphere. The approach is based on the forward-adjoint perturbation theory. In the first part we develop the theoretical background for a linearization of radiative transfer in spherical geometry. Using an operator formulation of radiative transfer allows one to derive the linearization principles in a universally valid notation. The application of the derived principles is demonstrated for a radiative transfer problem in simplified spherical geometry in the second part of this paper. Here, we calculate the derivatives of the radiance at the top of the atmosphere with respect to the absorption properties of a trace gas species in the case of a nadir-viewing satellite instrument
An immersed boundary method for modeling a dirty geometry data
Onishi, Keiji; Tsubokura, Makoto
2017-11-01
We present a robust, fast, and low preparation cost immersed boundary method (IBM) for simulating an incompressible high Re flow around highly complex geometries. The method is achieved by the dispersion of the momentum by the axial linear projection and the approximate domain assumption satisfying the mass conservation around the wall including cells. This methodology has been verified against an analytical theory and wind tunnel experiment data. Next, we simulate the problem of flow around a rotating object and demonstrate the ability of this methodology to the moving geometry problem. This methodology provides the possibility as a method for obtaining a quick solution at a next large scale supercomputer. This research was supported by MEXT as ``Priority Issue on Post-K computer'' (Development of innovative design and production processes) and used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science.
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
Energy Technology Data Exchange (ETDEWEB)
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z. [Institute of Applied Physics and Computational Mathematics, Beijing, 100094 (China)
2013-07-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
Combinatorial geometry domain decomposition strategies for Monte Carlo simulations
International Nuclear Information System (INIS)
Li, G.; Zhang, B.; Deng, L.; Mo, Z.; Liu, Z.; Shangguan, D.; Ma, Y.; Li, S.; Hu, Z.
2013-01-01
Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)
Interoperable mesh and geometry tools for advanced petascale simulations
International Nuclear Information System (INIS)
Diachin, L; Bauer, A; Fix, B; Kraftcheck, J; Jansen, K; Luo, X; Miller, M; Ollivier-Gooch, C; Shephard, M S; Tautges, T; Trease, H
2007-01-01
SciDAC applications have a demonstrated need for advanced software tools to manage the complexities associated with sophisticated geometry, mesh, and field manipulation tasks, particularly as computer architectures move toward the petascale. The Center for Interoperable Technologies for Advanced Petascale Simulations (ITAPS) will deliver interoperable and interchangeable mesh, geometry, and field manipulation services that are of direct use to SciDAC applications. The premise of our technology development goal is to provide such services as libraries that can be used with minimal intrusion into application codes. To develop these technologies, we focus on defining a common data model and data-structure neutral interfaces that unify a number of different services such as mesh generation and improvement, front tracking, adaptive mesh refinement, shape optimization, and solution transfer operations. We highlight the use of several ITAPS services in SciDAC applications
Polynomials in finite geometries and combinatorics
Blokhuis, A.; Walker, K.
1993-01-01
It is illustrated how elementary properties of polynomials can be used to attack extremal problems in finite and euclidean geometry, and in combinatorics. Also a new result, related to the problem of neighbourly cylinders is presented.
Algebra, Geometry and Mathematical Physics Conference
Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander
2014-01-01
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
Attitudes of High School Students towards Geometry
Directory of Open Access Journals (Sweden)
Esat Avcı
2014-12-01
Full Text Available In this research, attitudes of high school students towards geometry were investigated in terms of gender, grade, types of the field and school. Population of research includes students who were studying at high school in five distincs of Mersin in 2013-2014 academical year. Sample of research includes 935 students from twelve high schools. Attitude scale which was developed by Su-Özenir (2008 was used for data collection. For data analysis, mean, standart deviation, t test and ANOVA were used. A meaningful difference between students’ attitudes towards geometry and variance of gender and grade level wasn’t observed, on the other hand a meaningful difference according to field and school type is observed.Key Words: Attitudes towards geometry, high school geometry lesson, attitude scale
Geometry, structure and randomness in combinatorics
Nešetřil, Jaroslav; Pellegrini, Marco
2014-01-01
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.
The elements of non-Euclidean geometry
Sommerville, D MY
2012-01-01
Renowned for its lucid yet meticulous exposition, this classic allows students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to more advanced topics. 1914 edition. Includes 133 figures.
The local index formula in noncommutative geometry
International Nuclear Information System (INIS)
Higson, N.
2003-01-01
These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas
Quantum geometry of bosonic strings - revisited
International Nuclear Information System (INIS)
Botelho, Luiz C.L.; Botelho, Raimundo C.L.; Universidade Federal Rural do Rio de Janeiro, RJ
1999-07-01
We review the original paper by A.M. Polyakov (Quantum Geometry of Bosonic Strings) with corrections and improvements the concepts exposed there and following as closely as possible to the original A.M. Polyakov's paper. (author)
Energy Technology Data Exchange (ETDEWEB)
Bejarano, Cecilia; Guzman, Maria Jose [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2015-02-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
10th China-Japan Geometry Conference
Miyaoka, Reiko; Tang, Zizhou; Zhang, Weiping
2016-01-01
Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists. The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, sympl...
An experimental study of passive regenerator geometries
DEFF Research Database (Denmark)
Engelbrecht, Kurt; Nielsen, Kaspar Kirstein; Pryds, Nini
2011-01-01
Active magnetic regenerative (AMR) systems are being investigated because they represent a potentially attractive alternative to vapor compression technology. The performance of these systems is dependent on the heat transfer and pressure drop performance of the regenerator geometry. Therefore th...
The geometry of René Descartes
Descartes, René
1954-01-01
The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." - John Stuart Mill.
VIII International Meeting on Lorentzian Geometry
Flores, José; Palomo, Francisco; GeLoMa 2016; Lorentzian geometry and related topics
2017-01-01
This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathem...
Homological mirror symmetry and tropical geometry
Catanese, Fabrizio; Kontsevich, Maxim; Pantev, Tony; Soibelman, Yan; Zharkov, Ilia
2014-01-01
The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory, and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Ge...
International Nuclear Information System (INIS)
Bejarano, Cecilia; Guzman, Maria Jose; Ferraro, Rafael
2015-01-01
Null tetrads are shown to be a valuable tool in teleparallel theories of modified gravity. We use them to prove that Kerr geometry remains a solution for a wide family of f(T) theories of gravity. (orig.)
Geometry modeling for SAM-CE Monte Carlo calculations
International Nuclear Information System (INIS)
Steinberg, H.A.; Troubetzkoy, E.S.
1980-01-01
Three geometry packages have been developed and incorporated into SAM-CE, for representing in three dimensions the transport medium. These are combinatorial geometry - a general (non-lattice) system, complex combinatorial geometry - a very general system with lattice capability, and special reactor geometry - a special purpose system for light water reactor geometries. Their different attributes are described
Geometry and quantization of moduli spaces
Andersen, Jørgen; Riera, Ignasi
2016-01-01
This volume is based on four advanced courses held at the Centre de Recerca Matemàtica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY
Enrique Gonzalo Reyes Garcia
2004-01-01
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...
Geometry and topology of wild translation surfaces
Randecker, Anja
2016-01-01
A translation surface is a two-dimensional manifold, equipped with a translation structure. It can be obtained by considering Euclidean polygons and identifying their edges via translations. The vertices of the polygons form singularities if the translation structure can not be extended to them. We study translation surfaces with wild singularities, regarding the topology (genus and space of ends), the geometry (behavior of the singularities), and how the topology and the geometry are related.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Perspectives in Analysis, Geometry, and Topology
Itenberg, I V; Passare, Mikael
2012-01-01
The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry
International Nuclear Information System (INIS)
Hartong, Jelle; Obers, Niels A.
2015-01-01
Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry
Energy Technology Data Exchange (ETDEWEB)
Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes, Université Libre de Bruxelles,C.P. 231, 1050 Brussels (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2015-07-29
Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1
A SPECT reconstruction method for extending parallel to non-parallel geometries
International Nuclear Information System (INIS)
Wen Junhai; Liang Zhengrong
2010-01-01
Due to its simplicity, parallel-beam geometry is usually assumed for the development of image reconstruction algorithms. The established reconstruction methodologies are then extended to fan-beam, cone-beam and other non-parallel geometries for practical application. This situation occurs for quantitative SPECT (single photon emission computed tomography) imaging in inverting the attenuated Radon transform. Novikov reported an explicit parallel-beam formula for the inversion of the attenuated Radon transform in 2000. Thereafter, a formula for fan-beam geometry was reported by Bukhgeim and Kazantsev (2002 Preprint N. 99 Sobolev Institute of Mathematics). At the same time, we presented a formula for varying focal-length fan-beam geometry. Sometimes, the reconstruction formula is so implicit that we cannot obtain the explicit reconstruction formula in the non-parallel geometries. In this work, we propose a unified reconstruction framework for extending parallel-beam geometry to any non-parallel geometry using ray-driven techniques. Studies by computer simulations demonstrated the accuracy of the presented unified reconstruction framework for extending parallel-beam to non-parallel geometries in inverting the attenuated Radon transform.
Thermodynamic Geometry and Hawking Radiation
Bellucci, S
2010-01-01
This work explores the role of thermodynamic fluctuations in the two parameter Hawking radiating black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation frequency of the black holes. In the due course of the Hawking radiations, we find that the intrinsic geometric description exhibits an intriguing set of exact pair correction functions and global correlation lengths. We investigate the nature of the constant amplitude radiation and find that it's not stable under fluctuations of the mass and frequency. Subsequently, the consideration of the York model decreasing amplitude radiation demonstrates that thermodynamic fluctuations are globally stable in the small frequency region. In connection with quantum gravity refinements, we take an account of the logarithmic correction into the constant amplitude and York amplitude over the Hawking radiation. In both considerations, we notice that the nature of the possible parametric fluctuations may precisely be ascertained w...
Remote monitoring demonstration
International Nuclear Information System (INIS)
Caskey, Susan; Olsen, John
2006-01-01
The recently upgraded remote monitoring system at the Joyo Experimental Reactor uses a DCM-14 camera module and GEMINI software. The final data is compatible both with the IAEA-approved GARS review software and the ALIS software that was used for this demonstration. Features of the remote monitoring upgrade emphasized compatibility with IAEA practice. This presentation gives particular attention to the selection process for meeting network security considerations at the O'arai site. The Joyo system is different from the NNCA's ACPF system, in that it emphasizes use of IAEA standard camera technology and data acquisition and transmission software. In the demonstration itself, a temporary virtual private network (VPN) between the meeting room and the server at Sandia in Albuquerque allowed attendees to observe data stored from routine transmissions from the Joyo Fresh Fuel Storage to Sandia. Image files from a fuel movement earlier in the month showed Joyo workers and IAEA inspectors carrying out a transfer. (author)
Commercial incineration demonstration
International Nuclear Information System (INIS)
Borduin, L.C.; Neuls, A.S.
1981-01-01
Low-level radioactive wastes (LLW) generated by nuclear utilities presently are shipped to commercial burial grounds for disposal. Substantially increasing shipping and disposal charges have sparked renewed industry interest in incineration and other advanced volume reduction techniques as potential cost-saving measures. Repeated inquiries from industry sources regarding LLW applicability of the Los Alamos controlled-air incineration (CAI) design led DOE to initiate this commercial demonstration program in FY-1980. The selected program approach to achieving CAI demonstration at a utility site is a DOE sponsored joint effort involving Los Alamos, a nuclear utility, and a liaison subcontractor. Required development tasks and responsibilities of the particpants are described. Target date for project completion is the end of FY-1985
Photovoltaic demonstration projects
Energy Technology Data Exchange (ETDEWEB)
Kaut, W [Commission of the European Communities, Brussels (Belgium); Gillett, W B; Hacker, R J [Halcrow Gilbert Associates Ltd., Swindon (GB)
1992-12-31
This publication, comprising the proceedings of the fifth contractor`s meeting organized by the Commission of the European Communities, Directorate-General for Energy, provides an overview of the photovoltaic demonstration projects which have been supported in the framework of the energy demonstration programme since 1983. It includes reports by each of the contractors who submitted proposals in 1987 and 1988, describing progress within their projects. Projects accepted from earlier calls for proposals and not yet completed were reviewed by a rapporteur and are discussed in the summary section. The results of the performance monitoring of all projects and the lessons drawn from the practical experience of the projects are also presented in the summaries and conclusions. Contractors whose projects were submitted in 1989 were also present at the meeting and contributed to the reported discussions. This proceeding is divided into four sessions (General, Housing, technical presentations, other applications) and 24 papers are offered.
Energy Technology Data Exchange (ETDEWEB)
Thron, Jonathan Louis [Los Alamos National Laboratory; Mac Arthur, Duncan W [Los Alamos National Laboratory; Kondratov, Sergey [VNIIEF; Livke, Alexander [VNIIEF; Razinkov, Sergey [VNIIEF
2010-01-01
An attribute measurement system (AMS) measures a number of unclassified attributes of potentially classified material. By only displaying these unclassified results as red or green lights, the AMS protects potentially classified information while still generating confidence in the measurement result. The AVNG implementation that we describe is an AMS built by RFNC - VNIIEF in Sarov, Russia. To provide additional confidence, the AVNG was designed with two modes of operation. In the secure mode, potentially classified measurements can be made with only the simple red light/green light display. In the open mode, known unclassified material can be measured with complete display of the information collected from the radiation detectors. The AVNG demonstration, which occurred in Sarov, Russia in June 2009 for a joint US/Russian audience, included exercising both modes of AVNG operation using a number of multi-kg plutonium sources. In addition to describing the demonstration, we will show photographs and/or video taken of AVNG operation.
Antares: preliminary demonstrator results
International Nuclear Information System (INIS)
Kouchner, A.
2000-05-01
The ANTARES collaboration is building an undersea neutrino telescope off Toulon (Mediterranean sea) with effective area ∼ 0.1 km 2 . An extensive study of the site properties has been achieved together with software analysis in order to optimize the performance of the detector. Results are summarized here. An instrumented line, linked to shore for first time via an electro-optical cable, has been immersed late 1999. The preliminary results of this demonstrator line are reported. (author)
Energy Technology Data Exchange (ETDEWEB)
Aguayo, Estanislao; Fast, James E.; Hoppe, Eric W.; Keillor, Martin E.; Kephart, Jeremy D.; Kouzes, Richard T.; LaFerriere, Brian D.; Merriman, Jason H.; Orrell, John L.; Overman, Nicole R.; Avignone, Frank T.; Back, Henning O.; Combs, Dustin C.; Leviner, L.; Young, A.; Barabash, Alexander S.; Konovalov, S.; Vanyushin, I.; Yumatov, Vladimir; Bergevin, M.; Chan, Yuen-Dat; Detwiler, Jason A.; Loach, J. C.; Martin, R. D.; Poon, Alan; Prior, Gersende; Vetter, Kai; Bertrand, F.; Cooper, R. J.; Radford, D. C.; Varner, R. L.; Yu, Chang-Hong; Boswell, M.; Elliott, S.; Gehman, Victor M.; Hime, Andrew; Kidd, M. F.; LaRoque, B. H.; Rielage, Keith; Ronquest, M. C.; Steele, David; Brudanin, V.; Egorov, Viatcheslav; Gusey, K.; Kochetov, Oleg; Shirchenko, M.; Timkin, V.; Yakushev, E.; Busch, Matthew; Esterline, James H.; Tornow, Werner; Christofferson, Cabot-Ann; Horton, Mark; Howard, S.; Sobolev, V.; Collar, J. I.; Fields, N.; Creswick, R.; Doe, Peter J.; Johnson, R. A.; Knecht, A.; Leon, Jonathan D.; Marino, Michael G.; Miller, M. L.; Robertson, R. G. H.; Schubert, Alexis G.; Wolfe, B. A.; Efremenko, Yuri; Ejiri, H.; Hazama, R.; Nomachi, Masaharu; Shima, T.; Finnerty, P.; Fraenkle, Florian; Giovanetti, G. K.; Green, M.; Henning, Reyco; Howe, M. A.; MacMullin, S.; Phillips, D.; Snavely, Kyle J.; Strain, J.; Vorren, Kris R.; Guiseppe, Vincente; Keller, C.; Mei, Dong-Ming; Perumpilly, Gopakumar; Thomas, K.; Zhang, C.; Hallin, A. L.; Keeter, K.; Mizouni, Leila; Wilkerson, J. F.
2011-09-03
A brief review of the history and neutrino physics of double beta decay is given. A description of the MAJORANA DEMONSTRATOR research and development program, including background reduction techniques, is presented in some detail. The application of point contact (PC) detectors to the experiment is discussed, including the effectiveness of pulse shape analysis. The predicted sensitivity of a PC detector array enriched to 86% to 76Ge is given.
IGCC technology and demonstration
Energy Technology Data Exchange (ETDEWEB)
Palonen, J [A. Ahlstrom Corporation, Karhula (Finland). Hans Ahlstrom Lab.; Lundqvist, R G [A. Ahlstrom Corporation, Helsinki (Finland); Staahl, K [Sydkraft AB, Malmoe (Sweden)
1997-12-31
Future energy production will be performed by advanced technologies that are more efficient, more environmentally friendly and less expensive than current technologies. Integrated gasification combined cycle (IGCC) power plants have been proposed as one of these systems. Utilising biofuels in future energy production will also be emphasised since this lowers substantially carbon dioxide emissions into the atmosphere due to the fact that biomass is a renewable form of energy. Combining advanced technology and biomass utilisation is for this reason something that should and will be encouraged. A. Ahlstrom Corporation of Finland and Sydkraft AB of Sweden have as one part of company strategies adopted this approach for the future. The companies have joined their resources in developing a biomass-based IGCC system with the gasification part based on pressurised circulating fluidized-bed technology. With this kind of technology electrical efficiency can be substantially increased compared to conventional power plants. As a first concrete step, a decision has been made to build a demonstration plant. This plant, located in Vaernamo, Sweden, has already been built and is now in commissioning and demonstration stage. The system comprises a fuel drying plant, a pressurised CFB gasifier with gas cooling and cleaning, a gas turbine, a waste heat recovery unit and a steam turbine. The plant is the first in the world where the integration of a pressurised gasifier with a gas turbine will be realised utilising a low calorific gas produced from biomass. The capacity of the Vaernamo plant is 6 MW of electricity and 9 MW of district heating. Technology development is in progress for design of plants of sizes from 20 to 120 MWe. The paper describes the Bioflow IGCC system, the Vaernamo demonstration plant and experiences from the commissioning and demonstration stages. (orig.)
IGCC technology and demonstration
Energy Technology Data Exchange (ETDEWEB)
Palonen, J. [A. Ahlstrom Corporation, Karhula (Finland). Hans Ahlstrom Lab.; Lundqvist, R.G. [A. Ahlstrom Corporation, Helsinki (Finland); Staahl, K. [Sydkraft AB, Malmoe (Sweden)
1996-12-31
Future energy production will be performed by advanced technologies that are more efficient, more environmentally friendly and less expensive than current technologies. Integrated gasification combined cycle (IGCC) power plants have been proposed as one of these systems. Utilising biofuels in future energy production will also be emphasised since this lowers substantially carbon dioxide emissions into the atmosphere due to the fact that biomass is a renewable form of energy. Combining advanced technology and biomass utilisation is for this reason something that should and will be encouraged. A. Ahlstrom Corporation of Finland and Sydkraft AB of Sweden have as one part of company strategies adopted this approach for the future. The companies have joined their resources in developing a biomass-based IGCC system with the gasification part based on pressurised circulating fluidized-bed technology. With this kind of technology electrical efficiency can be substantially increased compared to conventional power plants. As a first concrete step, a decision has been made to build a demonstration plant. This plant, located in Vaernamo, Sweden, has already been built and is now in commissioning and demonstration stage. The system comprises a fuel drying plant, a pressurised CFB gasifier with gas cooling and cleaning, a gas turbine, a waste heat recovery unit and a steam turbine. The plant is the first in the world where the integration of a pressurised gasifier with a gas turbine will be realised utilising a low calorific gas produced from biomass. The capacity of the Vaernamo plant is 6 MW of electricity and 9 MW of district heating. Technology development is in progress for design of plants of sizes from 20 to 120 MWe. The paper describes the Bioflow IGCC system, the Vaernamo demonstration plant and experiences from the commissioning and demonstration stages. (orig.)
Lunar Water Resource Demonstration
Muscatello, Anthony C.
2008-01-01
In cooperation with the Canadian Space Agency, the Northern Centre for Advanced Technology, Inc., the Carnegie-Mellon University, JPL, and NEPTEC, NASA has undertaken the In-Situ Resource Utilization (ISRU) project called RESOLVE. This project is a ground demonstration of a system that would be sent to explore permanently shadowed polar lunar craters, drill into the regolith, determine what volatiles are present, and quantify them in addition to recovering oxygen by hydrogen reduction. The Lunar Prospector has determined these craters contain enhanced hydrogen concentrations averaging about 0.1%. If the hydrogen is in the form of water, the water concentration would be around 1%, which would translate into billions of tons of water on the Moon, a tremendous resource. The Lunar Water Resource Demonstration (LWRD) is a part of RESOLVE designed to capture lunar water and hydrogen and quantify them as a backup to gas chromatography analysis. This presentation will briefly review the design of LWRD and some of the results of testing the subsystem. RESOLVE is to be integrated with the Scarab rover from CMIJ and the whole system demonstrated on Mauna Kea on Hawaii in November 2008. The implications of lunar water for Mars exploration are two-fold: 1) RESOLVE and LWRD could be used in a similar fashion on Mars to locate and quantify water resources, and 2) electrolysis of lunar water could provide large amounts of liquid oxygen in LEO, leading to lower costs for travel to Mars, in addition to being very useful at lunar outposts.
Waste and Disposal: Demonstration
International Nuclear Information System (INIS)
Neerdael, B.; Buyens, M.; De Bruyn, D.; Volckaert, G.
2002-01-01
Within the Belgian R and D programme on geological disposal, demonstration experiments have become increasingly important. In this contribution to the scientific report 2001, an overview is given of SCK-CEN's activities and achievements in the field of large-scale demonstration experiments. In 2001, main emphasis was on the PRACLAY project, which is a large-scale experiment to demonstrate the construction and the operation of a gallery for the disposal of HLW in a clay formation. The PRACLAY experiment will contribute to enhance understanding of water flow and mass transport in dense clay-based materials as well as to improve the design of the reference disposal concept. In the context of PRACLAY, a surface experiment (OPHELIE) has been developed to prepare and to complement PRACLAY-related experimental work in the HADES Underground Research Laboratory. In 2001, efforts were focussed on the operation of the OPHELIE mock-up. SCK-CEN also contributed to the SELFRAC roject which studies the self-healing of fractures in a clay formation
Physics- and engineering knowledge-based geometry repair system for robust parametric CAD geometries
Li, Dong
2012-01-01
In modern multi-objective design optimisation, an effective geometry engine is becoming an essential tool and its performance has a significant impact on the entire process. Building a parametric geometry requires difficult compromises between the conflicting goals of robustness and flexibility. The work presents a solution for improving the robustness of parametric geometry models by capturing and modelling relative engineering knowledge into a surrogate model, and deploying it automatically...