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)
Siddharth Gautam; S Mitra; R Mukhopadhyay
2008-10-01
Molecular dynamics in restricted geometries is known to exhibit anomalous behaviour. Diffusion, translational or rotational, of molecules is altered significantly on confinement in restricted geometries. Quasielastic neutron scattering (QENS) offers a unique possibility of studying molecular motion in such systems. Both time scales involved in the motion and the geometry of motion can be studied using QENS. Molecular dynamics (MD) simulation not only provides insight into the details of the different types of motion possible but also does not suffer limitations of the experimental set-up. Here we report the effect of confinement on molecular dynamics in various restricted geometries as studied by QENS and MD simulations: An example where the QENS technique provided direct evidence of phase transition associated with change in the dynamical behaviour of the molecules is also discussed.
An Optical Demonstration of Fractal Geometry
Scannel, Billy; Taylor, Richard
2012-01-01
We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting images are modeled by ray tracing procedures and both sets of images undergo fractal analysis. We offer this as a novel demonstration of fractal geometry, utilizing the aesthetic appeal of these images to motivate an intuitive understanding of the resulting scaling plots and associated fractal dimensions.
Imaging molecular geometry with electron momentum spectroscopy
Wang, Enliang; Shan, Xu; Tian, Qiguo; Yang, Jing; Gong, Maomao; Tang, Yaguo; Niu, Shanshan; Chen, Xiangjun
2016-12-01
Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF4 and O-O distance in CO2 with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.
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
Energy Technology Data Exchange (ETDEWEB)
Ulman, Kanchan [Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064 (India); Narasimhan, Shobhana [Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064 (India); Sheikh Saqr Laboratory, ICMS, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064 (India); Delin, Anna [Department of Materials and Nanophysics, School of Information and Communication Technology, Electrum 229, Royal Institute of Technology (KTH), SE-16440 Kista (Sweden); Department of Physics and Astronomy, Uppsala University, Box 516, SE-75120 Uppsala (Sweden); SeRC (Swedish e-Science Research Center), KTH, SE-10044 Stockholm (Sweden)
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%.
Identification of the Molecule-Metal Bonding Geometries of Molecular Nanowires
Demir, Firuz
2011-01-01
Molecular nanowires in which a single molecule bonds chemically to two metal electrodes and forms a stable electrically conducting bridge between them have been studied intensively for more than a decade. However the experimental determination of the bonding geometry between the molecule and electrodes has remained elusive. Here we demonstrate by means of ab initio calculations that inelastic tunneling spectroscopy (IETS) can determine these geometries. We identify the bonding geometries at the gold-sulfur interfaces of propanedithiolate molecules bridging gold electrodes that give rise to the specific IETS signatures that were observed in recent experiments.
Mathematical aspects of molecular replacement. II. Geometry of motion spaces.
Chirikjian, Gregory S; Yan, Yan
2012-03-01
Molecular replacement (MR) is a well established computational method for phasing in macromolecular crystallography. In MR searches, spaces of motions are explored for determining the appropriate placement of rigid models of macromolecules in crystallographic asymmetric units. In the first paper of this series, it was shown that this space of motions, when endowed with an appropriate composition operator, forms an algebraic structure called a quasigroup. In this second paper, the geometric properties of these MR search spaces are explored and analyzed. This analysis includes the local differential geometry, global geometry and symmetry properties of these spaces.
Kinetics of binding and geometry of cells on molecular biochips
Energy Technology Data Exchange (ETDEWEB)
Chechetkin, V.R. [Theoretical Department of Division for Perspective Investigations, Troitsk Institute of Innovation and Thermonuclear Investigations (TRINITI), Troitsk 142190, Moscow Region (Russian Federation)]. E-mail: chechet@biochip.ru
2007-07-02
We examine how the shape of cells and the geometry of experiment affect the reaction-diffusion kinetics at the binding between target and probe molecules on molecular biochips. In particular, we compare the binding kinetics for the probes immobilized on surface of the hemispherical and flat circular cells, the limit of thin slab of analyte solution over probe cell as well as hemispherical gel pads and cells printed in gel slab over a substrate. It is shown that hemispherical geometry provides significantly faster binding kinetics and ensures more spatially homogeneous distribution of local (from a pixel) signals over a cell in the transient regime. The advantage of using thin slabs with small volume of analyte solution may be hampered by the much longer binding kinetics needing the auxiliary mixing devices. Our analysis proves that the shape of cells and the geometry of experiment should be included to the list of essential factors at biochip designing.
MOLECULAR THERMODYNAMICS OF MICELLIZATION: MICELLE SIZE DISTRIBUTIONS AND GEOMETRY TRANSITIONS
Directory of Open Access Journals (Sweden)
M. S. Santos
Full Text Available Abstract Surfactants are amphiphilic molecules that can spontaneously self-assemble in solution, forming structures known as micelles. Variations in temperature, pH, and electrolyte concentration imply changes in the interactions between surfactants and micelle stability conditions, including micelle size distribution and micelle shape. Here, molecular thermodynamics is used to describe and predict conditions of micelle formation in surfactant solutions by directly calculating the minimum Gibbs free energy of the system, corresponding to the most stable condition of the surfactant solution. In order to find it, the proposed methodology takes into account the micelle size distribution and two possible geometries (spherical and spherocylindrical. We propose a numerical optimization methodology where the minimum free energy can be reached faster and in a more reliable way. The proposed models predict the critical micelle concentration well when compared to experimental data, and also predict the effect of salt on micelle geometry transitions.
A molecular dynamics study of freezing in a confined geometry
Ma, Wen-Jong; Banavar, Jayanth R.; Koplik, Joel
1992-01-01
The dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls is studied by computer simulation. The time development of ordering is quantified and a novel freezing mechanism is observed. The liquid forms layers and subsequent in-plane ordering within a layer is accompanied by a sharpening of the layer in the transverse direction. The effects of channel size, the methods of quench, the liquid-wall interaction and the roughness of walls on the freezing mechanism are elucidated. Comparison with recent experiments on freezing in confined geometries is presented.
A molecular dynamics study of freezing in a confined geometry
Ma, Wen-Jong; Banavar, Jayanth R.; Koplik, Joel
1992-01-01
The dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls is studied by computer simulation. The time development of ordering is quantified and a novel freezing mechanism is observed. The liquid forms layers and subsequent in-plane ordering within a layer is accompanied by a sharpening of the layer in the transverse direction. The effects of channel size, the methods of quench, the liquid-wall interaction and the roughness of walls on the freezing mechanism are elucidated. Comparison with recent experiments on freezing in confined geometries is presented.
The Complete Molecular Geometry of Salicyl Aldehyde from Rotational Spectroscopy
Dorosh, O.; Bialkowska-Jaworska, E.; Kisiel, Z.; Pszczolkowski, L.; Kanska, M.; Krygowski, T. M.; Maeder, H.
2013-06-01
Salicyl aldehyde is a well known planar molecule containing an internal hydrogen bond. In preparing the publication of our previous report of the study of its rotational spectrum we have taken the opportunity to update the structure determination of this molecule to the complete r_e^{SE} geometry. The molecule contains 15 atoms and we have used supersonic expansion FTMW spectroscopy to obtain rotational constants for a total 26 different isotopic species, including all singly substitued species relative to the parent molecule. The ^{13}C and ^{18}O substitutions were measured in natural abundance, while deuterium substitutions were carried out synthetically. The r_e^{SE} determination requires the calculation of vibration-rotation changes in rotational constants from an ab initio anharmonic force field, which necessitates some compromises in the level of calculation for a molecule of the size of salicyl aldehyde. For this reason we studied the five lowest vibrationally excited states, by using the combination of room-temperature mm-wave spectroscopy and waveguide Fourier transform cm-wave spectroscopy. The experimental excited state rotational constants were then used to calibrate the anharmonic force field calculation. The resulting r_e^{SE} geometry is compared with other types of geometry determination possible from this data, with emphasis on the effect of the near zero principal coordinate of the important C_2 atom. Z.Kisiel et al., 61^{st} OSU Symposium on Molecular Spectroscopy, The Ohio State University, Ohio 2006, RI-12.
A Demonstration of Underwater Bubble Capture by the Fundamental Acoustic Mode in Spherical Geometry
Directory of Open Access Journals (Sweden)
Umaporn KONTHARAK
2008-01-01
Full Text Available Nowadays, scientific demonstrations have become a crucial part of scientific learning. Acoustic waves are normally demonstrated in air via Kundt’s tube, but a physical demonstration for underwater acoustic waves is still lacking. In this paper, we address one of the aspects by demonstrating a way to acoustically-trap gas bubbles in a spherical, water-filled flask resonating at its first fundamental mode. The theory of acoustic waves in a spherical geometry, particularly the fundamental mode, is reviewed. The full description of the experimental setup is expressed both acoustically and electronically. By using this method, we show that a gas bubble can be stabilized in the middle of a flask at an acoustic frequency of 21.16 kHz, the acoustic fundamental frequency of the flask.
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
Designing an Educative Curriculum Unit for Teaching Molecular Geometry in High School Chemistry
Makarious, Nader N.
2017-01-01
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…
Suzuki, Hiroshi
1967-01-01
Electronic Absorption Spectra and Geometry of Organic Molecules: An Application of Molecular Orbital Theory focuses on electronic absorption spectra of organic compounds and molecules. The book begins with the discussions on molecular spectra, electronic absorption spectra of organic compounds, and practical measures of absorption intensity. The text also focuses on molecular orbital theory and group theory. Molecular state functions; fundamental postulates of quantum theory; representation of symmetry groups; and symmetry operations and symmetry groups are described. The book also dis
Transient Changes in Molecular Geometries and How to Model Them
DEFF Research Database (Denmark)
Dohn, Asmus Ougaard
changes in molecular structure, vibrations and solvation. In this thesis, we employ our recently developed Quantum-/Molecular -Mechanical Direct Dynamics method to do simulations of transition metal complexes in solution, to uncover their energy dissipation channels, and how they are affected...... quantum mechanic descriptions, to ascertain the accuracy of the quantum model in the Direct Dynamics simulations. We then test - and improve - the framework for calculating the experimental X-ray Diffuse Scattering Difference signal from (any kind of) Molecular Dynamics (MD) simulations. Comparisons......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...
DEFF Research Database (Denmark)
Zhang, Fei; Brandt, Rasmus Guldbæk; Gu, Zhuowei
2015-01-01
, Ph(DPP)2 and PhDMe(DPP)2 with similar chemical components but different molecular geometries. Due to its more twisted molecular conformation, PhDMe(DPP)2 shows more blue-shifted absorption bands, higher electron mobility, and better miscibility with the polymer donor poly(3-hexylthiophene) (P3HT...
Geant4 Applications for Modeling Molecular Transport in Complex Vacuum Geometries
Singal, J; Schindler, R
2013-01-01
This letter discusses a novel use of the Geant4 simulation toolkit to model molecular transport in a vacuum environment, in the molecular flow regime. The Geant4 toolkit was originally developed by the high energy physics community to simulate the interactions of elementary particles within complex detector systems. Here its capabilities are utilized to model molecular vacuum transport in geometries where other techniques are impractical. The techniques are verified with an application representing a simple vacuum geometry that has been studied previously both analytically and by basic Monte Carlo simulation. We discuss the use of an application with a very complicated geometry, that of the Large Synoptic Survey Telescope camera cryostat, to determine probabilities of transport of contaminant molecules to optical surfaces where control of contamination is crucial.
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,…
Experimental demonstration of a controllable electrostatic molecular beam splitter.
Deng, Lianzhong; Liang, Yan; Gu, Zhenxing; Hou, Shunyong; Li, Shengqiang; Xia, Yong; Yin, Jianping
2011-04-01
We experimentally demonstrate a controllable electrostatic beam splitter for guided ND3 molecules with a single Y-shaped charged wire and a homogeneous bias field generated by a charged metallic parallel-plate capacitor. We study the dependences of the splitting ratio R of the guided ND3 beam and its relative guiding efficiency η on the voltage difference between two output arms of the splitter. The influences of the molecular velocity v and the cutting position L on the splitting ratio R are investigated as well, and the guiding and splitting dynamic processes of cold molecules are simulated. Our study shows that the splitting ratio R of our splitter can be conveniently adjusted from 10% to 90% by changing ΔU from -6 kV to +6 kV, and the simulated results are consistent with our experimental ones.
Single Molecular Demonstration of Modulating Charge Inversion of DNA
Wang, Yanwei; Wang, Ruxia; Cao, Bozhi; Guo, Zilong; Yang, Guangcan
2016-12-01
Charge inversion of DNA is a counterintuitive phenomenon in which the effective charge of DNA switches its sign from negative to positive in the presence of multivalent counterions. The underlying microscopic mechanism is still controversial whether it is driven by a specific chemical affinity or electrostatic ion correlation. It is well known that DNA shows no charge inversion in normal aqueous solution of trivalent counterions though they can induce the conformational compaction of DNA. However, in the same trivalent counterion condition, we demonstrate for the first time the occurrence of DNA charge inversion by decreasing the dielectric constant of solution to make the electrophoretic mobility of DNA increase from a negative value to a positive value. In contrast, the charge inversion of DNA induced by quadrivalent counterions can be canceled out by increasing the dielectric constant of solution. The physical modulation of DNA effective charge in two ways unambiguously demonstrates that charge inversion of DNA is a predominantly electrostatic phenomenon driven by the existence of a strongly correlated liquid (SCL) of counterions at the DNA surface. This conclusion is also supported by the measurement of condensing and unraveling forces of DNA condensates by single molecular MT.
A phenomenological relationship between molecular geometry change and conformational energy change
Bodi, Andras; Bjornsson, Ragnar; Arnason, Ingvar
2010-08-01
A linear correlation is established between the change in the axial/equatorial conformational energy difference and the change in the molecular geometry transformation during conformational inversion in substituted six-membered ring systems, namely in the 1-substituted cyclohexane/silacyclohexane, cyclohexane/ N-substituted piperidine and 1-substituted silacyclohexane/ P-substituted phosphorinane compound families, and for the analogous gauche/anti conformational isomerism in 1-substituted propanes/1-silapropanes. The nuclear repulsion energy parameterizes the molecular geometry, and changes in the conformational energy between the related compound families are linearly correlated with the changes in the nuclear repulsion energy difference based on DFT (B3LYP, M06-2X), G3B3, and CBS-QB3 calculations. This correlation reproduces the sometimes remarkable contrast between the conformational behavior of analogous compounds, e.g., the lack of a general equatorial preference in silacyclohexanes.
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.
Krčo, Marko
2016-01-01
We present a geometry-independent method for determining the shapes of radial volume density profiles of astronomical objects whose geometries are unknown, based on a single column density map. Such profiles are often critical to understand the physics and chemistry of molecular cloud cores, in which star formation takes place. The method presented here does not assume any geometry for the object being studied, thus removing a significant source of bias. Instead it exploits contour self-similarity in column density maps which appears to be common in data for astronomical objects. Our method may be applied to many types of astronomical objects and observable quantities so long as they satisfy a limited set of conditions which we describe in detail. We derive the method analytically, test it numerically, and illustrate its utility using 2MASS-derived dust extinction in molecular cloud cores. While not having made an extensive comparison of different density profiles, we find that the overall radial density dist...
Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method
DEFF Research Database (Denmark)
Christensen, Anders Steen; Svendsen, Casper Steinmann; Fedorov, Dmitri G
2014-01-01
The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory...... 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...
DEFF Research Database (Denmark)
Wang, Yanwei; Peters, Günther H.J.; Hansen, Flemming Yssing
2008-01-01
We present a new framework for the description of macromolecules subject to confining geometries. The two main ingredients are a new computational method and the definition of a new molecular size parameter. The computational method, hereafter referred to the confinement analysis from bulk...... 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....
Trevisan, Cynthia S.; Rescigno, Thomas N.; McCurdy, C. William
2012-06-01
Compex Kohn variational calculations of the molecular frame photoelectron distributions (MFPADs) for 1s core ionization of CH4, NH3, and H2O are presented for ejected electron energies below 25 eV. Surprisingly, in these three cases there are energy ranges in which the photoelectron MFPADs effectively form ``images'' of the molecular geometry. Comparison with recent momentum imaging experiments on methane at the Advanced Light Source verify this effect. Simultaneous double Auger decay in these molecules can produce dissociation into three charged fragments, e.g., CH2^+ + 2 H^+, allowing the complete orientation of the molecule and therefore the measurement of 3D MFPADs that test these predictions. In other Auger decay channels the measurement of 3D MFPADs verifies axial recoil (prompt dissociation) or probes its absence in the Auger dissociation dynamics of small molecules.
Cage rattling does not correlate with the local geometry in molecular liquids
Bernini, S; Leporini, D
2016-01-01
Molecular-dynamics simulations of a liquid of short linear molecules have been performed to investigate the correlation between the particle dynamics in the cage of the neighbors and the local geometry. The latter is characterized in terms of the size and the asphericity of the Voronoi polyhedra. The correlation is found to be poor. In particular, in spite of the different Voronoi volume around the end and the inner monomers of a molecule, all the monomers exhibit coinciding displacement distribution when they are caged (as well as at longer times during the structural relaxation). It is concluded that the fast dynamics during the cage trapping is a non-local collective process involving monomers beyond the nearest neighbours.
Local geometry of electromagnetic fields and its role in molecular multipole transitions
Yang, Nan
2010-01-01
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the fields and field gradients at a single point in space. Many configurations cannot be generated from a single plane wave, regardless of polarization, but any allowed configuration can be generated by superposition of multiple plane waves. There is no local configuration of the fields and gradients that requires near-field effects. Second, we derive a set of local electromagnetic quantities, where each couples to a particular multipole transition. These quantities are small or zero in plane waves, but can be large in regions of certain superpositions of plane waves. Our findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions. The proposed experiments provide information on molecular structure that is inaccessi...
Jaeger, C.R.; Debowski, M.A.; Manners, I.; Vancso, G.J.
1999-01-01
Ab initio molecular orbital calculations at the MP2/6-31G* level of theory have been used to study the molecular geometry, electronic structure, and the thermal stability of six-membered phosphazene and heterophosphazene rings. The studies included the phosphazene ring [NPCl2]3, the carbophosphazene
Molecular Hydrogen in Diffuse Interstellar Clouds of Arbitrary Three-Dimensional Geometry
Spaans, M; Spaans, Marco; Neufeld, David A.
1997-01-01
We have constructed three-dimensional models for the equilibrium abundance of molecular hydrogen within diffuse interstellar clouds of arbitrary geometry that are illuminated by ultraviolet radiation. The position-dependent photo- dissociation rate of H$_2$ within such clouds was computed using a 26-ray approximation to model the attenuation of the incident ultraviolet radiation field by dust and by H$_2$ line absorption. We have applied our modeling technique to the isolated diffuse cloud G236+39, assuming that the cloud has a constant density and that the thickness of the cloud along the line of sight is at every point proportional to the 100 um continuum intensity measured by IRAS. We find that our model can successfully account for observed variations in the ratio of 100 umu continuum intensity to HI column density, with larger values of that ratio occurring along lines of sight in which the molecular hydrogen fraction is expected to be largest. Using a standard chi^2 analysis to assess the goodness of fi...
Local geometry of electromagnetic fields and its role in molecular multipole transitions.
Yang, Nan; Cohen, Adam E
2011-05-12
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the fields and field gradients at a single point in space. Many configurations cannot be generated from a single plane wave, regardless of polarization, but any allowed configuration can be generated by superposition of multiple plane waves. There is no local configuration of the fields and gradients that requires near-field effects. Second, we derive a set of local electromagnetic quantities, each of which couples to a particular multipole transition. These quantities are small or zero in plane waves, but can be large in regions of certain superpositions of plane waves. Our findings provide a systematic framework for designing far-field and near-field experiments to drive multipole transitions. The proposed experiments provide information on molecular structure that is inaccessible to other spectroscopic techniques and open the possibility for new types of optical control of molecules.
Tested Demonstrations: Diffusion of Gases--Kinetic Molecular Theory of Gases.
Gilbert, George L., Ed.
1984-01-01
Provided are procedures and list of materials needed to demonstrate that the pressure inside a container with a porous surface can be changed due to the rate of diffusion of low molecular weight gases. Typical results obtained are included. (JN)
A Demonstration of the Molecular Basis of Sickle-Cell Anemia.
Fox, Marty; Gaynor, John J.
1996-01-01
Describes a demonstration that permits the separation of different hemoglobin molecules within two to three hours. Introduces students to the powerful technique of gel electrophoresis and illustrates the molecular basis of sickle-cell anemia. (JRH)
Energy Technology Data Exchange (ETDEWEB)
Ghobadi, Ahmadreza F.; Elliott, J. Richard, E-mail: elliot1@uakron.edu [Department of Chemical and Biomolecular Engineering, The University of Akron, Akron Ohio 44325 (United States)
2014-09-07
In Paper I [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 139(23), 234104 (2013)], we showed that how a third-order Weeks–Chandler–Anderson (WCA) Thermodynamic Perturbation Theory and molecular simulation can be integrated to characterize the repulsive and dispersive contributions to the Helmholtz free energy for realistic molecular conformations. To this end, we focused on n-alkanes to develop a theory for fused and soft chains. In Paper II [A. F. Ghobadi and J. R. Elliott, J. Chem. Phys. 141(2), 024708 (2014)], we adapted the classical Density Functional Theory and studied the microstructure of the realistic molecular fluids in confined geometries and vapor-liquid interfaces. We demonstrated that a detailed consistency between molecular simulation and theory can be achieved for both bulk and inhomogeneous phases. In this paper, we extend the methodology to molecules with partial charges such as carbon dioxide, water, 1-alkanols, nitriles, and ethers. We show that the electrostatic interactions can be captured via an effective association potential in the framework of Statistical Associating Fluid Theory (SAFT). Implementation of the resulting association contribution in assessing the properties of these molecules at confined geometries and interfaces presents satisfactory agreement with molecular simulation and experimental data. For example, the predicted surface tension deviates less than 4% comparing to full potential simulations. Also, the theory, referred to as SAFT-γ WCA, is able to reproduce the specific orientation of hydrophilic head and hydrophobic tail of 1-alkanols at the vapor-liquid interface of water.
Directory of Open Access Journals (Sweden)
Giuseppe eMercurio
2014-01-01
Full Text Available We present an analysis method of normal incidence x-ray standing wave (NIXSW data that allows detailed adsorption geometries of complex molecules to be retrieved. This method (Fourier vector analysis is based on the comparison of both the coherence and phase of NIXSW data to NIXSW simulations of different molecular geometries as the relevant internal degrees of freedom are tuned. We introduce this analysis method using the prototypical molecular switch azobenzene (AB adsorbed on the Ag(111 surface as a model system. The application of the Fourier vector analysis to AB/Ag(111 provides, on the one hand, detailed adsorption geometries including dihedral angles, and on the other hand, insights into the dynamics of molecules and their bonding to the metal substrate. This analysis scheme is generally applicable to any adsorbate, it is necessary for molecules with potentially large distortions, and will be particularly valuable for molecules whose distortion on adsorption can be mapped on a limited number of internal degrees of freedom.
Stanyon, Roscoe; Wienberg, Johannes; Romagno, D.; Bigoni, F.; Jauch, Anna; Cremer, Thomas
1992-01-01
The existence of an apomorphic reciprocal chromosomal translocation in the gorilla lineage has been asserted or denied by various cytogeneticists. We employed a new molecular cytogenetic strategy (chromosomal in situ suppression hybridization) combined with high-resolution banding, replication sequence analysis, and fluorochrome staining to demonstrate that a reciprocal translocation between ancestral chromosomes homologous to human chromosome 5 and 17 has indeed occurred.
Battino, Rubin
1983-01-01
Describes the design, construction, and use of oversize lecture-demonstration atomic/molecular models. These models appeal to both concrete and formal operational students. Also describes construction and use of an "spdf" sandwich board and an experiment using attribute blocks. (JN)
Directory of Open Access Journals (Sweden)
Sagi Filin
2012-01-01
Full Text Available Terrestrial laser scanning is becoming a standard for 3D modeling of complex scenes. Results of the scan contain detailed geometric information about the scene; however, the lack of semantic details still constitutes a gap in ensuring this data is usable for mapping. This paper proposes a framework for recognition of objects in laser scans; aiming to utilize all the available information, range, intensity and color information integrated into the extraction framework. Instead of using the 3D point cloud, which is complex to process since it lacks an inherent neighborhood structure, we propose a polar representation which facilitates low-level image processing tasks, e.g., segmentation and texture modeling. Using attributes of each segment, a feature space analysis is used to classify segments into objects. This process is followed by a fine-tuning stage based on graph-cut algorithm, which considers the 3D nature of the data. The proposed algorithm is demonstrated on tree extraction and tested on scans containing complex objects in addition to trees. Results show a very high detection level and thereby the feasibility of the proposed framework.
Geometry from Information Geometry
Caticha, Ariel
2015-01-01
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe the full geometry of space but only its conformal geometry -- the geometry up to local changes of scale. Remarkably, this is precisely what is needed to model "physical" space in general relativity.
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.
Batyuk, Alexander; Wu, Yufan; Honegger, Annemarie; Heberling, Matthew M; Plückthun, Andreas
2016-04-24
DARPin libraries, based on a Designed Ankyrin Repeat Protein consensus framework, are a rich source of binding partners for a wide variety of proteins. Their modular structure, stability, ease of in vitro selection and high production yields make DARPins an ideal starting point for further engineering. The X-ray structures of around 30 different DARPin complexes demonstrate their ability to facilitate crystallization of their target proteins by restricting flexibility and preventing undesired interactions of the target molecule. However, their small size (18 kDa), very hydrophilic surface and repetitive structure can limit the DARPins' ability to provide essential crystal contacts and their usefulness as a search model for addressing the crystallographic phase problem in molecular replacement. To optimize DARPins for their application as crystallization chaperones, rigid domain-domain fusions of the DARPins to larger proteins, proven to yield high-resolution crystal structures, were generated. These fusions were designed in such a way that they affect only one of the terminal capping repeats of the DARPin and do not interfere with residues involved in target binding, allowing to exchange at will the binding specificities of the DARPin in the fusion construct. As a proof of principle, we designed rigid fusions of a stabilized version of Escherichia coli TEM-1 β-lactamase to the C-terminal capping repeat of various DARPins in six different relative domain orientations. Five crystal structures representing four different fusion constructs, alone or in complex with the cognate target, show the predicted relative domain orientations and prove the validity of the concept.
Sagdinc, Seda; Kandemirli, Fatma; Bayari, Sevgi Haman
2007-02-01
Sertraline hydrochloride is a highly potent and selective inhibitor of serotonin (5HT). It is a basic compound of pharmaceutical application for antidepressant treatment (brand name: Zoloft). Ab initio and density functional computations of the vibrational (IR) spectrum, the molecular geometry, the atomic charges and polarizabilities were carried out. The infrared spectrum of sertraline is recorded in the solid state. The observed IR wave numbers were analysed in light of the computed vibrational spectrum. On the basis of the comparison between calculated and experimental results and the comparison with related molecules, assignments of fundamental vibrational modes are examined. The X-ray geometry and experimental frequencies are compared with the results of our theoretical calculations.
Schneider, Thomas D.
2010-01-01
The relationship between information and energy is key to understanding biological systems. We can display the information in DNA sequences specifically bound by proteins by using sequence logos, and we can measure the corresponding binding energy. These can be compared by noting that one of the forms of the second law of thermodynamics defines the minimum energy dissipation required to gain one bit of information. Under the isothermal conditions that molecular machines function this is joules per bit ( is Boltzmann's constant and T is the absolute temperature). Then an efficiency of binding can be computed by dividing the information in a logo by the free energy of binding after it has been converted to bits. The isothermal efficiencies of not only genetic control systems, but also visual pigments are near 70%. From information and coding theory, the theoretical efficiency limit for bistate molecular machines is ln 2 = 0.6931. Evolutionary convergence to maximum efficiency is limited by the constraint that molecular states must be distinct from each other. The result indicates that natural molecular machines operate close to their information processing maximum (the channel capacity), and implies that nanotechnology can attain this goal. PMID:20562221
Schneider, Thomas D
2010-10-01
The relationship between information and energy is key to understanding biological systems. We can display the information in DNA sequences specifically bound by proteins by using sequence logos, and we can measure the corresponding binding energy. These can be compared by noting that one of the forms of the second law of thermodynamics defines the minimum energy dissipation required to gain one bit of information. Under the isothermal conditions that molecular machines function this is [Formula in text] joules per bit (kB is Boltzmann's constant and T is the absolute temperature). Then an efficiency of binding can be computed by dividing the information in a logo by the free energy of binding after it has been converted to bits. The isothermal efficiencies of not only genetic control systems, but also visual pigments are near 70%. From information and coding theory, the theoretical efficiency limit for bistate molecular machines is ln 2=0.6931. Evolutionary convergence to maximum efficiency is limited by the constraint that molecular states must be distinct from each other. The result indicates that natural molecular machines operate close to their information processing maximum (the channel capacity), and implies that nanotechnology can attain this goal.
Linenberger, Kimberly J.; Cole, Renee S.; Sarkar, Somnath
2011-01-01
We present a guided-inquiry experiment using Spartan Student Version, ready to be adapted and implemented into a general chemistry laboratory course. The experiment provides students an experience with Spartan Molecular Modeling software while discovering the relationships between the structure and properties of molecules. Topics discussed within…
Filamentary flow and magnetic geometry in evolving cluster-forming molecular cloud clumps
Klassen, Mikhail; Kirk, Helen
2016-01-01
We present an analysis of the relationship between the orientation of magnetic fields and filaments that form in 3D magnetohydrodynamic simulations of cluster-forming, turbulent molecular cloud clumps. We examine simulated cloud clumps with size scales of L ~ 2-4 pc and densities of n ~ 400-1000 cm^-3. Many molecular clouds have Alfven Mach numbers near unity, a regime insufficiently explored by numerical simulations. We simulated two cloud clumps of different masses, one in virial equilibrium, the other strongly gravitationally bound, but with the same initial turbulent velocity field and similar mass-to-flux ratio. We apply various techniques to analyze the filamentary and magnetic structure of the resulting cloud, including the DisPerSE filament-finding algorithm in 3D. The largest structure that forms is a 1-2 parsec-long filament, with smaller connecting sub-filaments. We find that in our trans-Alfvenic clouds, wherein magnetic forces and turbulence are comparable, coherent orientation of the magnetic fi...
Filamentary flow and magnetic geometry in evolving cluster-forming molecular cloud clumps
Klassen, Mikhail; Pudritz, Ralph E.; Kirk, Helen
2017-02-01
We present an analysis of the relationship between the orientation of magnetic fields and filaments that form in 3D magnetohydrodynamic simulations of cluster-forming, turbulent molecular cloud clumps. We examine simulated cloud clumps with size scales of L ∼ 2-4 pc and densities of n ∼ 400-1000 cm-3 with Alfvén Mach numbers near unity. We simulated two cloud clumps of different masses, one in virial equilibrium, the other strongly gravitationally bound, but with the same initial turbulent velocity field and similar mass-to-flux ratio. We apply various techniques to analyse the filamentary and magnetic structure of the resulting cloud, including the DISPERSE filament-finding algorithm in 3D. The largest structure that forms is a 1-2 parsec-long filament, with smaller connecting sub-filaments. We find that our simulated clouds, wherein magnetic forces and turbulence are comparable, coherent orientation of the magnetic field depends on the virial parameter. Sub-virial clumps undergo strong gravitational collapse and magnetic field lines are dragged with the accretion flow. We see evidence of filament-aligned flow and accretion flow on to the filament in the sub-virial cloud. Magnetic fields oriented more parallel in the sub-virial cloud and more perpendicular in the denser, marginally bound cloud. Radiative feedback from a 16 M⊙ star forming in a cluster in one of our simulation's ultimately results in the destruction of the main filament, the formation of an H II region, and the sweeping up of magnetic fields within an expanding shell at the edges of the H II region.
Ufimtsev, Ivan S; Martinez, Todd J
2009-10-13
We demonstrate that a video gaming machine containing two consumer graphical cards can outpace a state-of-the-art quad-core processor workstation by a factor of more than 180× in Hartree-Fock energy + gradient calculations. Such performance makes it possible to run large scale Hartree-Fock and Density Functional Theory calculations, which typically require hundreds of traditional processor cores, on a single workstation. Benchmark Born-Oppenheimer molecular dynamics simulations are performed on two molecular systems using the 3-21G basis set - a hydronium ion solvated by 30 waters (94 atoms, 405 basis functions) and an aspartic acid molecule solvated by 147 waters (457 atoms, 2014 basis functions). Our GPU implementation can perform 27 ps/day and 0.7 ps/day of ab initio molecular dynamics simulation on a single desktop computer for these systems.
Non-unity molecular heritability demonstrated by continuous evolution in vitro
Schmitt, T.; Lehman, N.
1999-01-01
INTRODUCTION: When catalytic RNA is evolved in vitro, the molecule's chemical reactivity is usually the desired selection target. Sometimes the phenotype of a particular RNA molecule cannot be unambiguously determined from its genotype, however. This can occur if a nucleotide sequence can adopt multiple folded states, an example of non-unity heritability (i.e. one genotype gives rise to more than one phenotype). In these cases, more rounds of selection are required to achieve a phenotypic shift. We tested the influence of non-unity heritability at the molecular level by selecting for variants of a ligase ribozyme via continuous evolution. RESULTS: During 20 bursts of continuous evolution of a 152-nucleotide ligase ribozyme in which the Mg2+ concentration was periodically lowered, a nine-error variant of the starting 'wild-type' molecule became dominant in the last eight bursts. This variant appears to be more active than the wild type. Kinetic analyses of the mutant suggest that it may not possess a higher first-order catalytic rate constant, however. Examination of the multiple RNA conformations present under the continuous evolution conditions suggests that the mutant is superior to the wild type because it is less likely to misfold into inactive conformers. CONCLUSIONS: The evolution of genotypes that are more likely to exhibit a particular phenotype is an epiphenomenon usually ascribed only to complex living systems. We show that this can occur at the molecular level, demonstrating that in vitro systems may have more life-like characteristics than previously thought, and providing additional support for an RNA world.
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.
Non-unity molecular heritability demonstrated by continuous evolution in vitro
Schmitt, T.; Lehman, N.
1999-01-01
INTRODUCTION: When catalytic RNA is evolved in vitro, the molecule's chemical reactivity is usually the desired selection target. Sometimes the phenotype of a particular RNA molecule cannot be unambiguously determined from its genotype, however. This can occur if a nucleotide sequence can adopt multiple folded states, an example of non-unity heritability (i.e. one genotype gives rise to more than one phenotype). In these cases, more rounds of selection are required to achieve a phenotypic shift. We tested the influence of non-unity heritability at the molecular level by selecting for variants of a ligase ribozyme via continuous evolution. RESULTS: During 20 bursts of continuous evolution of a 152-nucleotide ligase ribozyme in which the Mg2+ concentration was periodically lowered, a nine-error variant of the starting 'wild-type' molecule became dominant in the last eight bursts. This variant appears to be more active than the wild type. Kinetic analyses of the mutant suggest that it may not possess a higher first-order catalytic rate constant, however. Examination of the multiple RNA conformations present under the continuous evolution conditions suggests that the mutant is superior to the wild type because it is less likely to misfold into inactive conformers. CONCLUSIONS: The evolution of genotypes that are more likely to exhibit a particular phenotype is an epiphenomenon usually ascribed only to complex living systems. We show that this can occur at the molecular level, demonstrating that in vitro systems may have more life-like characteristics than previously thought, and providing additional support for an RNA world.
Suresh, S; Gunasekaran, S; Srinivasan, S
2014-05-05
The solid phase FT-IR and FT-Raman spectra of 2-[2-[2-[(2,6-dichlorophenyl)amino]phenyl]acetyl] oxyacetic acid (Aceclofenac) 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 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies were scaled and have been compared with experimental by 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 employed to study 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 (MESP) were also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
Wu, Cheng-Da; Fang, Te-Hua; Lin, Jen-Fin
2014-10-01
Molecular dynamics simulations are used to investigate how the nanoimprint lithography mechanism influences the filling interaction and mechanical deformation on polymethylmethacrylate (PMMA) surfaces. The effects of two mold geometries and various taper angles were investigated using stress, slip vector, molecular trajectories, and applied force analysis. For the PMMA formation mechanism on a concave-like mold imprint, the molecules were extruded upward into the mold space after the molecules on two sides were downward compressed by the mold. The formation mechanism is opposite to that for the tip-like mold imprint because the molecules are firstly compressed downward by the tip. The results show that the slowest filled areas of the pattern were at the two corners of the tip where stress value was low. The filling speed in both the tip-like mold and the concave-like mold imprint increased with the taper angle increased due to filling space and smaller capillary flow. Due to the effect of capillary flow, the concave-like mold needs much more loading force to transfer the pattern than the tip-like mold. The loading force and curve oscillation increased with the taper angle in the tip-like mold imprint, but they significantly increased with decreasing taper angle in the concave-like mold. The high stress was mainly concentrated on the molecules near the tip and underneath the mold for the tip-like mold and the concave-like mold imprint, respectively. The relationship of the magnitude of taper angle to the loading force is similar to stress and slip vector.
Pan, Albert C; Weinreich, Thomas M; Piana, Stefano; Shaw, David E
2016-03-01
Molecular dynamics (MD) simulations can describe protein motions in atomic detail, but transitions between protein conformational states sometimes take place on time scales that are infeasible or very expensive to reach by direct simulation. Enhanced sampling methods, the aim of which is to increase the sampling efficiency of MD simulations, have thus been extensively employed. The effectiveness of such methods when applied to complex biological systems like proteins, however, has been difficult to establish because even enhanced sampling simulations of such systems do not typically reach time scales at which convergence is extensive enough to reliably quantify sampling efficiency. Here, we obtain sufficiently converged simulations of three proteins to evaluate the performance of simulated tempering, a member of a widely used class of enhanced sampling methods that use elevated temperature to accelerate sampling. Simulated tempering simulations with individual lengths of up to 100 μs were compared to (previously published) conventional MD simulations with individual lengths of up to 1 ms. With two proteins, BPTI and ubiquitin, we evaluated the efficiency of sampling of conformational states near the native state, and for the third, the villin headpiece, we examined the rate of folding and unfolding. Our comparisons demonstrate that simulated tempering can consistently achieve a substantial sampling speedup of an order of magnitude or more relative to conventional MD.
DEFF Research Database (Denmark)
Brandt, Rasmus Guldbaek; Zhang, Fei; Andersen, Thomas Rieks
2016-01-01
In this paper, we investigate three diketopyrrolopyrrole (DPP) based small molecular non-fullerene acceptors, namely Ph(DPP)3, Ph(DPP)2, and PhDMe(DPP)2, focusing on molecular geometry effects on the frontier orbital level, light absorption, molecular configuration, electron mobility, thin film...... morphology, and photovoltaic performance of both spin-coated ITO based and roll coated large area, ITO- and vacuum-free organic solar cells (OSCs). For spin-coated devices based on P3HT as the donor polymer the solar cells gave power conversion efficiencies (PCEs) in the following order for (P3HT:PhDMe(DPP)2...
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...
Hedin, Marshal; Thomas, Steven M
2010-01-01
The phalangodid harvestmen (Opiliones: Laniatores) fauna of the southeastern United States has remained obscure since original descriptions of many genera and species over 60 years ago. The obscurity of this interesting group is pervasive, with uncertainty regarding basic systematic information such as generic limits, species limits, and geographic distributions. This situation is unfortunate, as the fauna includes several cave-obligate forms of interest from both conservation and evolutionary perspectives, and the group likely exhibits interesting biogeographic patterns because of their low dispersal ability. Here, we use DNA sequence data from two genes to reconstruct phylogenetic relationships of southeastern phalangodid taxa, for a sample of all described genera from the region. Our results demonstrate that the southeastern fauna is likely monophyletic, and is most-closely related to western North American phalangodids with a similar penis morphology. Within the southeastern clade, trends in the evolution of penis morphology correspond broadly to molecular phylogenetic patterns, although penis evolution is overall relatively conservative in the group. Biogeographically, it appears that western taxa in the southeast (i.e., from west of the Appalachian Valley) are early diverging, with later diversification in the montane southern Blue Ridge, and subsequent diversification back towards the west. This W>E>W pattern has been observed in other groups from the southeast. The multiple cave-modified species in the region are genetically divergent and appear phylogenetically isolated; explicit topological hypothesis testing suggests that troglomorphism has evolved convergently in at least three independent lineages. The total number of species in the region remains uncertain-mitochondrial COI data reveal many highly divergent, geographically coherent groups that might represent undescribed species, but these divergent mitochondrial lineages do not always exhibit
Asaji, Tetsuo; Seliger, Janez; Zagar, Veselko; Ishida, Hiroyuki
2010-07-01
Proton transfer in hydrogen-bonded organic co-crystals of chloranilic acid with some organic bases was investigated by nuclear quadrupole resonance (NQR) spectroscopy. The (35)Cl NQR frequencies of chloranilic acid molecule as well as (14)N NQR frequencies of the organic base molecule were measured with the conventional pulse methods as well as double-resonance methods, respectively. The extent of proton transfer in the O...H...N hydrogen bond was estimated from Townes-Dailey analysis of the (14)N NQR parameters. The (35)Cl NQR frequency and molecular geometry of chloranilic acid are correlated to the extent of proton transfer in the protonation process of the organic base molecule. It is shown that the hydrogen bond affects the pi-electron system of chloranilic acid. Geometry dependence of the O...H...N hydrogen bond, i.e. the H-N valence bond order versus the hydrogen-bond geometry correlation is also discussed.
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.
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
陈勇; 庞美丽; 程凯歌; 王英; 孟继本
2012-01-01
Stable nitronyl nitroxide radical and imino nitroxide radical were incorporated into the benzene rings of novel photochromic 7,7＇-dimethyl-[2,2＇-bi-lH-indene]-3,3＇-diethyl-3,3＇-dihydroxy-l,l＇-dione （1）, leading to the synthesis of novel multifunctional compounds 4 and 5. The photochromic properties, ESR spectroscopy and magnetic proper- ties of the title compounds were investigated. Compounds 4 and 5 possess visible photochromism upon photoirra- diation, and their ESR signals undergo secular broadening after photoirradiation. The magnetic susceptibility meas- urement shows that the antiferromagnetic interaction of 4 and 5 becomes stronger after photoirradiation. In compounds 4 and 5 there are two kinds of spin centers after photoirradiation： one is nitroxide radical, and the other is photo-generated radicals from two indanone moieties. Our results demonstrated that the colour and magnetic properties of compounds 4 and 5 could be modulated by photoirradiation.
Correa-Garhwal, Sandra M; Garb, Jessica E
2014-12-08
Spider silks have outstanding mechanical properties. Most research has focused on dragline silk proteins (major ampullate spidroins, MaSps) from orb-weaving spiders. Using silk gland expression libraries from the haplogyne spider Scytodes thoracica, we discovered two novel spidroins (S. thoracica fibroin 1 and 2). The amino acid composition of S. thoracica silk glands and dragline fibers suggest that fibroin 1 is the major component of S. thoracica dragline silk. Fibroin 1 is dominated by glycine-alanine motifs, and lacks sequence motifs associated with orb-weaver MaSps. We hypothesize fibroin 2 is a piriform or aciniform silk protein, based on amino acid composition, spigot morphology, and phylogenetic analyses. S. thoracica's dragline silk is less tough than previously reported, but is still comparable to other dragline silks. Our analyses suggest that dragline silk proteins evolved multiple times. This demonstrates that spider dragline silk is more diverse than previously understood, providing alternative high performance silk designs.
Ergunay, Koray; Gunay, Filiz; Erisoz Kasap, Ozge; Oter, Kerem; Gargari, Sepandar; Karaoglu, Taner; Tezcan, Seda; Cabalar, Mehmet; Yildirim, Yakup; Emekdas, Gürol; Alten, Bulent; Ozkul, Aykut
2014-07-01
West Nile virus (WNV), a mosquito-borne flavivirus with significant impact on human and animal health, has recently demonstrated an expanded zone of activity globally. The aim of this study is to investigate the frequency and distribution of WNV infections in potential vectors and several mammal and avian species in Turkey, where previous data indicate viral circulation. The study was conducted in 15 provinces across Turkey during 2011-2013. In addition, the entomological study was extended to 4 districts of the Turkish Republic of Northern Cyprus. WNV exposure was determined in humans, horses, sheep and ducks from Mersin, Sanliurfa, Van and Kars provinces of Turkey, via the detection of neutralizing antibodies. WNV RNA was sought in human and equine samples from Mersin, Adana and Mugla provinces. Field-collected mosquitoes from 92 sites at 46 locations were characterized morphologically and evaluated for viral RNA. Neutralizing antibodies were identified in 10.5% of the 1180 samples studied and detected in all species evaluated. Viral nucleic acids were observed in 5.9% of 522 samples but only in horses. A total of 2642 mosquito specimens belonging to 15 species were captured, where Ochlerotatus caspius (52.4%), Culex pipiens sensu lato (24.2%) comprise the most frequent species. WNV RNA was detected in 4 mosquito pools (1.9%), that comprise Oc. caspius Cx. pipiens s.l. and DNA barcoding revealed the presence of Cx. quinquefasciatus and Cx. perexiguus mosquitoes in infected Culex pools. All WNV partial sequences were characterized as lineage 1 clade 1a. These findings indicate a widespread WNV activity in Turkey, in Eastern Thrace and Mediterranean-Aegean regions as well as Southeastern and Northeastern Anatolia.
Guggenheimer, Heinrich W
1977-01-01
This is a text of local differential geometry considered as an application of advanced calculus and linear algebra. The discussion is designed for advanced undergraduate or beginning graduate study, and presumes of readers only a fair knowledge of matrix algebra and of advanced calculus of functions of several real variables. The author, who is a Professor of Mathematics at the Polytechnic Institute of New York, begins with a discussion of plane geometry and then treats the local theory of Lie groups and transformation groups, solid differential geometry, and Riemannian geometry, leading to a
Institute of Scientific and Technical Information of China (English)
QI; Yuanhua; GUAN; Daren; LIU; Chengbu
2006-01-01
The density functional theory (DFT) combining with the non-equilibrium Green functions (NEGF) method is applied to the study of the electronic transport properties for a Di-thiol-benzene (DTB) molecule coupled to two Au(111) surfaces. The dependence of the transport properties on the bias, the coupling geometry of the molecule-electrode interface, and the intermolecular interaction are examined in detail. The results show that the existence of the hydrogen atom at the end of the DTB molecule would significantly decrease the transmission coefficients, and then the differential conductance (dI/dV). By changing the position of the DTB molecule located between two electrodes a maximum value of calculated current is observed. It is also found that the intermolecular interaction will strongly influence the transport properties of the system studied.
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).
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A.; Plecháč, Petr
2015-08-01
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.
Kalligiannaki, Evangelia; Harmandaris, Vagelis; Katsoulakis, Markos A; Plecháč, Petr
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.
Pottmann, Helmut
2014-11-26
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.
Maor, Eli
2014-01-01
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur
Graustein, William C
2006-01-01
This first course in differential geometry presents the fundamentals of the metric differential geometry of curves and surfaces in a Euclidean space of three dimensions. Written by an outstanding teacher and mathematician, it explains the material in the most effective way, using vector notation and technique. It also provides an introduction to the study of Riemannian geometry.Suitable for advanced undergraduates and graduate students, the text presupposes a knowledge of calculus. The first nine chapters focus on the theory, treating the basic properties of curves and surfaces, the mapping of
Directory of Open Access Journals (Sweden)
L. O. Olasunkanmi
2013-01-01
Full Text Available Theoretical study of the molecular geometries, electronic and thermodynamic properties of dipyrido-(3,2-a:2,3-c-phenazine (dppz was carried out in the gas phase under standard conditions using PM6 Hamiltonian in semiempirical model. Effects of chlorine substituents on these properties were also investigated. The results showed that all the electronic and thermodynamic properties investigated were affected by the number and relative position of chlorine substituents. Variations in some properties are not significant for some isomeric congeners, having the same number of chlorine substituents, while a number of properties showed general variation with both the number and position of chlorine substituents. Successive addition of one chlorine atom after the other at adjacent position to the last chlorine substituent increases the total energy by 241 eV and decreases the LUMO-HOMO gap by an average value of 0.124 eV. Geometry and energy optimization show that all the molecules considered are planar.
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...
Spackman, Peter R; Jayatilaka, Dylan; Karton, Amir
2016-09-14
We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H-X, 49 X-Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ∼4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0.0019 (D
Spackman, Peter R.; Jayatilaka, Dylan; Karton, Amir
2016-09-01
We examine the basis set convergence of the CCSD(T) method for obtaining the structures of the 108 neutral first- and second-row species in the W4-11 database (with up to five non-hydrogen atoms). This set includes a total of 181 unique bonds: 75 H—X, 49 X—Y, 43 X=Y, and 14 X≡Y bonds (where X and Y are first- and second-row atoms). As reference values, geometries optimized at the CCSD(T)/aug'-cc-pV(6+d)Z level of theory are used. We consider the basis set convergence of the CCSD(T) method with the correlation consistent basis sets cc-pV(n+d)Z and aug'-cc-pV(n+d)Z (n = D, T, Q, 5) and the Weigend-Ahlrichs def2-n ZVPP basis sets (n = T, Q). For each increase in the highest angular momentum present in the basis set, the root-mean-square deviation (RMSD) over the bond distances is decreased by a factor of ˜4. For example, the following RMSDs are obtained for the cc-pV(n+d)Z basis sets 0.0196 (D), 0.0050 (T), 0.0015 (Q), and 0.0004 (5) Å. Similar results are obtained for the aug'-cc-pV(n+d)Z and def2-n ZVPP basis sets. The double-zeta and triple-zeta quality basis sets systematically and significantly overestimate the bond distances. A simple and cost-effective way to improve the performance of these basis sets is to scale the bond distances by an empirical scaling factor of 0.9865 (cc-pV(D+d)Z) and 0.9969 (cc-pV(T+d)Z). This results in RMSDs of 0.0080 (scaled cc-pV(D+d)Z) and 0.0029 (scaled cc-pV(T+d)Z) Å. The basis set convergence of larger basis sets can be accelerated via standard basis-set extrapolations. In addition, the basis set convergence of explicitly correlated CCSD(T)-F12 calculations is investigated in conjunction with the cc-pVnZ-F12 basis sets (n = D, T). Typically, one "gains" two angular momenta in the explicitly correlated calculations. That is, the CCSD(T)-F12/cc-pVnZ-F12 level of theory shows similar performance to the CCSD(T)/cc-pV(n+2)Z level of theory. In particular, the following RMSDs are obtained for the cc-pVnZ-F12 basis sets 0
Kufareva, Irina; Stephens, Bryan S.; Holden, Lauren G.; Qin, Ling; Zhao, Chunxia; Kawamura, Tetsuya; Abagyan, Ruben; Handel, Tracy M.
2014-01-01
Chemokines and their receptors regulate cell migration during development, immune system function, and in inflammatory diseases, making them important therapeutic targets. Nevertheless, the structural basis of receptor:chemokine interaction is poorly understood. Adding to the complexity of the problem is the persistently dimeric behavior of receptors observed in cell-based studies, which in combination with structural and mutagenesis data, suggest several possibilities for receptor:chemokine complex stoichiometry. In this study, a combination of computational, functional, and biophysical approaches was used to elucidate the stoichiometry and geometry of the interaction between the CXC-type chemokine receptor 4 (CXCR4) and its ligand CXCL12. First, relevance and feasibility of a 2:1 stoichiometry hypothesis was probed using functional complementation experiments with multiple pairs of complementary nonfunctional CXCR4 mutants. Next, the importance of dimers of WT CXCR4 was explored using the strategy of dimer dilution, where WT receptor dimerization is disrupted by increasing expression of nonfunctional CXCR4 mutants. The results of these experiments were supportive of a 1:1 stoichiometry, although the latter could not simultaneously reconcile existing structural and mutagenesis data. To resolve the contradiction, cysteine trapping experiments were used to derive residue proximity constraints that enabled construction of a validated 1:1 receptor:chemokine model, consistent with the paradigmatic two-site hypothesis of receptor activation. The observation of a 1:1 stoichiometry is in line with accumulating evidence supporting monomers as minimal functional units of G protein-coupled receptors, and suggests transmission of conformational changes across the dimer interface as the most probable mechanism of altered signaling by receptor heterodimers. PMID:25468967
Kufareva, Irina; Stephens, Bryan S; Holden, Lauren G; Qin, Ling; Zhao, Chunxia; Kawamura, Tetsuya; Abagyan, Ruben; Handel, Tracy M
2014-12-16
Chemokines and their receptors regulate cell migration during development, immune system function, and in inflammatory diseases, making them important therapeutic targets. Nevertheless, the structural basis of receptor:chemokine interaction is poorly understood. Adding to the complexity of the problem is the persistently dimeric behavior of receptors observed in cell-based studies, which in combination with structural and mutagenesis data, suggest several possibilities for receptor:chemokine complex stoichiometry. In this study, a combination of computational, functional, and biophysical approaches was used to elucidate the stoichiometry and geometry of the interaction between the CXC-type chemokine receptor 4 (CXCR4) and its ligand CXCL12. First, relevance and feasibility of a 2:1 stoichiometry hypothesis was probed using functional complementation experiments with multiple pairs of complementary nonfunctional CXCR4 mutants. Next, the importance of dimers of WT CXCR4 was explored using the strategy of dimer dilution, where WT receptor dimerization is disrupted by increasing expression of nonfunctional CXCR4 mutants. The results of these experiments were supportive of a 1:1 stoichiometry, although the latter could not simultaneously reconcile existing structural and mutagenesis data. To resolve the contradiction, cysteine trapping experiments were used to derive residue proximity constraints that enabled construction of a validated 1:1 receptor:chemokine model, consistent with the paradigmatic two-site hypothesis of receptor activation. The observation of a 1:1 stoichiometry is in line with accumulating evidence supporting monomers as minimal functional units of G protein-coupled receptors, and suggests transmission of conformational changes across the dimer interface as the most probable mechanism of altered signaling by receptor heterodimers.
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
Keaveny, Eric E; Pivkin, Igor V; Maxey, Martin; Em Karniadakis, George
2005-09-08
The purpose of this study is to compare the results from molecular-dynamics and dissipative particle dynamics (DPD) simulations of Lennard-Jones (LJ) fluid and determine the quantitative effects of DPD coarse graining on flow parameters. We illustrate how to select the conservative force coefficient, the cut-off radius, and the DPD time scale in order to simulate a LJ fluid. To show the effects of coarse graining and establish accuracy in the DPD simulations, we conduct equilibrium simulations, Couette flow simulations, Poiseuille flow simulations, and simulations of flow around a periodic array of square cylinders. For the last flow problem, additional comparisons are performed against continuum simulations based on the spectral/hp element method.
Liszt, H S
2009-01-01
To interpret the galactic center H II region complexes as constituents of a barred galaxy's nuclear star-forming ring, we compare 18cm VLA radiocontinuumm, $8-22\\mu$ MSX IR and 2.6mm BTL and ARO12m CO emission in the inner few hundred pc. Galactic center H II regions are comparable in their IR appearance, luminosity and SED to M17 or N!0, but the IR light distribution is strongly modified by extinction at 8-22$\\mu$, locally and overall. In Sgr B2 at $l > 0.6$\\degr strong radio H II regions are invisible in the IR. In two favorable cases, extinction from individual galactic center molecular clouds is shown to have $\\tau \\ga 1$ at 8-22$\\mu$ independent of wavelength. The gas kinematics are mostly rotational but with systematic $\\pm 30-50$ \\kms non-circular motion. Sgr B and C both show the same shell and high-velocity cap structure. The H II regions lie in a slightly-inclined ring of radius $\\approx$ 180 pc (1.2\\degr) whose near side appears at higher latitude and lower velocity and contains Sgr B. Sgr C is on ...
Energy Technology Data Exchange (ETDEWEB)
Oie, Tetsuro
1980-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Oie, Tetsuro
1980-07-28
A purpose of the present studies is twofold: (1) development of an empirical potential function (EDF) 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 (Ch1 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.
Thomson, Shaun; Hansen, Patricia; Straka, Sharon; Chen, Philip; Triolo, Jack; Bettini, Ron; Carosso, Paolo; Carosso, Nancy
1997-01-01
The use of molecular adsorbers, in order to aid in the reduction of the spacecraft contamination levels, is discussed. Molecular adsorbers are characterized by an extremely large surface area, molecularly-porous substructure, and processing charged sites capable of retaining molecular contaminant species. Molecular adsorbers were applied on two Hubble Space Telescope servicing missions, as well as on the tropical rainfall measuring mission. The use of molecular adsorbers carries the potential for low cost, easy fabrication and integration of reliable means for reducing the contamination level around spacecraft.
Martineau, Louis C
2012-06-21
A mechanistic model of uncoupling of oxidative phosphorylation by lipophilic weak acids (i.e. proton shuttles) was developed for the purposes of predicting the relative activity of xenobiotics of widely varying structure and of guiding the design of optimized derivatives. The model is based on thermodynamic premises not formulated elsewhere that allow for the calculation of steady-state conditions and of rate of energy dissipation on the basis of acid-dissociation and permeability behavior, the later estimated from partitioning behavior and geometric considerations. Moreover, permeability of either the neutral or of the ionized species is proposed to be effectively enhanced under conditions of asymmetrical molecular distribution. Finally, special considerations were developed to accommodate multi-protic compounds. The comparison of predicted to measured activity for a diverse testset of 48 compounds of natural origin spanning a wide range of activity yielded a Spearman's rho of 0.90. The model was used to tentatively identify several novel proton shuttles, as well as to elucidate core structures particularly conducive to proton shuttle activity from which optimized derivatives can be designed. Principles of design were formulated and examples of derivatives projected to be active at concentrations on the order of 10(-7)M are proposed. Among these are di-protic compounds predicted to shuttle two protons per cycle iteration and proposed to maximally exploit the proton shuttle mechanism. This work promotes the design of highly active, yet easily-metabolized uncouplers for therapeutic applications, namely the indirect activation of AMP-kinase, as well as for various industrial applications where low persistence is desirable.
Berger, Marcel
2010-01-01
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces,
Burdette, A C
1971-01-01
Analytic Geometry covers several fundamental aspects of analytic geometry needed for advanced subjects, including calculus.This book is composed of 12 chapters that review the principles, concepts, and analytic proofs of geometric theorems, families of lines, the normal equation of the line, and related matters. Other chapters highlight the application of graphing, foci, directrices, eccentricity, and conic-related topics. The remaining chapters deal with the concept polar and rectangular coordinates, surfaces and curves, and planes.This book will prove useful to undergraduate trigonometric st
Robinson, Gilbert de B
2011-01-01
This brief undergraduate-level text by a prominent Cambridge-educated mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement for Gilbert de B. Robinson's text, which is the result of several years of teaching and learning the most effective methods from discussions with students. Topics include lines and planes, determinants and linear equations, matrices, groups and linear transformations, and vectors and vector spaces. Additional subjects range from conics and quadrics to homogeneous coordinates and projective geom
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.
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Pottmann, Helmut; Eigensatz, Michael; Vaxman, A.; Wallner, Johannes
2015-01-01
Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural
Guda, Sergey A; Guda, Alexander A; Soldatov, Mikhail A; Lomachenko, Kirill A; Bugaev, Aram L; Lamberti, Carlo; Gawelda, Wojciech; Bressler, Christian; Smolentsev, Grigory; Soldatov, Alexander V; Joly, Yves
2015-09-08
Accurate modeling of the X-ray absorption near-edge spectra (XANES) is required to unravel the local structure of metal sites in complex systems and their structural changes upon chemical or light stimuli. Two relevant examples are reported here concerning the following: (i) the effect of molecular adsorption on 3d metals hosted inside metal-organic frameworks and (ii) light induced dynamics of spin crossover in metal-organic complexes. In both cases, the amount of structural models for simulation can reach a hundred, depending on the number of structural parameters. Thus, the choice of an accurate but computationally demanding finite difference method for the ab initio X-ray absorption simulations severely restricts the range of molecular systems that can be analyzed by personal computers. Employing the FDMNES code [Phys. Rev. B, 2001, 63, 125120] we show that this problem can be handled if a proper diagonalization scheme is applied. Due to the use of dedicated solvers for sparse matrices, the calculation time was reduced by more than 1 order of magnitude compared to the standard Gaussian method, while the amount of required RAM was halved. Ni K-edge XANES simulations performed by the accelerated version of the code allowed analyzing the coordination geometry of CO and NO on the Ni active sites in CPO-27-Ni MOF. The Ni-CO configuration was found to be linear, while Ni-NO was bent by almost 90°. Modeling of the Fe K-edge XANES of photoexcited aqueous [Fe(bpy)3](2+) with a 100 ps delay we identified the Fe-N distance elongation and bipyridine rotation upon transition from the initial low-spin to the final high-spin state. Subsequently, the X-ray absorption spectrum for the intermediate triplet state with expected 100 fs lifetime was theoretically predicted.
Petersen, Peter
2016-01-01
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...
Kreyszig, Erwin
1991-01-01
An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
Energy Technology Data Exchange (ETDEWEB)
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.
1994-03-01
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 {approximately}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 {approximately}80--90% of the uranium exists as hexavalent UO{sub 2}{sup 2+} species even though many source terms consisted of tetravalent uranium species such as UO{sub 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.
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...
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
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
Suresh, S.; Gunasekaran, S.; Srinivasan, S.
2014-11-01
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.
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.
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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.
Chan, Charlene J.; Salaita, Khalid
2012-01-01
Demonstrating how surface chemistry and self-assembled monolayers (SAMs) control the macroscopic properties of materials is challenging as it often necessitates the use of specialized instrumentation. In this hands-on experiment, students directly measure a macroscopic property, the floatation of glass coverslips on water as a function of…
Milocco, C; Kamyingkird, K; Desquesnes, M; Jittapalapong, S; Herbreteau, V; Chaval, Y; Douangboupha, B; Morand, S
2013-02-01
In this study, we investigated the molecular evidence of Trypanosoma evansi in wild rodents from Cambodia, Lao PDR and Thailand. Between November 2007 and June 2009, 1664 rodents were trapped at eight sites representative of various ecological habitats. Of those animals, 94 were tested by direct microscopic blood examination, 633 using the Card Agglutination Test for Trypanosomes (CATT/T. evansi) and 145 by Polymerase Chain Reaction (PCR) with two sets of primers: TRYP1 (amplifying ITS1 of ribosomal DNA of all trypanosomes) and TBR (amplifying satellite genomic DNA of Trypanozoon parasites). Using TRYP1, based on the size of the PCR products, 15 samples from the three countries were positive for Trypanosoma lewisi (two were confirmed by sequencing), and three were positive for Trypanozoon (one was confirmed by sequencing and three by TBR primers); the specificity of the primers failed as rodent DNA was amplified in some cases. Using TBR, six samples were positive for Trypanozoon (one was confirmed by sequencing); as T. evansi is the only species of the Trypanozoon sub-genus possibly present in Asian rodents, these results confirmed its presence in rodents from Thailand (Rattus tanezumi) and Cambodia (R. tanezumi, Niviventer fulvescens & Maxomys surifer). Further investigations are necessary to establish the situation in Lao PDR. None of the 16 samples most strongly positive to the CATT proved to be positive for Trypanozoon by PCR. The merits of the CATT for such studies were not confirmed. Studying the urban and rural circulation of these parasites in rodents will enable an evaluation of human exposure and infection risk, as human infections by T. evansi were recently described in India and by T. lewisi in India and Thailand. As sequencing PCR products is expensive, the development of new molecular and serological tools for rodents would be very useful.
Demonstration of isotype GaN/AlN/GaN heterobarrier diodes by NH{sub 3}-molecular beam epitaxy
Energy Technology Data Exchange (ETDEWEB)
Fireman, Micha N.; Browne, David A.; Mazumder, Baishakhi; Speck, James S. [Materials Department, University of California, Santa Barbara, California 93106 (United States); Mishra, Umesh K. [Electrical and Computer Engineering Department, University of California, Santa Barbara, California 93106 (United States)
2015-05-18
The results of vertical transport through nitride heterobarrier structures grown by ammonia molecular beam epitaxy are presented. Structures are designed with binary layers to avoid the effects of random alloy fluctuations in ternary nitride barriers. The unintentional incorporation of Ga in the AlN growth is investigated by atom probe tomography and is shown to be strongly dependent on both the NH{sub 3} flowrate and substrate temperature growth parameters. Once nominally pure AlN layer growth conditions are achieved, structures consisting of unintentionally doped (UID) GaN spacer layers adjacent to a nominally pure AlN are grown between two layers of n+ GaN, from which isotype diodes are fabricated. Varying the design parameters of AlN layer thickness, UID spacer layer thickness, and threading dislocation density show marked effects on the vertical transport characteristics of these structures. The lack of significant temperature dependence, coupled with Fowler-Nordheim and/or Milliken-Lauritsen analysis, point to a prevalently tunneling field emission mechanism through the AlN barrier. Once flatband conditions in the UID layer are achieved, electrons leave the barrier with significant energy. This transport mechanism is of great interest for applications in hot electron structures.
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Catherine Cordonnier
2017-04-01
Full Text Available Pneumocystis jirovecii pneumonia (PCP is a life-threatening infection in hematology. Although occasionally reported, the role of interhuman transmission of P. jirovecii in PCP, compared to that of reactivation, remains an unresolved question; the recommendation to isolate PCP patients in the hematology ward are not well evidence-based. Following an unexpected increase in the number of febrile pneumonia patients with P. jirovecii DNA detected in respiratory samples in our hematology ward, we explored 12 consecutive patients from November 2015 to May 2016. Genotyping of P jirovecii was performed using microsatellite markers. The frequency of simultaneous occupancy of these 12 patients in the same unit on the same day from 4 months prior to the first diagnosis was recorded. In three patients, the P. jirovecii genotype could not be determined because DNA was insufficient. One rare single genotype (Gt2 was found in four of the other nine, all allogeneic stem cell transplant recipients. The transmission map showed that these 4 patients had multiple opportunities to meet on the same day (median, 6.5; range, 4–10 at the daycare center. It was much less among the eight non-Gt2 patients (median, 1; range, 0–9; P = 0.048. This study, based on modern molecular technics, strongly suggests that interhuman transmission of P. jirovecii between allogeneic stem cell transplant recipients is possible. P. jirovecii DNA detected in respiratory specimens supports that isolation and respiratory precautions be recommended in such cases in the hematology ward.
TRIANGLE-SHAPED DC CORONA DISCHARGE DEVICE FOR MOLECULAR DECOMPOSITION
The paper discusses the evaluation of electrostatic DC corona discharge devices for the application of molecular decomposition. A point-to-plane geometry corona device with a rectangular cross section demonstrated low decomposition efficiencies in earlier experimental work. The n...
Korolev, Nikolay; Yu, Hang; Lyubartsev, Alexander P; Nordenskiöld, Lars
2014-10-01
The positively charged N-terminal histone tails play a crucial role in chromatin compaction and are important modulators of DNA transcription, recombination, and repair. The detailed mechanism of the interaction of histone tails with DNA remains elusive. To model the unspecific interaction of histone tails with DNA, all-atom molecular dynamics (MD) simulations were carried out for systems of four DNA 22-mers in the presence of 20 or 16 short fragments of the H4 histone tail (variations of the 16-23 a. a. KRHRKVLR sequence, as well as the unmodified fragment a. a.13-20, GGAKRHRK). This setup with high DNA concentration, explicit presence of DNA-DNA contacts, presence of unstructured cationic peptides (histone tails) and K(+) mimics the conditions of eukaryotic chromatin. A detailed account of the DNA interactions with the histone tail fragments, K(+) and water is presented. Furthermore, DNA structure and dynamics and its interplay with the histone tail fragments binding are analysed. The charged side chains of the lysines and arginines play major roles in the tail-mediated DNA-DNA attraction by forming bridges and by coordinating to the phosphate groups and to the electronegative sites in the minor groove. Binding of all species to DNA is dynamic. The structure of the unmodified fully-charged H4 16-23 a.a. fragment KRHRKVLR is dominated by a stretched conformation. The H4 tail a. a. fragment GGAKRHRK as well as the H4 Lys16 acetylated fragment are highly flexible. The present work allows capturing typical features of the histone tail-counterion-DNA structure, interaction and dynamics.
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).
Seidler, Tomasz; Stadnicka, Katarzyna; Champagne, Benoît
2014-05-13
The linear [χ((1))] and second-order nonlinear [χ((2))] optical susceptibilities of the 2-methyl-4-nitroaniline (MNA) crystal are calculated within the local field theory, which consists of first computing the molecular properties, accounting for the dressing effects of the surroundings, and then taking into account the local field effects. Several aspects of these calculations are tackled with the aim of monitoring the convergence of the χ((1)) and χ((2)) predictions with respect to experiment by accounting for the effects of (i) the dressing field within successive approximations, of (ii) the first-order ZPVA corrections, and of (iii) the geometry. With respect to the reference CCSD-based results, besides double hybrid functionals, the most reliable exchange-correlation functionals are LC-BLYP for the static χ((1)) and CAM-B3LYP (and M05-2X, to a lesser extent) for the dynamic χ((1)) but they strongly underestimate χ((2)). Double hybrids perform better for χ((2)) but not necessarily for χ((1)), and, moreover, their performances are much similar to MP2, which is known to slightly overestimate β, with respect to high-level coupled-clusters calculations and, therefore, χ((2)). Other XC functionals with less HF exchange perform poorly with overestimations/underestimations of χ((1))/χ((2)), whereas the HF method leads to underestimations of both. The first-order ZPVA corrections, estimated at the B3LYP level, are usually small but not negligible. Indeed, after ZPVA corrections, the molecular polarizabilities and first hyperpolarizabilities increase by 2% and 5%, respectively, whereas their impact is magnified on the macroscopic responses with enhancements of χ((1)) by up to 5% and of χ((2)) by as much as 10%-12% at λ = 1064 nm. The geometry plays also a key role in view of predicting accurate susceptibilities, particularly for push-pull π-conjugated compounds such as MNA. So, the geometry optimized using periodic boundary conditions is characterized
Goldberg, C.S.; Pilliod, D.S.; Arkle, R.S.; Waits, L.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.
Hilbert, completeness and geometry
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Giorgio Venturi
2011-11-01
Full Text Available This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory.
Bär, Christian; Schwarz, Matthias
2012-01-01
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Mebs, Stefan; Chilleck, Maren Annika; Meindl, Kathrin; Hübschle, Christian Bertram
2014-06-19
Despite numerous advanced and widely distributed bonding theories such as MO, VB, NBO, AIM, and ELF/ELI-D, complex modes of bonding such as M-Cp*((R)) interactions (hapticities) in asymmetrical metallocenes or weak intramolecular interactions (e.g., hydrogen-hydrogen (H···H) bonds) still remain a challenge for these theories in terms of defining whether or not an atom-atom interaction line (a "chemical bond") should be drawn. In this work the intramolecular Zn-C(Cp*(R)) (R = Me, -(CH2)2NMe2, and -(CH2)3NMe2) and H···H connectivity of a systematic set of 12 zincocene-related compounds is analyzed in terms of AIM and ELI-D topology combined with the recently introduced aspherical stockholder fragment (ASF) surfaces. This computational analysis unravels a distinct dependency of the AIM and ELI-D topology against the molecular geometry for both types of interactions, which confirms and extends earlier findings on smaller sets of compounds. According to these results the complete real-space topology including strong, medium, and weak interactions of very large compounds such as proteins may be reliably predicted by sole inspection of accurately determined molecular geometries, which would on the one hand afford new applications (e.g., accurate estimation of numbers, types, and strengths of intra- and intermolecular interactions) and on the other hand have deep implications on the significance of the method.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Digital Differential Geometry Processing
Institute of Scientific and Technical Information of China (English)
Xin-Guo Liu; Hu-Jun Bao; Qun-Sheng Peng
2006-01-01
The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient,Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.
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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.
Institute of Scientific and Technical Information of China (English)
GUO Enli; MO Xiaohuan
2006-01-01
In this paper,a survey on Riemann-Finsler geometry is given.Non-trivial examples of Finsler metrics satisfying different curvature conditions are presented.Local and global results in Finsler geometry are analyzed.
Geometry essentials for dummies
Ryan, Mark
2011-01-01
Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque
Introduction to projective geometry
Wylie, C R
2008-01-01
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include w
Affine and Projective Geometry
Bennett, M K
1995-01-01
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY. This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory
Symplectic geometries on supermanifolds
Lavrov, P M
2007-01-01
Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with an non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of different symplectic geometries on supermanifolds.
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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
Laboulais, C; Le Bret, M; Gabarro-Arpa, J; Laboulais, Cyril; Ouali, Mohammed; Bret, Marc Le; Gabarro-Arpa, Jacques
2001-01-01
Protein structures can be encoded into binary sequences, these are used to define a Hamming distance in conformational space: the distance between two different molecular conformations is the number of different bits in their sequences. Each bit in the sequence arises from a partition of conformational space in two halves. Thus, the information encoded in the binary sequences is also used to characterize the regions of conformational space visited by the system. We apply this distance and their associated geometric structures, to the clustering and analysis of conformations sampled during a 4 ns molecular dynamics simulation of the HIV-1 integrase catalytic core. The cluster analysis of the simulation shows a division of the trajectory into two segments of 2.6 and 1.4 ns length, which are qualitatively different: the data points to the fact that equilibration is only reached at the end of the first segment. Some length of the paper is devoted to compare the Hamming distance to the r.m.s. deviation measure. Th...
Gualtieri, Marco
2010-01-01
Generalized Kahler geometry is the natural analogue of Kahler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We explore the fundamental aspects of this geometry, including its equivalence with the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2,2) supersymmetry, as well as the relation to holomorphic Dirac geometry and the resulting derived deformation theory. We also explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kahler geometry.
Methods for euclidean geometry
Byer, Owen; Smeltzer, Deirdre L
2010-01-01
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In several cases, the new ideas used in solving specific problems later developed into independent areas of mathematics. This book is primarily a geometry textbook, but studying geometry in this way will also develop students' appreciation of the subject and of mathematics as a whole. For instance, despite the fact that the analytic method has been part of mathematics for four centuries, it is rarely a tool a student considers using when faced with a geometry problem. Methods for Euclidean Geometry explores the application of a broad range of mathematical topics to the solution of Euclidean problems.
How effective is graphene nanopore geometry on DNA sequencing?
Satarifard, Vahid; Ejtehadi, Mohammad Reza
2015-01-01
In this paper we investigate the effects of graphene nanopore geometry on homopolymer ssDNA pulling process through nanopore using steered molecular dynamic (SMD) simulations. Different graphene nanopores are examined including axially symmetric and asymmetric monolayer graphene nanopores as well as five layer graphene polyhedral crystals (GPC). The pulling force profile, moving fashion of ssDNA, work done in irreversible DNA pulling and orientations of DNA bases near the nanopore are assessed. Simulation results demonstrate the strong effect of the pore shape as well as geometrical symmetry on free energy barrier, orientations and dynamic of DNA translocation through graphene nanopore. Our study proposes that the symmetric circular geometry of monolayer graphene nanopore with high pulling velocity can be used for DNA sequencing.
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.
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
Euclidean geometry and transformations
Dodge, Clayton W
1972-01-01
This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
Introduction to finite geometries
Kárteszi, F
1976-01-01
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geo
Sands, Robert; And Others
1982-01-01
Procedures for two demonstrations are provided. The solubility of ammonia gas in water is demonstrated by introducing water into a closed can filled with the gas, collapsing the can. The second demonstration relates scale of standard reduction potentials to observed behavior of metals in reactions with hydrogen to produce hydrogen gas. (Author/JN)
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
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....... It is shown that the excessive charge essentially affects the optimized geometry of strontium clusters. Ionization of small strontium clusters results in the alteration of the magic numbers. The strong dependence of the DOS spectra on details of ionic structure allows one to perform a reliable geometry...
Euclidean Geometry via Programming.
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability and compares it to…
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Geometry of multihadron production
Energy Technology Data Exchange (ETDEWEB)
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
1996-01-01
Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics. Designs and Finite Geometries serves as an excellent reference, providing insight into some of the most important research issues in the field.
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Bergshoeff, Eric A.; Riccioni, Fabio; Alvarez-Gaumé, L.
2011-01-01
We probe doubled geometry with dual fundamental branes. i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundam
Rutherford, Nicola J; Brooks, Mieu; Giasson, Benoit I
2016-08-08
Pathological inclusions containing aggregated, highly phosphorylated (at serine129) α-synuclein (αS pSer129) are characteristic of a group of neurodegenerative diseases termed synucleinopathies. Antibodies to the pSer129 epitope can be highly sensitive in detecting αS inclusions in human tissue and experimental models of synucleinopathies. However, the generation of extensively specific pSer129 antibodies has been problematic, in some cases leading to the misinterpretation of αS inclusion pathology. One common issue is cross-reactivity to the low molecular mass neurofilament subunit (NFL) phosphorylated at Ser473. Here, we generated a series of monoclonal antibodies to the pSer129 αS and pSer473 NFL epitopes. We determined the relative abilities of the known αS kinases, polo-like kinases (PLK) 1, 2 and 3 and casein kinase (CK) II in phosphorylating NFL and αS, while using this information to characterize the specificity of the new antibodies. NFL can be phosphorylated by PLK1, 2 and 3 at Ser473; however CKII shows the highest phosphorylation efficiency and specificity for this site. Conversely, PLK3 is the most efficient kinase at phosphorylating αS at Ser129, but there is overlay in the ability of these kinases to phosphorylate both epitopes. Antibody 4F8, generated to the pSer473 NFL epitope, was relatively specific for phosphorylated NFL, however it could uniquely cross-react with pSer129 αS when highly phosphorylated, further showing the structural similarity between these phospho-epitopes. All of the new pSer129 antibodies detected pathological αS inclusions in human brains and mouse and cultured cell experimental models of induced synucleinopathies. Several of these pSer129 αS antibodies reacted with the pSer473 NFL epitope, but 2 clones (LS3-2C2 and LS4-2G12) did not. However, LS3-2C2 demonstrated cross-reactivity with other proteins. Our findings further demonstrate the difficulties in generating specific pSer129 αS antibodies, but highlights
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.
Chemistry as a diagnostic of prestellar core geometry
Tritsis, A.; Tassis, K.; Willacy, K.
2016-05-01
We present a new method for assessing the intrinsic 3D shape of prestellar cores from molecular column densities. We have employed hydrodynamic simulations of contracting, isothermal cores considering three intrinsic geometries: spherical, cylindrical/filamentary and disc-like. We have coupled our hydrodynamic simulations with non-equilibrium chemistry. We find that (a) when cores are observed very elongated (i.e. for aspect ratios ≤0.15) the intrinsic 3D geometry can be probed by their 2D molecular emission maps, since these exhibit significant qualitative morphological differences between cylindrical and disc-like cores. Specifically, if a disc-like core is observed as a filamentary object in dust emission, then it will be observed as two parallel filaments in N2H+; (b) for cores with higher aspect ratios (i.e. 0.15-0.9) we define a metric Δ that quantifies whether a molecular column density profile is centrally peaked, depressed or flat. We have identified one molecule (CN) for which Δ as a function of the aspect ratio probes the 3D geometry of the core; and (c) for cores with almost circular projections (i.e. for aspect ratios ˜1), we have identified three molecules (OH, CO and H2CO) that can be used to probe the intrinsic 3D shape by close inspection of their molecular column density radial profiles. We alter the temperature and the cosmic ray ionization rate and demonstrate that our method is robust against the choice of parameters.
Gilbert, George L., Ed.
1983-01-01
Free radical chlorination of methane is used in organic chemistry to introduce free radical/chain reactions. In spite of its common occurrence, demonstrations of the reaction are uncommon. Therefore, such a demonstration is provided, including background information, preparation of reactants/reaction vessel, introduction of reactants, irradiation,…
Gilbert, George L., Ed.
1983-01-01
Discusses a supplement to the "water to rose" demonstration in which a pink color is produced. Also discusses blood buffer demonstrations, including hydrolysis of sodium bicarbonate, simulated blood buffer, metabolic acidosis, natural compensation of metabolic acidosis, metabolic alkalosis, acidosis treatment, and alkalosis treatment. Procedures…
Yelon, Stephen; Maddocks, Peg
1986-01-01
Describes four-step approach to educational demonstration: tell learners they will have to perform; what they should notice; describe each step before doing it; and require memorization of steps. Examples illustrate use of this process to demonstrate a general mental strategy, and industrial design, supervisory, fine motor, and specific…
Gilbert, George L., Ed.
1987-01-01
Describes two laboratory demonstrations in chemistry. One uses dry ice, freon, and freezer bags to demonstrate volume changes, vapor-liquid equilibrium, a simulation of a rain forest, and vaporization. The other uses the clock reaction technique to illustrate fast reactions and kinetic problems in releasing carbon dioxide during respiration. (TW)
Gilbert, George L., Ed.
1986-01-01
Outlines a simple, inexpensive way of demonstrating electroplating using the reaction between nickel ions and copper metal. Explains how to conduct a demonstration of the electrolysis of water by using a colored Na2SO4 solution as the electrolyte so that students can observe the pH changes. (TW)
Riemann-Finsler Geometry with Applications to Information Geometry
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. In this paper we briefly introduce RiemannFinsler geometry, by which we establish Information Geometry on a much broader base,so that the potential applications of Information Geometry will be beyond statistics.
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
Bonola, Roberto
2010-01-01
This is an excellent historical and mathematical view by a renowned Italian geometer of the geometries that have risen from a rejection of Euclid's parallel postulate. Students, teachers and mathematicians will find here a ready reference source and guide to a field that has now become overwhelmingly important.Non-Euclidean Geometry first examines the various attempts to prove Euclid's parallel postulate-by the Greeks, Arabs, and mathematicians of the Renaissance. Then, ranging through the 17th, 18th and 19th centuries, it considers the forerunners and founders of non-Euclidean geometry, such
Santo, J
1999-01-01
The ALICE Geometry Database project consists of the development of a set of data structures to store the geometrical information of the ALICE Detector. This Database will be used in Simulation, Reconstruction and Visualisation and will interface with existing CAD systems and Geometrical Modellers.At the present time, we are able to read a complete GEANT3 geometry, to store it in our database and to visualise it. On disk, we store different geometry files in hierarchical fashion, and all the nodes, materials, shapes, configurations and transformations distributed in this tree structure. The present status of the prototype and its future evolution will be presented.
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Kulczycki, Stefan
2008-01-01
This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff
Gilbert, George L.
1990-01-01
Included are three demonstrations that include the phase change of ice when under pressure, viscoelasticity and colloid systems, and flame tests for metal ions. The materials, procedures, probable results, and applications to real life situations are included. (KR)
Gilbert, George L., Ed.
1980-01-01
Presented is a Corridor Demonstration which can be set up in readily accessible areas such as hallways or lobbies. Equipment is listed for a display of three cells (solar cells, fuel cells, and storage cells) which develop electrical energy. (CS)
Gilbert, George L., Ed.
1987-01-01
Presents three demonstrations suitable for undergraduate chemistry classes. Focuses on experiments with calcium carbide, the induction by iron of the oxidation of iodide by dichromate, and the classical iodine clock reaction. (ML)
Elementary differential geometry
Pressley, Andrew
2001-01-01
Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood Differential geometry is concerned with the precise mathematical formulation of some of these questions, and with trying to answer them using calculus techniques It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces while keeping the prerequisites to an absolute minimum Nothing more than first courses in linear algebra and multivariate calculus are required, and the most direct and straightforward approach is used at all times Numerous diagrams illustrate both the ideas in the text and the examples of curves and surfaces discussed there The book will provide an invaluable resource to all those taking a first course in differential geometry, for their lecture...
Kumaresan, S
2005-01-01
Including Affine and projective classification of Conics, 2 point homogeneity's of the planes, essential isometrics, non euclidean plan geometrics, in this book, the treatment of Geometry goes beyond the Kleinian views.
Lectures on Symplectic Geometry
Silva, Ana Cannas
2001-01-01
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and cl...
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Geometry of differential equations
Khovanskiĭ, A; Vassiliev, V
1998-01-01
This volume contains articles written by V. I. Arnold's colleagues on the occasion of his 60th birthday. The articles are mostly devoted to various aspects of geometry of differential equations and relations to global analysis and Hamiltonian mechanics.
Facilitating Understandings of Geometry.
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
Introduction to tropical geometry
Maclagan, Diane
2015-01-01
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of t...
Melzak, Z A
2008-01-01
Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. 1983 edition.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Derived logarithmic geometry I
Steffen, Sagave; Timo, Schurg; Gabriele, Vezzosi
2016-01-01
In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \\'etale maps and use this to define derived log stacks.
Busemann, Herbert
2005-01-01
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text examines Desarguesian spaces, perpendiculars and parallels, covering spaces, the influence of the sign of the curvature on geodesics, more. 1955 edition. Includes 66 figures.
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2002-01-01
The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...
Hohmann, Manuel
2014-01-01
From general relativity we have learned the principles of general covariance and local Lorentz invariance, which follow from the fact that we consider observables as tensors on a spacetime manifold whose geometry is modeled by a Lorentzian metric. Approaches to quantum gravity, however, hint towards a breaking of these symmetries and the possible existence of more general, non-tensorial geometric structures. Possible implications of these approaches are non-tensorial transformation laws between different observers and an observer-dependent notion of geometry. In this work we review two different frameworks for observer dependent geometries, which may provide hints towards a quantization of gravity and possible explanations for so far unexplained phenomena: Finsler spacetimes and Cartan geometry on observer space. We discuss their definitions, properties and applications to observers, field theories and gravity.
Implosions and hypertoric geometry
DEFF Research Database (Denmark)
Dancer, A.; Kirwan, F.; Swann, A.
2013-01-01
The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion.......The geometry of the universal hyperkahler implosion for SU (n) is explored. In particular, we show that the universal hyperkahler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperkahler implosion....
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Schreiber, Urs
2016-01-01
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey examples and problems of interest. In section 3 we survey the abstract cohesive homotopy theory that serves to make all this precise and tractable.
Punzi, Raffaele; Wohlfarth, Mattias N R
2008-01-01
We reveal the non-metric geometry underlying omega-->0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking constrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
Energy Technology Data Exchange (ETDEWEB)
Punzi, Raffaele [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: raffaele.punzi@desy.de; Schuller, Frederic P. [Max Planck Institut fuer Gravitationsphysik, Albert Einstein Institut, Am Muehlenberg 1, 14467 Potsdam (Germany)], E-mail: fps@aei.mpg.de; Wohlfarth, Mattias N.R. [Zentrum fuer Mathematische Physik und II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)], E-mail: mattias.wohlfarth@desy.de
2008-12-11
We reveal the non-metric geometry underlying {omega}{yields}0 Brans-Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
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
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)
DEFF Research Database (Denmark)
Jensen, Tine Wirenfeldt; Bay, Gina
In this demonstration we present and discuss two interrelated on-line learning resources aimed at supporting international students at Danish universities in building study skills (the Study Metro) and avoiding plagiarism (Stopplagiarism). We emphasize the necessity of designing online learning r...
Generalist predators can regulate herbivore populations through a variety of mechanisms, but food webs are complex and defining the strength of trophic linkages can be difficult. Molecular gut-content analysis has revolutionized our understanding of these systems. Using this technology, we examined ...
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...
Bondi accretion in trumpet geometries
Miller, August J.; Baumgarte, Thomas W.
2017-02-01
The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Emergent Complex Network Geometry
Wu, Zhihao; Rahmede, Christoph; Bianconi, Ginestra
2014-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geo...
Computational synthetic geometry
Bokowski, Jürgen
1989-01-01
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to stud...
Supersymmetry and noncommutative geometry
Beenakker, Wim; Suijlekom, Walter D van
2016-01-01
In this work the question whether noncommutative geometry allows for supersymmetric theories is addressed. Noncommutative geometry has seen remarkable applications in high energy physics, viz. the geometrical interpretation of the Standard Model, however such a question has not been answered in a conclusive way so far. The book starts with a systematic analysis of the possibilities for so-called almost-commutative geometries on a 4-dimensional, flat background to exhibit not only a particle content that is eligible for supersymmetry, but also have a supersymmetric action. An approach is proposed in which the basic `building blocks' of potentially supersymmetric theories and the demands for their action to be supersymmetric are identified. It is then described how a novel kind of soft supersymmetry breaking Lagrangian arises naturally from the spectral action. Finally, the above formalism is applied to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model. This book is ...
Wetterich, C
2012-01-01
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes the "physical geometry"? We resolve this "metric ambiguity" by an investigation of the most general form of the quantum effective action for several metrics. In the long-distance limit the physical metric is universal and accounts for a massless graviton. Other degrees of freedom contained in the various metric candidates describe very massive scalars and symmetric second rank tensors. They only play a role at microscopic distances, typically around the Planck length. The universality of geometry at long distances extends to the vierbein and the connection. On the other hand, for distances and time intervals of Planck size geometry looses its universal meaning. Time is born with the big bang.
Cecil, Thomas E
2015-01-01
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hy...
Zheng, Fangyang
2002-01-01
The theory of complex manifolds overlaps with several branches of mathematics, including differential geometry, algebraic geometry, several complex variables, global analysis, topology, algebraic number theory, and mathematical physics. Complex manifolds provide a rich class of geometric objects, for example the (common) zero locus of any generic set of complex polynomials is always a complex manifold. Yet complex manifolds behave differently than generic smooth manifolds; they are more coherent and fragile. The rich yet restrictive character of complex manifolds makes them a special and interesting object of study. This book is a self-contained graduate textbook that discusses the differential geometric aspects of complex manifolds. The first part contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. The second part discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles, and gives a brief account of the surface classifi...
Integral Geometry and Holography
Czech, Bartlomiej; McCandlish, Samuel; Sully, James
2015-01-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
The Geometry of Conventionality
Weatherall, James Owen
2013-01-01
Hans Reichenbach famously argued that the geometry of spacetime is conventional in relativity theory, in the sense that one can freely choose the spacetime metric so long as one is willing to postulate a "universal force field". Here we make precise a sense in which the field Reichenbach defines fails to be a "force". We then argue that there is an interesting and perhaps tenable sense in which geometry is conventional in classical spacetimes. We conclude with a no-go result showing that the variety of conventionalism available in classical spacetimes does not extend to relativistic spacetimes.
Bowyer, Adrian
1983-01-01
A Programmer's Geometry provides a guide in programming geometric shapes. The book presents formulas and examples of computer representation and coding of geometry. Each of the nine chapters of the text deals with the representation and solution of a specific geometrical problem, such as areas, vectors, and volumes. The last chapter provides a brief discussion on generating image through a computer. The codes presented in the book are written in FORTRAN 77. The text will be of great use to programmers who are working on projects that involve geometric calculations.
Yale, Paul B
2012-01-01
This book is an introduction to the geometry of Euclidean, affine, and projective spaces with special emphasis on the important groups of symmetries of these spaces. The two major objectives of the text are to introduce the main ideas of affine and projective spaces and to develop facility in handling transformations and groups of transformations. Since there are many good texts on affine and projective planes, the author has concentrated on the n-dimensional cases.Designed to be used in advanced undergraduate mathematics or physics courses, the book focuses on ""practical geometry,"" emphasi
Eisenhart, L P
1927-01-01
The use of the differential geometry of a Riemannian space in the mathematical formulation of physical theories led to important developments in the geometry of such spaces. The concept of parallelism of vectors, as introduced by Levi-Civita, gave rise to a theory of the affine properties of a Riemannian space. Covariant differentiation, as developed by Christoffel and Ricci, is a fundamental process in this theory. Various writers, notably Eddington, Einstein and Weyl, in their efforts to formulate a combined theory of gravitation and electromagnetism, proposed a simultaneous generalization o
Participatory Lecture Demonstrations.
Battino, Rubin
1979-01-01
The use of participatory lecture demonstrations in the classroom is described. Examples are given for the following topics: chromatography, chemical kinetics, balancing equations, the gas laws, kinetic molecular theory, Henry's law of gas solubility, electronic energy levels in atoms, and translational, vibrational, and rotational energies of…
Geometry and scaling of cosmic voids
Gaite, Jose
2008-01-01
CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objective is to understand the geometry of cosmic voids in relation to a fractal structure of matter. We intend to distinguish monofractal voids from multifractal voids, regarding their scaling properties. We plan to analyse voids in the distributions of mass concentrations (halos) in a multifractal and their relation to galaxy voids. METHODS: We make a statistical analysis of point distributions based on the void probability function and correlation functions. We assume that voids are spherical and devise a simple spherical void finder. For continuous mass distributions, we employ the methods of fractal geometry. We confirm the analytical predictions with numerical simula...
Universal correlators from geometry
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Temuerhan, Mine; Sinkovics, Annamaria [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: sinkovic@science.uva.nl
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion. (author)
Universal Correlators from Geometry
Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-11-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Universal Correlators from Geometry
Dijkgraaf, R; Temurhan, M; Dijkgraaf, Robbert; Sinkovics, Annamaria; Temurhan, Mine
2004-01-01
Matrix model correlators show universal behaviour at short distances. We provide a derivation for these universal correlators by inserting probe branes in the underlying effective geometry. We generalize these results to study correlators of branes and their universal behaviour in the Calabi-Yau crystals, where we find a role for a generalized brane insertion.
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
Diophantine geometry an introduction
Hindry, Marc
2000-01-01
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Advanced geometries and regimes
Energy Technology Data Exchange (ETDEWEB)
Bulanov, S. S. [Univeristy of California, Berkeley, CA, 94720 (United States); Bulanov, S. V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Turchetti, G. [Dipartimento di Fisica, Università di Bologna and INFN Sezione di Bologna, Via Irnerio, 46-I-40126 Bologna (Italy); Limpouch, J.; Klimo, O.; Psikal, J. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague, Czech Republic and Czech Technical University in Prague, FNSPE, Brehova 7, 115 19 Prague (Czech Republic); Antici, P. [Dipartimento di Energetica ed INFM, Università di Roma, La Sapienza, 00165 Roma (Italy); Margarone, D.; Korn, G. [Institute of Physics of the ASCR, ELI-Beamlines/HiLASE project, Na Slovance 2, 18221 Prague (Czech Republic)
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Spacetime and Euclidean Geometry
Brill, D R; Brill, Dieter; Jacobson, Ted
2004-01-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm
2011-01-01
This paper applies I.M. Gelfand's distinction between adequate and non-adequate use of mathematical language in different contexts to the newly opened window of model-based measurements of intracellular dynamics. The specifics of geometry and dynamics on the mesoscale of cell physiology are elabo...
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
Hartshorne, Robin
2000-01-01
In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And ...
Boyer, Carl B
2012-01-01
Designed as an integrated survey of the development of analytic geometry, this study presents the concepts and contributions from before the Alexandrian Age through the eras of the great French mathematicians Fermat and Descartes, and on through Newton and Euler to the "Golden Age," from 1789 to 1850.
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
Energy Technology Data Exchange (ETDEWEB)
Vidas, E.H. [Energy and Environmental Analysis, Inc., Arlington, VA (United States)
1995-04-01
A prototype of the GASIS database and retrieval software has been developed and is the subject of this poster session and computer demonstration. The prototype consists of test or preliminary versions of the GASIS Reservoir Data System and Source Directory datasets and the software for query and retrieval. The prototype reservoir database covers the Rocky Mountain region and contains the full GASIS data matrix (all GASIS data elements) that will eventually be included on the CD-ROM. It is populated for development purposes primarily by the information included in the Rocky Mountain Gas Atlas. The software has been developed specifically for GASIS using Foxpro for Windows. The application is an executable file that does not require Foxpro to run. The reservoir database software includes query and retrieval, screen display, report generation, and data export functions. Basic queries by state, basin, or field name will be assisted by scrolling selection lists. A detailed query screen will allow record selection on the basis of any data field, such as depth, cumulative production, or geological age. Logical operators can be applied to any-numeric data element or combination of elements. Screen display includes a {open_quotes}browse{close_quotes} display with one record per row and a detailed single record display. Datasets can be exported in standard formats for manipulation with other software packages. The Source Directory software will allow record retrieval by database type or subject area.
An introduction to Minkowski geometries
Farnsworth, David L.
2016-07-01
The fundamental ideas of Minkowski geometries are presented. Learning about Minkowski geometries can sharpen our students' understanding of concepts such as distance measurement. Many of its ideas are important and accessible to undergraduate students. Following a brief overview, distance and orthogonality in Minkowski geometries are thoroughly discussed and many illustrative examples and applications are supplied. Suggestions for further study of these geometries are given. Indeed, Minkowski geometries are an excellent source of topics for undergraduate research and independent study.
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.
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
Lee, Jeongseog; Safdi, Benjamin R
2014-01-01
Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Reny...
Spectral Geometry and Causality
Kopf, T
1996-01-01
For a physical interpretation of a theory of quantum gravity, it is necessary to recover classical spacetime, at least approximately. However, quantum gravity may eventually provide classical spacetimes by giving spectral data similar to those appearing in noncommutative geometry, rather than by giving directly a spacetime manifold. It is shown that a globally hyperbolic Lorentzian manifold can be given by spectral data. A new phenomenon in the context of spectral geometry is observed: causal relationships. The employment of the causal relationships of spectral data is shown to lead to a highly efficient description of Lorentzian manifolds, indicating the possible usefulness of this approach. Connections to free quantum field theory are discussed for both motivation and physical interpretation. It is conjectured that the necessary spectral data can be generically obtained from an effective field theory having the fundamental structures of generalized quantum mechanics: a decoherence functional and a choice of...
Multivariate calculus and geometry
Dineen, Seán
2014-01-01
Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Bengtsson, Ingemar; Zyczkowski, Karol
2007-12-01
Preface; 1. Convexity, colours and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Density matrices and entropies; 13. Distinguishability measures; 14. Monotone metrics and measures; 15. Quantum entanglement; Epilogue; Appendices; References; Index.
Differential geometry and thermodynamics
Quevedo, H
2003-01-01
In this work we present the first steps of a new approach to the study of thermodynamics in the context of differential geometry. We introduce a fundamental differential 1-form and a metric on a pseudo-Euclidean manifold coordinatized by means of the extensive thermodynamic variables. The study of the connection and the curvature of these objects is initialized in this work by using Cartan structure equations. (Author)
Krauss, L M; Krauss, Lawrence M.; Turner, Michael S.
1999-01-01
The recognition that the cosmological constant may be non-zero forces us to re-evaluate standard notions about the connection between geometry and the fate of our Universe. An open Universe can recollapse, and a closed Universe can expand forever. As a corollary, we point out that there is no set of cosmological observations we can perform that will unambiguously allow us to determine what the ultimate destiny of the Universe will be.
Inflation from quantum geometry.
Bojowald, Martin
2002-12-23
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present day cosmological acceleration is so tiny.
DEFF Research Database (Denmark)
Tamke, Martin; Ramsgaard Thomsen, Mette; Riiber Nielsen, Jacob
2009-01-01
The versatility of wood constructions and traditional wood joints for the production of non standard elements was in focus of a design based research. Herein we established a seamless process from digital design to fabrication. A first research phase centered on the development of a robust parame...... parametric model and a generic design language a later explored the possibilities to construct complex shaped geometries with self registering joints on modern wood crafting machines. The research was carried out as collaboration with industrial partners....
Integral geometry and holography
Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-01
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts — points, distances and angles — are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.
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...
Generalised Geometry and Flux Vacua
Larfors, Magdalena
2015-01-01
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\\mathcal{N}}=1$ flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.
Dokukin, M. E.; Guz, N. V.; Woodworth, C.D.; Sokolov, I.
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. PMID:25844044
Ritz, Christiane M; Martins, Ludwig; Mecklenburg, Rainer; Goremykin, Vadim; Hellwig, Frank H
2007-08-01
The tropical Andes harbor a major part of the world's plant biodiversity. The montane cacti of the tribes Browningieae, Cereeae, and Trichocereeae underwent extensive radiation and thus are well suited as a model group to study the diversification of Andean plants. We reconstructed their phylogeny employing three noncoding chloroplast regions and explained it in the context of the geological history of South America. We found that the clade of cephalia-bearing cacti with naked pericarpels is centered in northeastern Brazil, whereas almost all other clades comprise Andean species. The spatial split between the clades was probably caused by the Andean uplift and the concurrent formation of intracontinental marine basins in the Tertiary. The phylogenetic reconstructions based on parsimony and Bayesian approaches do not reflect the traditional delimitation of the tribes and of the large genera. Our results suggest that Rebutia s.l. and Echinopsis s.l. are not monophyletic and that Sulcorebutia, Weingartia, and Cintia should be united into one genus. Even though this "Weingartia-complex" and the genus Gymnocalycium are similar in size and morphological diversity, Gymnocalycium has a very high molecular divergence suggesting a comparably older radiation.
Williamson, Rodney Lowell
Total geometry optimizations are reported for Cr(CO)_6, HMn(CO)_5 , Fe(CO)_5, Ni(CO) _4, Cr(C_6H _6)_2, Fe(C_5H _5)_2, Ni(C_4 H_4)_2, Cr(NO) _4, (C_5H _5)Mn(CO)_3, and (C _6H_6)Cr(CO) _3. A variety of basis sets were examined, and, based on the results, a relatively compact and accurate basis set is proposed. Addition of electron correlation at the perfect pairing GVB level reduced the average difference in the metal-cyclopentadienyl bond length of 0.08 A. Optimization of the geometry of TiCl_4 and TiCl_3CH_3 at the self-consistent-field (SCF) level results in Ti-Cl bond lengths longer than the experimental values, even when d- and f-type polarization functions are added to the basis set. The bond lengths remain too long even as the Hartree-Fock limit is approached because the SCF level of theory over-estimates the noble-gas-like Cl cdotsCl repulsions, which hinder close Ti -Cl approach. The Ti-C-H angle of TiCl_3 CH_3 is calculated to be close to tetrahedral geometry with little flattening of the hydrogen atoms, which apparently was observed in the electron diffraction. These same calculations do predict the anomalously low methyl-rocking frequency for the titanium complex in agreement with the experimental IR. The large positive geminal hydrogen coupling constant observed in the NMR experiment is due primarily to the sigma -donor and pi-acceptor character of the TiCl_3 moiety and not to any flattening of the methyl group. The structure and bonding of (Cr(Cp)(CO) _2) _2 was examined by optimizing the geometry of the dimer, fragment moiety, and analogous stable monomers. The optimized structure of Cr(Cp)(CO)_2N has a "piano stool" geometry with a fragment moiety geometry nearly identical to the geometry of the fragment moiety in the dimer. Examination of x-ray and theoretical geometries of monomers with the fragment moiety bonded to single ligand show that the geometry of the fragment moiety is insensitive to the ligands bonded to it. Van der Waals calculations
Fast rendering of scanned room geometries
DEFF Research Database (Denmark)
Olesen, Søren Krarup; Markovic, Milos; Hammershøi, Dorte
2014-01-01
.g. the range detection sensors used in the kinect device. This device provides a high rate of range data, which can be combined to give a very detailed map of the surrounding geometry. Such data was captured and has been presented in an earlier paper, incl. a demonstration of the principle of voxel...
Introductory non-Euclidean geometry
Manning, Henry Parker
1963-01-01
This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
Geometry for the Secondary School
Moalem, D.
1977-01-01
A sequential but non-axiomatic high school geometry course which includes Euclidean, transformation, and analytic geometry and vectors and matrices, and emphasizes the invariance property of transformations, is outlined. Sample problems, solutions, and comments are included. (MN)
Linear connections on matrix geometries
Madore, J; Mourad, J; Madore, John; Masson, Thierry; Mourad, Jihad
1994-01-01
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique metric connection.
Editors, LearningExpress
2010-01-01
Whether you're new to geometry or just looking for a refresher, this completely revised and updated third edition of Geometry Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with geometry essentials, Geometry Success in 20 Minutes a Day is an invaluable resource for both students and adults.
Geometry induced sequence of nanoscale Frank–Kasper and quasicrystal mesophases in giant surfactants
Energy Technology Data Exchange (ETDEWEB)
Yue, Kan; Huang, Mingjun; Marson, Ryan L.; He, Jinlin; Huang, Jiahao; Zhou, Zhe; Wang, Jing; Liu, Chang; Yan, Xuesheng; Wu, Kan; Guo, Zaihong; Liu, Hao; Zhang, Wei; Ni, Peihong; Wesdemiotis, Chrys; Zhang, Wen-Bin; Glotzer, Sharon C.; Cheng, Stephen Z.D. (Akron); (Soochow); (Michigan)
2016-11-28
Frank–Kasper (F-K) and quasicrystal phases were originally identified in metal alloys and only sporadically reported in soft materials. These unconventional sphere-packing schemes open up possibilities to design materials with different properties. The challenge in soft materials is how to correlate complex phases built from spheres with the tunable parameters of chemical composition and molecular architecture. Here, we report a complete sequence of various highly ordered mesophases by the self-assembly of specifically designed and synthesized giant surfactants, which are conjugates of hydrophilic polyhedral oligomeric silsesquioxane cages tethered with hydrophobic polystyrene tails. We show that the occurrence of these mesophases results from nanophase separation between the heads and tails and thus is critically dependent on molecular geometry. Variations in molecular geometry achieved by changing the number of tails from one to four not only shift compositional phase boundaries but also stabilize F-K and quasicrystal phases in regions where simple phases of spheroidal micelles are typically observed. These complex self-assembled nanostructures have been identified by combining X-ray scattering techniques and real-space electron microscopy images. Brownian dynamics simulations based on a simplified molecular model confirm the architecture-induced sequence of phases. Our results demonstrate the critical role of molecular architecture in dictating the formation of supramolecular crystals with “soft” spheroidal motifs and provide guidelines to the design of unconventional self-assembled nanostructures.
Thermodynamic geometry of minimum-dissipation driven barrier crossing
Sivak, David A.; Crooks, Gavin E.
2016-11-01
We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.
Teaching of Geometry in Bulgaria
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
2015-01-01
This stimulating volume offers a broad collection of the principles of geometry and trigonometry and contains colorful diagrams to bring mathematical principles to life. Subjects are enriched by references to famous mathematicians and their ideas, and the stories are presented in a very comprehensible way. Readers investigate the relationships of points, lines, surfaces, and solids. They study construction methods for drawing figures, a wealth of facts about these figures, and above all, methods to prove the facts. They learn about triangle measure for circular motion, sine and cosine, tangent
Abhyankar, Shreeram Shankar
1964-01-01
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from
Dooner, David B
2012-01-01
Building on the first edition published in 1995 this new edition of Kinematic Geometry of Gearing has been extensively revised and updated with new and original material. This includes the methodology for general tooth forms, radius of torsure', cylinder of osculation, and cylindroid of torsure; the author has also completely reworked the '3 laws of gearing', the first law re-written to better parallel the existing 'Law of Gearing" as pioneered by Leonard Euler, expanded from Euler's original law to encompass non-circular gears and hypoid gears, the 2nd law of gearing describing a unique relat
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Akopyan, A V
2007-01-01
The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca
REA, The Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Geometry I includes methods of proof, points, lines, planes, angles, congruent angles and line segments, triangles, parallelism, quadrilaterals, geometric inequalities, and geometric
The noncommutative geometry of Zitterbewegung
Eckstein, Michał; Miller, Tomasz
2016-01-01
Based on the mathematics of noncommutative geometry, we model a 'classical' Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung - the 'trembling motion' of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's 'internal space'. Furthermore, we show that the latter does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Higgs-like field. We discuss a table-top experiment in the domain of quantum simulation to test the predictions of the model and outline the consequences of our model for quantum gauge theories.
Geometry of Spinning Ellis Wormholes
Chew, Xiao Yan; Kunz, Jutta
2016-01-01
We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for non-symmetric wormholes. We present mass formulae for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limiting configurations corresponding to an extremal Kerr black hole. Moreover, we analyze the geodesics of these wormholes, and show that they possess bound orbits.
The Distance Geometry of Music
Demaine, Erik D; Meijer, Henk; Rappaport, David; Taslakian, Perouz; Toussaint, Godfried T; Winograd, Terry; Wood, David R
2007-01-01
We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\\emph{ostinatos}) from traditional world music. We prove that these \\emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \\emph{evenness}. We also show that essentially all Euclidean rhythms are \\emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful prop...
Interfacial geometry dictates cancer cell tumorigenicity
Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.
2016-08-01
Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.
Strontium clusters: electronic and geometry shell effects
DEFF Research Database (Denmark)
Lyalin, Andrey G.; Solov'yov, Ilia; Greiner, Walter
2008-01-01
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......The optimized structure and electronic properties of neutral, singly and doubly charged strontium clusters have been investigated using it 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, and spectra of the density of electronic states (DOS). It is demonstrated that the size-evolution of structural and electronic properties of strontium clusters...
Veronese geometry and the electroweak vacuum moduli space
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui, E-mail: hey@maths.ox.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); School of Physics, NanKai University, Tianjin 300071 (China); Merton College, University of Oxford, Oxford OX1 4JD (United Kingdom); Jejjala, Vishnu, E-mail: vishnu@neo.phys.wits.ac.za [Centre for Theoretical Physics, NITheP, and School of Physics, University of the Witwatersrand, Johannesburg, WITS 2050 (South Africa); Matti, Cyril, E-mail: Cyril.Matti.1@city.ac.uk [Department of Mathematics, City University, London, Northampton Square, London EC1V 0HB (United Kingdom); Nelson, Brent D., E-mail: b.nelson@neu.edu [Department of Physics, Northeastern University, Boston, MA 02115 (United States); ICTP, Strada Costiera 11, Trieste 34014 (Italy)
2014-09-07
We explain the origin of the Veronese surface in the vacuum moduli space geometry of the MSSM electroweak sector. While this result appeared many years ago using techniques of computational algebraic geometry, it has never been demonstrated analytically. Here, we present an analytical derivation of the vacuum geometry of the electroweak theory by understanding how the F- and D-term relations lead to the Veronese surface. We moreover give a detailed description of this geometry, realising an extra branch as a zero-dimensional point when quadratic Higgs lifting deformations are incorporated into the superpotential.
Byron, S.
1985-03-01
The low pressure gas-filled thyratron is scalable in the long dimension. Internally the tube is formed as a tetrode, with an auxiliary grid placed between the cathode and the control grid. A dc or pulsed power source drives the auxiliary grid both to insure uniform cathode emission and to provide a grid-cathode plasma prior to commutation. The high voltage holdoff structure consists of the anode, the control grid and its electrostatic shielding baffles, and a main quartz insulator. A small gas flow supply and exhaust system is used that eliminates the need for a hydrogen reservoir and permits other gases, such as helium, to be used. The thyratron provides a low inductance, high current, long lifetime switch configuration: useful for switch-on applications involving large scale lasers and other similar loads that are distributed in a linear geometry.
Critique of information geometry
Energy Technology Data Exchange (ETDEWEB)
Skilling, John, E-mail: skilling@eircom.net [Maximum Entropy Data Consultants Ltd, Kenmare (Ireland)
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Covariant Macroscopic Quantum Geometry
Hogan, Craig J
2012-01-01
A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Stockem, A.; Fiuza, F.; Silva, L. O.; Antici, P.; Margarone, D.; Korn, G.
2013-08-01
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project. At the request of the Proceedings Editors and Dr. Stepan Bulanov, University of California, Berkeley, the above article has been updated to include three additional authors: A. Stockem, F. Fiuza, and L. O. Silva. All additional authors have consented to their name being added to the paper. Furthermore, the updated article PDF contains amendments to a number of references as detailed within the pages attached to the end of the updated article PDF file. The updated article was re-published on 8 August 2013.
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
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…
Klein geometries, parabolic geometries and differential equations of finite type
Abadoglu, Ender
2009-01-01
We define the infinitesimal and geometric orders of an effective Klein geometry G/H. Using these concepts, we prove i) For any integer m>1, there exists an effective Klein geometry G/H of infinitesimal order m such that G/H is a projective variety (Corollary 9). ii) An effective Klein geometry G/H of geometric order M defines a differential equation of order M+1 on G/H whose global solution space is G (Proposition 18).
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
Chemistry as a diagnostic of prestellar core geometry
Tritsis, A.; Tassis, K.; Willacy, K
2016-01-01
We present a new method for assessing the intrinsic 3D shape of prestellar cores from molecular column densities. We have employed hydrodynamic simulations of contracting, isothermal cores considering three intrinsic geometries: spherical, cylindrical/filamentary and disk-like. We have coupled our hydrodynamic simulations with non-equilibrium chemistry. We find that a) when cores are observed very elongated (i.e. for aspect ratios $\\le$ 0.15) the intrinsic 3D geometry can be probed by their 2...
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...
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...
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François;
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Finding Proofs in Tarskian Geometry
Beeson, Michael; Wos, Larry
2016-01-01
We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some \\Otter proofs in Tarskian geometry (solving challenges issued in Wos's 1998...
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
2012-01-01
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Planetary Image Geometry Library
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Digital geometry in image processing
Mukhopadhyay, Jayanta
2013-01-01
Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing. The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of
Initiation to global Finslerian geometry
Akbar-Zadeh, Hassan
2006-01-01
After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, p
Speziale, Simone
2013-01-01
We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in discussing the interpretation of spin networks as the quantization of twisted geometries. The classical formalism can be extended in a natural way to null hypersurfaces, with the Euclidean polyhedra replaced by null polyhedra with space-like faces, and SU(2) by the little group ISO(2). The main difference is that the simplicity constraints present in the formalims are all first class, and the symplectic reduction selects only the helicity subgroup of the little group. As a consequence, information on the shapes of the polyhedra is lost, and the result is a much simpler, abelian geometric picture. It can be described by an Euclidean singular structure on the 2-dimensional space-like surface defined by a foliation of space-time by null hypersurfaces. This geometric structure is na...
Bhatia, Rajendra
2013-01-01
This book is an outcome of the Indo-French Workshop on Matrix Information Geometries (MIG): Applications in Sensor and Cognitive Systems Engineering, which was held in Ecole Polytechnique and Thales Research and Technology Center, Palaiseau, France, in February 23-25, 2011. The workshop was generously funded by the Indo-French Centre for the Promotion of Advanced Research (IFCPAR). During the event, 22 renowned invited french or indian speakers gave lectures on their areas of expertise within the field of matrix analysis or processing. From these talks, a total of 17 original contribution or state-of-the-art chapters have been assembled in this volume. All articles were thoroughly peer-reviewed and improved, according to the suggestions of the international referees. The 17 contributions presented are organized in three parts: (1) State-of-the-art surveys & original matrix theory work, (2) Advanced matrix theory for radar processing, and (3) Matrix-based signal processing applications.
Functional integration over geometries
Mottola, E
1995-01-01
The geometric construction of the functional integral over coset spaces {\\cal M}/{\\cal G} is reviewed. The inner product on the cotangent space of infinitesimal deformations of \\cal M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber \\cal G, the functional measure on the coset space {\\cal M}/{\\cal G} is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev-Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where \\cal G is the group of coordinate reparametrizations of spacetime, the continuum functional integral over geometries, {\\it i.e.} metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the me...
Itin, Yakov
2007-01-01
The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the coframe gravity is an aim of this paper. We construct a complete class of the coframe connections which are linear in the first order derivatives of the coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Ma...
Directory of Open Access Journals (Sweden)
Šárka Nedomová
2013-01-01
Full Text Available Precise quantification of the profile of egg can provide a powerful tool for the analysis of egg shape for various biological problems. A new approach to the geometry of a Ostrich’s egg profile is presented here using an analysing the egg’s digital photo by edge detection techniques. The obtained points on the eggshell counter are fitted by the Fourier series. The obtained equations describing an egg profile have been used to calculate radii of curvature. The radii of the curvature at the important point of the egg profile (sharp end, blunt end and maximum thickness are independent on the egg shape index. The exact values of the egg surface and the egg volume have been obtained. These quantities are also independent on the egg shape index. These quantities can be successively estimated on the basis of simplified equations which are expressed in terms of the egg length, L¸ and its width, B. The surface area of the eggshells also exhibits good correlation with the egg long circumference length. Some limitations of the most used procedures have been also shown.
Geometries from field theories
Aoki, Sinya; Kikuchi, Kengo; Onogi, Tetsuya
2015-10-01
We propose a method to define a d+1-dimensional geometry from a d-dimensional quantum field theory in the 1/N expansion. We first construct a d+1-dimensional field theory from the d-dimensional one via the gradient-flow equation, whose flow time t represents the energy scale of the system such that trArr 0 corresponds to the ultraviolet and trArr infty to the infrared. We then define the induced metric from d+1-dimensional field operators. We show that the metric defined in this way becomes classical in the large-N limit, in the sense that quantum fluctuations of the metric are suppressed as 1/N due to the large-N factorization property. As a concrete example, we apply our method to the O(N) nonlinear σ model in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.
Optimum Stirling engine geometry
Energy Technology Data Exchange (ETDEWEB)
Senft, J.R. [University of Wisconsin, River Walls, WI (United States). Mathematics Dept.
2002-07-01
This paper combines the author's work on mechanical efficiency of reciprocating engines with the classic Schmidt thermodynamic model for Stirling engines and revisits the problem of identifying optimal engine geometry. All previous optimizations using the Schmidt theory focused on obtaining a maximal specific indicated cyclic work. This does not necessarily produce the highest shaft output. Indeed, some optima based upon indicated work would yield engines that cannot run at all due to excessive intrinsic mechanical losses. The analysis presented in this paper shows how to optimize for shaft or brake work output. Specifically, it presents solutions to the problem of finding the piston-to-displacer swept volume ratio and phase angle which will give the maximum brake output for a given total swept volume, given temperature extremes, a given mean operating pressure, and a given engine mechanism effectiveness. The paper covers the split-cylinder or gamma-type Stirling in detail, serving as a model for similar analysis of the other Stirling engine configurations. (author)
Symbolic computations in applied differential geometry
Gragert, P.K.H.; Kersten, P. H. M.; Martini, R.
1983-01-01
The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples have been included in the text to demonstrate the concrete manipulations in practice. In the appendix, a list of programs discussed in the paper is added.
Graph-based representation for multiview image geometry.
Maugey, Thomas; Ortega, Antonio; Frossard, Pascal
2015-05-01
In this paper, we propose a new geometry representation method for multiview image sets. Our approach relies on graphs to describe the multiview geometry information in a compact and controllable way. The links of the graph connect pixels in different images and describe the proximity between pixels in 3D space. These connections are dependent on the geometry of the scene and provide the right amount of information that is necessary for coding and reconstructing multiple views. Our multiview image representation is very compact and adapts the transmitted geometry information as a function of the complexity of the prediction performed at the decoder side. To achieve this, our graph-based representation (GBR) carefully selects the amount of geometry information needed before coding. This is in contrast with depth coding, which directly compresses with losses the original geometry signal, thus making it difficult to quantify the impact of coding errors on geometry-based interpolation. We present the principles of this GBR and we build an efficient coding algorithm to represent it. We compare our GBR approach to classical depth compression methods and compare their respective view synthesis qualities as a function of the compactness of the geometry description. We show that GBR can achieve significant gains in geometry coding rate over depth-based schemes operating at similar quality. Experimental results demonstrate the potential of this new representation.
Surrogate Modeling for Geometry Optimization
DEFF Research Database (Denmark)
Rojas Larrazabal, Marielba de la Caridad; Abraham, Yonas; Holzwarth, Natalie;
2009-01-01
A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used.......A new approach for optimizing the nuclear geometry of an atomic system is described. Instead of the original expensive objective function (energy functional), a small number of simpler surrogates is used....
Analytic Geometry, A Tentative Guide.
Helwig, G. Alfred; And Others
This teacher's guide for a semester course in analytic geometry is based on the text "Analytic Geometry" by W. K. Morrill. Included is a daily schedule of suggested topics and homework assignments. Specific teaching hints are also given. The content of the course includes point and plane vectors, straight lines, point and space vectors, planes,…
Shafarevich, Igor Rostislavovich
1994-01-01
Shafarevich Basic Algebraic Geometry 2 The second edition of Shafarevich's introduction to algebraic geometry is in two volumes. The second volume covers schemes and complex manifolds, generalisations in two different directions of the affine and projective varieties that form the material of the first volume. Two notable additions in this second edition are the section on moduli spaces and representable functors, motivated by a discussion of the Hilbert scheme, and the section on Kähler geometry. The book ends with a historical sketch discussing the origins of algebraic geometry. From the Zentralblatt review of this volume: "... one can only respectfully repeat what has been said about the first part of the book (...): a great textbook, written by one of the leading algebraic geometers and teachers himself, has been reworked and updated. As a result the author's standard textbook on algebraic geometry has become even more important and valuable. Students, teachers, and active researchers using methods of al...
Index Theorems on Torsional Geometries
Kimura, Tetsuji
2007-01-01
We study various topological invariants on a differential geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH=0. By using the identification between the Clifford algebra on a geometry and the canonical quantization condition of fermion in the quantum mechanics, we construct the N=1 quantum mechanical sigma model in the Hamiltonian formalism and extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We improve the formulation of the Dirac index on the torsional geometry which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional geometry.
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.
The Geometry of Bourges Cathedral
Directory of Open Access Journals (Sweden)
Robert Bork
2014-09-01
Full Text Available This article presents a geometrical analysis of Bourges Cathedral, based on the application of computer-aided design (CAD techniques to the results of a recent and highly precise laser survey. This analysis reveals that the cathedral's original designer developed a tightly interlocking and strikingly unified design, in which the five-fold subdivision of the chevet ground plan set proportions that would be vertically extruded into an elevation that can be inscribed both within a square and within a series of progessively smaller equilaterial triangles. These results contribute to an ongoing debate about the use of ‘ad quadratum’ and ‘ad triangulum’ geometries in Gothic architecture, and they provide new evidence for the geometrical coherence of Gothic cathedral design. In methodological terms, meanwhile, this discussion demonstrates the potential of CAD-based geometrical analysis for the study of precisely surveyed medieval buildings. The sequence of images being analysed can be viewed as supplementary material at: http://dx.doi.org/10.5334/ah.bz.s1
Sheikhi, Masoome; Shahab, Siyamak; Filippovich, Liudmila; Khaleghian, Mehrnoosh; Dikusar, Evgenij; Mashayekhi, Mahsa
2017-10-01
In this present work, first time interaction between new synthesized derivative of the 4-((E)-((4-((E)-phenyldiazenyl)phenyl)imino)methyl)benzoic acid (E-PABA) and the BN(6,6-7) Nanotube for medical applications were studied. The geometries of the compounds E-PABA, the BN(6,6-7) Nanotube and the Complex BN(6,6-7)/E-PABA were optimized by Density Functional Theory (DFT) in the gas phase. The adsorption effect of the compound E-PABA on the electronic properties, chemical shift tensors and natural charge of the BN(6,6-7) Nanotube was investigated and discussed. The electronic spectra of the E-PABA and the Complex BN(6,6-7)/E-PABA in the gas phase carried out by Time Dependent Density Functional Theory (TD-DFT) for the foundation adsorption effect on maximum wavelength of the E-PABA.
The Geometry Description Markup Language
Institute of Scientific and Technical Information of China (English)
RadovanChytracek
2001-01-01
Currently,a lot of effort is being put on designing complex detectors.A number of simulation and reconstruction frameworks and applications have been developed with the aim to make this job easier.A very important role in this activity is played by the geometry description of the detector apparatus layout and its working environment.However,no real common approach to represent geometry data is available and such data can be found in various forms starting from custom semi-structured text files,source code (C/C++/FORTRAN),to XML and database solutions.The XML(Extensible Markup Language)has proven to provide an interesting approach for describing detector geometries,with several different but incompatible XML-based solutions existing.Therefore,interoperability and geometry data exchange among different frameworks is not possible at present.This article introduces a markup language for geometry descriptions.Its aim is to define a common approach for sharing and exchanging of geometry description data.Its requirements and design have been driven by experience and user feedback from existing projects which have their geometry description in XML.
Hamilton geometry: Phase space geometry from modified dispersion relations
Barcaroli, Leonardo; Gubitosi, Giulia; Loret, Niccoló; Pfeifer, Christian
2015-01-01
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a simultaneous description of both spacetime curvature and non-trivial momentum space geometry. We consider as explicit examples two models for Planck-scale modified dispersion relations, inspired from the $q$-de Sitter and $\\kappa$-Poincar\\'e quantum groups. In the first case we find the expressions for the momentum and position dependent curvature of spacetime and momentum space, while for the second case the manifold is flat and only the momentum space possesses a nonzero, momentum dependent curvature. In contrast, for a dispersion relation that is induced by a spacetime metric, as in General Relativity, the Hamilton geometry yields a flat momentum space and the usual curved spacetime geometry with only position dependent geometric objects.
Hull, C. M.
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Ho...
Linear algebra, geometry and transformation
Solomon, Bruce
2014-01-01
Vectors, Mappings and Linearity Numeric Vectors Functions Mappings and Transformations Linearity The Matrix of a Linear Transformation Solving Linear Systems The Linear SystemThe Augmented Matrix and RRE Form Homogeneous Systems in RRE Form Inhomogeneous Systems in RRE Form The Gauss-Jordan Algorithm Two Mapping Answers Linear Geometry Geometric Vectors Geometric/Numeric Duality Dot-Product Geometry Lines, Planes, and Hyperplanes System Geometry and Row/Column Duality The Algebra of Matrices Matrix Operations Special Matrices Matrix Inversion A Logical Digression The Logic of the Inversion Alg
Walsh, Edward T
2014-01-01
This introductory text is designed to help undergraduate students develop a solid foundation in geometry. Early chapters progress slowly, cultivating the necessary understanding and self-confidence for the more rapid development that follows. The extensive treatment can be easily adapted to accommodate shorter courses. Starting with the language of mathematics as expressed in the algebra of logic and sets, the text covers geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, space geometry, and coordinate geometry. Each chapter incl
Fallow), Stray
2009-01-01
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and angle calculations just make your head spin? Relax. With Head First 2D Geometry, you'll master everything from triangles, quads and polygons to the time-saving secrets of similar and congruent angles -- and it'll be quick, painless, and fun. Through entertaining stories and practical examples from the world around you, this book takes you beyond boring problems. You'll actually use what you learn to make real-life decisions, like using angles and parallel lines to crack a mysterious CSI case. Put geometry to work for you, and
Adler, Irving
1967-01-01
This richly detailed overview surveys the development and evolution of geometrical ideas and concepts from ancient times to the present. In addition to the relationship between physical and mathematical spaces, it examines the interactions of geometry, algebra, and calculus. The text proves many significant theorems and employs several important techniques. Chapters on non- Euclidean geometry and projective geometry form brief, self-contained treatments.More than 100 exercises with answers and 200 diagrams illuminate the text. Teachers, students (particularly those majoring in mathematics educa
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
Quantum Consequences of Parameterizing Geometry
Wanas, M. I.
2002-12-01
The marriage between geometrization and quantization is not successful, so far. It is well known that quantization of gravity , using known quantization schemes, is not satisfactory. It may be of interest to look for another approach to this problem. Recently, it is shown that geometries with torsion admit quantum paths. Such geometries should be parameterizied in order to preserve the quantum properties appeared in the paths. The present work explores the consequences of parameterizing such geometry. It is shown that quantum properties, appeared in the path equations, are transferred to other geometric entities.
Hull, C M
1993-01-01
The higher-spin geometries of $W_\\infty$-gravity and $W_N$-gravity are analysed and used to derive the complete non-linear structure of the coupling to matter and its symmetries. The symmetry group is a subgroup of the symplectic diffeomorphisms of the cotangent bundle of the world-sheet, and the $W_N$ geometry is obtained from a non-linear truncation of the $W_\\infty$ geometry. Quantum W-gravity is briefly discussed. (Talk given at {\\it Pathways to Fundamental Interactions}, the 16th John Hopkins Workshop on Current Problems in Particle Theory, Gothenborg, 1992.)
Thermal Phase in Bubbling Geometries
Institute of Scientific and Technical Information of China (English)
LIU Chang-Yong
2008-01-01
We use matrix model to study thermal phase in bubbling half-BPS type IIB geometries with SO(4)×SO(4) symmetry.Near the horizon limit,we find that thermal vacua of bubbling geometries have disjoint parts,and each part is one kind of phase of the thermal system.We connect the thermal dynamics of bubbling geometries with one-dimensional fermions thermal system.Finally,we try to give a new possible way to resolve information loss puzzle.
An improved combinatorial geometry model for arbitrary geometry in DSMC
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
Levav-Waynberg, Anat; Leikin, Roza
2012-01-01
The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…
Convex Geometry and Stoichiometry
Jer-Chin,
2011-01-01
We demonstrate the benefits of a convex geometric perspective for questions on chemical stoichiometry. We show that the balancing of chemical equations, the use of "mixtures" to explain multiple stoichiometry, and the half-reaction for balancing redox actions all yield nice convex geometric interpretations. We also relate some natural questions on reaction mechanisms with the enumeration of lattice points in polytopes. Lastly, it is known that a given reaction mechanism imposes linear constraints on observed stoichiometries. We consider the inverse question of deducing reaction mechanism consistent with a given set of linear stoichiometric restrictions.
Multiscale Talbot effects in Fibonacci geometry
Ho, I-Lin
2014-01-01
This article investigates the Talbot effects in Fibonacci geometry by introducing the cut-and-project construction, which allows for capturing the entire infinite Fibonacci structure into a single computational cell. Theoretical and numerical calculations demonstrate the Talbot foci of Fibonacci geometry at distances that are multiples $(\\tau+2)(F_{\\mu}+\\tau F_{\\mu+1} )^{-1}p/(2q)$ or $(\\tau+2)(L_{\\mu}+\\tau L_{\\mu+1} )^{-1}p/(2q)$ of the Talbot distance. Here, ($p$, $q$) are coprime integers, $\\mu$ is an integer, $\\tau$ is the golden mean, and $F_{\\mu}$ and $L_{\\mu}$ are Fibonacci and Lucas numbers, respectively. The image of a single Talbot focus exhibits a multiscale pattern due to the self-similarity of the scaling Fourier spectrum.
AC Dielectrophoresis Using Elliptic Electrode Geometry
Directory of Open Access Journals (Sweden)
S. M. Rezaul Hasan
2011-01-01
Full Text Available This paper presents negative AC dielectrophoretic investigations using elliptic electrode geometry. Simulations of the electric field gradient variation using various ratios of the semimajor and the semiminor axis were carried out to determine the optimum elliptic geometry for the dielectrophoretic electrokinetics of specimen in an assay with laminar (low Reynolds number fluid flow. Experimental setup of the elliptic electrode assembly using PCB fabrication and electrokinetic accumulation of specimen in a dielectrophoretic cage is also being reported. Using an actuating signal between 1 kHz and 1 MHz, successful trapping of 45 μm polystyrene beads suspended in distilled water was demonstrated due to negative dielectrophoresis near 100 kHz using the novel elliptic electrode.
Hyperbolic Metamaterials with Complex Geometry
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Zhukovsky, Sergei
2016-01-01
We investigate new geometries of hyperbolic metamaterialssuch as highly corrugated structures, nanoparticle monolayer assemblies, super-structured or vertically arranged multilayersand nanopillars. All structures retain basic propertiesof hyperbolic metamaterials, but have functionality improved...
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
An introduction to differential geometry
Willmore, T J
2012-01-01
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Instability of supersymmetric microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Moment methods in extremal geometry
De Laat, D.
2016-01-01
In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state
Guide to Computational Geometry Processing
DEFF Research Database (Denmark)
Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François
be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction......Optical scanning is rapidly becoming ubiquitous. From industrial laser scanners to medical CT, MR and 3D ultrasound scanners, numerous organizations now have easy access to optical acquisition devices that provide huge volumes of image data. However, the raw geometry data acquired must first......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Paper Interfaces for Learning Geometry
Bonnard, Quentin; Verma, Himanshu; Kaplan, Frédéric; Dillenbourg, Pierre
2012-01-01
Paper interfaces offer tremendous possibilities for geometry education in primary schools. Existing computer interfaces designed to learn geometry do not consider the integration of conventional school tools, which form the part of the curriculum. Moreover, most of computer tools are designed specifically for individual learning, some propose group activities, but most disregard classroom-level learning, thus impeding their adoption. We present an augmented reality based tabletop system with ...
Courant Algebroids in Parabolic Geometry
Armstrong, Stuart
2011-01-01
To a smooth manifold $M$, a parabolic geometry associates a principal bundle, which has a parabolic subgroup of a semisimple Lie group as its structure group, and a Cartan connection. We show that the adjoint tractor bundle of a regular normal parabolic geometry can be endowed with the structure of a Courant algebroid. This gives a class of examples of transitive Courant algebroids that are not exact.
Topology and geometry for physicists
Nash, Charles
2011-01-01
Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. ""Thoroughly recommended"" by The Physics Bulletin, this volume's physics applications range fr
Higgs mass in noncommutative geometry
Energy Technology Data Exchange (ETDEWEB)
Devastato, A.; Martinetti, P. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Lizzi, F. [Dipartimento di Fisica, Universita di Napoli Federico II, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli, Via Cintia, 80126 Napoli (Italy); Departament de Estructura i Constituents de la Materia, Universitat de Barcelona, Marti y Franques, Barcelona, Catalonia (Spain)
2014-09-11
In the noncommutative geometry approach to the standard model, an extra scalar field σ - initially suggested by particle physicist to stabilize the electroweak vacuum - makes the computation of the Higgs mass compatible with the 126 GeV experimental value. We give a brief account on how to generate this field from the Majorana mass of the neutrino, following the principles of noncommutative geometry. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
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 Common Geometry Module (CGM).
Energy Technology Data Exchange (ETDEWEB)
Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
Interaction of light and matter produces the appearance of materials. To deal with the immense complexity of nature, light and matter is modelled at a macroscopic level in computer graphics. This work is the first to provide the link between the microscopic physical theories of light and matter...... of a material and determine the contents of the material. The book is in four parts. Part I provides the link between microscopic and macroscopic theories of light. Part II describes how to use the properties of microscopic particles to compute the macroscopic properties of materials. Part III illustrates...... that we can use geometrical models to handle the large number of variables which appear when we construct appearance models from microscopic theories. Finally, Part IV provides detailed appearance models for natural water, ice, and milk to demonstrate how the theory is applied....
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.
Holomorphic Cartan geometries and rational curves
Biswas, Indranil
2010-01-01
We prove that any compact K\\"ahler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact K\\"ahler manifold.
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.
Useful Demonstrations for a Medial Biochemistry Course.
Ragatz, Barth H.; Modrak, Gina
1986-01-01
Describes six demonstrations used in a medical biochemistry course. These demonstrations focus on: (1) platelet aggregometry; (2) ion-transporting antibiotics; (3) glycosylated hemoglobin; (4) molecular models; (5) serum preparation; and (6) bioluminescence. (JN)
Pandey, Ravindra; Ghosh, Sampa; Mukhopadhyay, S; Ramasesha, S; Das, Puspendu K
2011-01-28
We report large quadratic nonlinearity in a series of 1:1 molecular complexes between methyl substituted benzene donors and quinone acceptors in solution. The first hyperpolarizability, β(HRS), which is very small for the individual components, becomes large by intermolecular charge transfer (CT) interaction between the donor and the acceptor in the complex. In addition, we have investigated the geometry of these CT complexes in solution using polarization resolved hyper-Rayleigh scattering (HRS). Using linearly (electric field vector along X direction) and circularly polarized incident light, respectively, we have measured two macroscopic depolarization ratios D=I(2ω,X,X)/I(2ω,Z,X) and D(')=I(2ω,X,C)/I(2ω,Z,C) in the laboratory fixed XYZ frame by detecting the second harmonic scattered light in a polarization resolved fashion. The experimentally obtained first hyperpolarizability, β(HRS), and the value of macroscopic depolarization ratios, D and D('), are then matched with the theoretically deduced values from single and double configuration interaction calculations performed using the Zerner's intermediate neglect of differential overlap self-consistent reaction field technique. In solution, since several geometries are possible, we have carried out calculations by rotating the acceptor moiety around three different axes keeping the donor molecule fixed at an optimized geometry. These rotations give us the theoretical β(HRS), D and D(') values as a function of the geometry of the complex. The calculated β(HRS), D, and D(') values that closely match with the experimental values, give the dominant equilibrium geometry in solution. All the CT complexes between methyl benzenes and chloranil or 1,2-dichloro-4,5-dicyano-p-benzoquinone investigated here are found to have a slipped parallel stacking of the donors and the acceptors. Furthermore, the geometries are staggered and in some pairs, a twist angle as high as 30° is observed. Thus, we have demonstrated in
Geometry optimization made simple with translation and rotation coordinates
Wang, Lee-Ping; Song, Chenchen
2016-06-01
The effective description of molecular geometry is important for theoretical studies of intermolecular interactions. Here we introduce a new translation-rotation-internal coordinate (TRIC) system which explicitly includes the collective translations and rotations of molecules, or parts of molecules such as monomers or ligands, as degrees of freedom. The translations are described as the centroid position and the orientations are represented with the exponential map parameterization of quaternions. When TRIC is incorporated into geometry optimization calculations, the performance is consistently superior to existing coordinate systems for a diverse set of systems including water clusters, organic semiconductor donor-acceptor complexes, and small proteins, all of which are characterized by nontrivial intermolecular interactions. The method also introduces a new way to scan the molecular orientations while allowing orthogonal degrees of freedom to relax. Our findings indicate that an explicit description of molecular translation and rotation is a natural way to traverse the many-dimensional potential energy surface.
General Construction of Tubular Geometry
Mukhopadhyay, Partha
2016-01-01
We consider the problem of locally describing tubular geometry around a submanifold embedded in a (pseudo)Riemannian manifold in its general form. Given the geometry of ambient space in an arbitrary coordinate system and equations determining the submanifold in the same system, we compute the tubular expansion coefficients in terms of this {\\it a priori data}. This is done by using an indirect method that crucially applies the tubular expansion theorem for vielbein previously derived. With an explicit construction involving the relevant coordinate and non-coordinate frames we verify consistency of the whole method up to quadratic order in vielbein expansion. Furthermore, we perform certain (long and tedious) higher order computation which verifies the first non-trivial spin connection term in the expansion for the first time. Earlier a similar method was used to compute tubular geometry in loop space. We explain this work in the light of our general construction.
Quantum geometry and gravitational entropy
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Conventionalism and integrable Weyl geometry
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
Wave propagation on microstate geometries
Keir, Joseph
2016-01-01
Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two and three charge supersymmetric microstate geometries, finding a number of surprising results. In both cases we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three charge microstates possess an ergoregion; these geometries therefore avoid Friedman's "ergosphere instability". In fact, in the three charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although this data must have nontrivial dependence on the Kaluza-Klein coordinate. In the two charge case we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform dec...
Euclidean geometry and its subgeometries
Specht, Edward John; Calkins, Keith G; Rhoads, Donald H
2015-01-01
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
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
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
Geometry Design of Wooden Barrels
Directory of Open Access Journals (Sweden)
Ivan CISMARU
2010-12-01
Full Text Available The aim of this paper is to present a design methodology of the wooden barrel geometry, as an algorithm of successive calculations. Thus, starting from the required elements (volume, length, shape, maximum height of storage space the user will be able to define the geometry which must be obtained by processing. Based on these calculations, one can define the structure, size and shape of the staves in order to establish the processing technology of both components and subassemblies (jacket and bottoms which are to form the final product by their assembling using metal circles.
Geometry, topology, and string theory
Energy Technology Data Exchange (ETDEWEB)
Varadarajan, Uday
2003-07-10
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...
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
Lectures on classical differential geometry
Struik, Dirk J
1988-01-01
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student.Writ
Gauging Geometry: A Didactic Lecture
Kannenberg, L
2016-01-01
Local inertial frame invariance is taken as the fundamental principle of physical geometry, where a local inertial frame is represented by a verbein. Invariance of the vierbein with respect to local Lorentz transformations then expresses local inertial frame invariance. The dynamics of physical geometry develops as a gauge theory of the verbein that is closely analogous to the Yang-Mills field provided the verbein connection and curvature correspond to the geometric potential and field respectively. The resulting theory is shown to be equivalent to Einstein's tensor form of relativistic gravitation.
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
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
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
NASA Bioreactor Demonstration System
2002-01-01
Leland W. K. Chung (left), Director, Molecular Urology Therapeutics Program at the Winship Cancer Institute at Emory University, is principal investigator for the NASA bioreactor demonstration system (BDS-05). With him is Dr. Jun Shu, an assistant professor of Orthopedics Surgery from Kuming Medical University China. The NASA Bioreactor provides a low turbulence culture environment which promotes the formation of large, three-dimensional cell clusters. Due to their high level of cellular organization and specialization, samples constructed in the bioreactor more closely resemble the original tumor or tissue found in the body. The Bioreactor is rotated to provide gentle mixing of fresh and spent nutrient without inducing shear forces that would damage the cells. The work is sponsored by NASA's Office of Biological and Physical Research. The bioreactor is managed by the Biotechnology Cell Science Program at NASA's Johnson Space Center (JSC). NASA-sponsored bioreactor research has been instrumental in helping scientists to better understand normal and cancerous tissue development. In cooperation with the medical community, the bioreactor design is being used to prepare better models of human colon, prostate, breast and ovarian tumors. Cartilage, bone marrow, heart muscle, skeletal muscle, pancreatic islet cells, liver and kidney are just a few of the normal tissues being cultured in rotating bioreactors by investigators. Credit: Emory University.
Teaching Activity-Based Taxicab Geometry
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Differential geometry meets the cell.
Marshall, Wallace F
2013-07-18
A new study by Terasaki et al. highlights the role of physical forces in biological form by showing that connections between stacked endoplasmic reticulum cisternae have a shape well known in classical differential geometry, the helicoid, and that this shape is a predictable consequence of membrane physics.
Energy Technology Data Exchange (ETDEWEB)
Byrd, M.
1997-10-01
The group SU(3) is parameterized in terms of generalized {open_quotes}Euler angles{close_quotes}. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is found, and some relevant comments about the geometry of the group manifold are made.
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Signature geometry and quantum engineering
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Instructional Identities of Geometry Students
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
Loop groups and noncommutative geometry
Carpi, Sebastiano
2015-01-01
We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group LG. The construction is based on certain supersymmetric conformal field theory models associated with LG.
3DHZETRN: Inhomogeneous Geometry Issues
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.
2017-01-01
Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.
The Basics of Information Geometry
Caticha, Ariel
2014-01-01
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".
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
Foucault pendulum through basic geometry
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
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…
Open problems in algebraic geometry
Edixhoven, S.J.; Moonen, B.J.J.; Oort, F.
2000-01-01
The open problems presented here were collected on the occasion of a workshop on Arithmetic Geometry at the University ofUtrecht, 26{30 June, 2000. This workshop was organized by the editors of the present article, and was made possible by support of: | NWO, the Netherlands Organization for
Data Imprecision in Computational Geometry
Löffler, M.
2009-01-01
The field of computational geometry is concerned with the design and analysis of geometric algorithms. For such algorithms, correctness and efficiency proofs are constructed, or problems are proven to be hard when no correct and efficient algorithms exist. In order to be able to do this, several ass
GEOMETRY AND COMPLEXITY IN ARCHITECTURE
Directory of Open Access Journals (Sweden)
RUSU Maria Ana
2015-06-01
Full Text Available As Constantin Brancuși (1876-1956 said „Simplicity is complexity itself“, simplicity and regularity through the use of basic geometric forms has always played a central role in architectural design, during the 20th century. A diachronic perspective, shows as the use of geometry and mathematics to describe built form provided a common basis for communication between the processes of design, fabrication and stability. Classic ways of representing geometry, based on descriptive methods, favor precise language of bidimensionality easy to represent in a rectangular coordinate system. In recent years, the importance of geometry has been re-emphasized by significant advances in the digital age, where computers are increasingly used in design, fabrication and construction to explore the art of the possible. Contemporary architecture transcend the limitations of Euclidean geometry and create new forms that are emerging through the convergence of complex systems, computational design and robotic fabrication devices, but which can also achieve higher levels of performance. Freeform architectural shapes and structures play an increasingly important role in 21st century architectural design. Through a series of examples, the paper relates to contemporary architectural explorations of complex, curvilinear surfaces in the digital age and discusses how it has required rethinking the mode in which we traditionally operate as architects. The analysis creates the possibility of comparisons between original and current design.
Absolute configuration determination using enantiomeric pairs of molecularly imprinted polymers.
Meador, Danielle S; Spivak, David A
2014-03-07
A new method for determination of absolute configuration (AC) is demonstrated using an enantiomeric pair of molecularly imprinted polymers, referred to as "DuoMIPs". The ratio of HPLC capacity factors (k') for the analyte on each of the DuoMIPs is defined as the γ factor and can be used to determine AC when above 1.2. A mnemonic based on the complementary binding geometry of the DuoMIPs was used to aid in understanding and prediction of AC.
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...
Directory of Open Access Journals (Sweden)
Drawert Brian
2012-06-01
Full Text Available Abstract Background 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. Results 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
Peptide encapsulation regulated by the geometry of carbon nanotubes.
Zhang, Zhi-Sen; Kang, Yu; Liang, Li-Jun; Liu, Ying-Chun; Wu, Tao; Wang, Qi
2014-02-01
In this work the encapsulation of an α-helical peptide in single carbon nanotubes (CNTs) with similar diameter and length but different geometry (armchair and zigzag) was investigated through molecular dynamics simulations and free energy calculations. Our simulation results showed that in vacuo it makes no evident difference whether the investigated peptide is encapsulated in armchair or zigzag CNTs; however, in aqueous solution the armchair CNT encapsulates the peptide remarkably easier than the zigzag CNT does. A detailed analysis revealed that the equilibrium conformation of the water molecules inside the CNTs with varying geometry mediates the peptide encapsulation. It suggests that the water molecules play an important role in regulating behaviors of biomolecules in bio-systems. Then the impact of the CNT geometry on the conformational changes of the confined peptide was studied. Analyses of secondary structures showed the α-helix of the peptide could be better maintained in the zigzag CNT.
An analysis of fractal geometry of macromolecular gelation
Institute of Scientific and Technical Information of China (English)
左榘; 陈天红; 冉少峰; 何炳林; 董宝中; 生文君; 杨恒林
1996-01-01
With fractal geometry theory and based on experiments, an analysis of fractal geometry behavior of gelation of macromolecules was carried out. Using the cross-linking copolymerization of styrene-divinylbenzene (DVB) as an example, through the determinations of the evolution of the molecular weight, size and the dependence of scattering intensity on the angle of macromolecules by employing laser and synchrotron small angle X-ray scattering, respectively, this chemical reaction was described quantitatively, its fractal behavior was analyzed and the fractal dimension was also measured. By avoiding the complex theories on gelation, this approach is based on modern physical techniques and theories to perform the analysis of the behavior of fractal geometry of macromolecular gelation and thus is able to reveal the rules of this kind of complicated gelation more essentially and profoundly.
Geometry of Membrane Sigma Models
Vysoky, Jan
2015-01-01
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathematical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better ...
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...
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 surfaces contact
Directory of Open Access Journals (Sweden)
Siegl J.
2007-11-01
Full Text Available This contribution deals with a geometrical exact description of contact between two given surfaces which are defined by the vector functions. These surfaces are substituted at a contact point by approximate surfaces of the second order in accordance with the Taylor series and consequently there is derived a differential surface of these second order surfaces. Knowledge of principal normal curvatures, their directions and the tensor (Dupin indicatrix of this differential surface are necessary for description of contact of these surfaces. For description of surface geometry the first and the second surface fundamental tensor and a further methods of the differential geometry are used. A geometrical visualisation of obtained results of this analysis is made. Method and results of this study will be applied to contact analysis of tooth screw surfaces of screw machines.
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...
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.
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...
Beyond core knowledge: Natural geometry
Spelke, Elizabeth; Lee, Sang Ah; Izard, Véronique
2010-01-01
For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. PMID:20625445
Gear geometry of cycloid drives
Institute of Scientific and Technical Information of China (English)
CHEN BingKui; FANG TingTing; LI ChaoYang; WANG ShuYan
2008-01-01
According to differential geometry and gear geometry,the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion.The correct meshing condition,contact line,contact ratio,calculating method for pin tooth's maximum contact point are developed.Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1,2,3 and -1,respectively.A general method called enveloping method to generate hypocycloid and epicycloid is put forward.The correct mesh-ing condition for cycloid pin wheel gearing is provided,and the contact line and the contact ratio are also discussed.
Geometry of polycrystals and microstructure
Directory of Open Access Journals (Sweden)
Ball John M.
2015-01-01
Full Text Available We investigate the geometry of polycrystals, showing that for polycrystals formed of convex grains the interior grains are polyhedral, while for polycrystals with general grain geometry the set of triple points is small. Then we investigate possible martensitic morphologies resulting from intergrain contact. For cubic-totetragonal transformations we show that homogeneous zero-energy microstructures matching a pure dilatation on a grain boundary necessarily involve more than four deformation gradients. We discuss the relevance of this result for observations of microstructures involving second and third-order laminates in various materials. Finally we consider the more specialized situation of bicrystals formed from materials having two martensitic energy wells (such as for orthorhombic to monoclinic transformations, but without any restrictions on the possible microstructure, showing how a generalization of the Hadamard jump condition can be applied at the intergrain boundary to show that a pure phase in either grain is impossible at minimum energy.
Gear geometry of cycloid drives
Institute of Scientific and Technical Information of China (English)
2008-01-01
According to differential geometry and gear geometry, the equation of meshing for small teeth difference planetary gearing and a universal equation of conjugated profile are established based on cylindrical pin tooth and given motion. The correct meshing condition, contact line, contact ratio, calculating method for pin tooth’s maximum contact point are developed. Investigation on the theory of conjugated meshing is carried out when the tooth difference numbers between pin wheel and cycloidal gear are 1, 2, 3 and ?1, respectively. A general method called enveloping method to generate hypocycloid and epicycloid is put forward. The correct meshing condition for cycloid pin wheel gearing is provided, and the contact line and the contact ratio are also discussed.
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.
Core foundations of abstract geometry.
Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S
2013-08-27
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
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.
Geometry for the accelerating universe
Punzi, R; Wohlfarth, M N R; Punzi, Raffaele; Schuller, Frederic P.; Wohlfarth, Mattias N.R.
2006-01-01
The Lorentzian spacetime metric is replaced by an area metric which naturally emerges as a generalized geometry in quantum string and gauge theory. Employing the area metric curvature scalar, the gravitational Einstein-Hilbert action is re-interpreted as dynamics for an area metric. Without the need for dark energy or fine-tuning, area metric cosmology explains the observed small acceleration of the late Universe.
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 ...
Black Holes as Effective Geometries
Balasubramanian, Vijay; El-Showk, Sheer; Messamah, Ilies
2008-01-01
Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective t...
Introduction to geometry and relativity
2013-01-01
This book provides a lucid introduction to both modern differential geometry and relativity for advanced undergraduates and first-year graduate students of applied mathematics and physical sciences. This book meets an overwhelming need for a book on modern differential geometry and relativity that is student-friendly, and which is also suitable for self-study. The book presumes a minimal level of mathematical maturity so that any student who has completed the standard Calculus sequence should be able to read and understand the book. The key features of the book are: Detailed solutions are provided to the Exercises in each chapter; Many of the missing steps that are often omitted from standard mathematical derivations have been provided to make the book easier to read and understand; A detailed introduction to Electrodynamics is provided so that the book is accessible to students who have not had a formal course in this area; In its treatment of modern differential geometry, the book employs both a modern, c...
Solution NMR structure of a designed metalloprotein and complementary molecular dynamics refinement.
Calhoun, Jennifer R; Liu, Weixia; Spiegel, Katrin; Dal Peraro, Matteo; Klein, Michael L; Valentine, Kathleen G; Wand, A Joshua; DeGrado, William F
2008-02-01
We report the solution NMR structure of a designed dimetal-binding protein, di-Zn(II) DFsc, along with a secondary refinement step employing molecular dynamics techniques. Calculation of the initial NMR structural ensemble by standard methods led to distortions in the metal-ligand geometries at the active site. Unrestrained molecular dynamics using a nonbonded force field for the metal shell, followed by quantum mechanical/molecular mechanical dynamics of DFsc, were used to relax local frustrations at the dimetal site that were apparent in the initial NMR structure and provide a more realistic description of the structure. The MD model is consistent with NMR restraints, and in good agreement with the structural and functional properties expected for DF proteins. This work demonstrates that NMR structures of metalloproteins can be further refined using classical and first-principles molecular dynamics methods in the presence of explicit solvent to provide otherwise unavailable insight into the geometry of the metal center.
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
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.
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
Towards a Nano Geometry? Geometry and Dynamics on Nano Scale
Booss-Bavnbek, Bernhelm
2012-01-01
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 elaborated - in contrast to the familiar Newtonian mechanics and the more recent, but by now also rather well established quantum field theories. Examples are given originating from the systems biology of insulin secreting pancreatic beta-cells and the mathematical challenges of an envisioned non-invasive control of magnetic nanoparticles.
An Observer-Based Foundation of Geometry
Bahreyni, Newshaw; Knuth, Kevin H.
2012-02-01
The fact that some events influence other events enables one to define a partially ordered set (poset) of events, often referred to as a causal set. A chain of events, called observer chain, can be quantified by labeling its events numerically. Other events in a poset may be quantified with respect to an observer chain/chains by projecting them onto the chain, resulting in a pair of numbers. Similarly, pairs of events, called intervals, can be quantified with four numbers. Under certain conditions, this leads to the Minkowski metric, Lorentz transformations and the mathematics of special relativity (Bahreyni & Knuth, APS March Meeting 2011). We exploit the same techniques to demonstrate that geometric concepts can be derived from order-theoretic concepts. We show how chains in a poset can be used to define points and line segments. Subsequent quantification results in the Pythagorean Theorem and the inner product as well as other geometric concepts and measures. Thus the geometry of space, which is assumed to be fundamental, emerges as a result of quantifying a partially ordered set. More importantly, this proposed foundation of geometry is entirely observer-based, which may provide a natural way toward integration with quantum mechanics.
Transfer of polarized line radiation in 2D cylindrical geometry
Milić, I.
2013-07-01
Aims: This paper deals with multidimensional NLTE polarized radiative transfer in the case of two level atom in the absence of lower level polarization. We aim to develop an efficient and robust method for 2D cylindrical geometry and to apply it to various axi-symmetrical astrophysical objects such as rings, disks, rotating stars, and solar prominences. Methods: We review the methods of short characteristics and Jacobi iteration applied to axisymmetric geometry. Then we demonstrate how to use a reduced basis for polarized intensity and polarized source function to self-consistently solve the coupled equations of radiative transfer and statistical equilibrium for linearly polarized radiation. We discuss some peculiarities that do not appear in Cartesian geometry, such as angular interpolation in performing the formal solution. We also show how to account for two different types of illuminating radiation. Results: The proposed method is tested on homogeneous, self-emitting cylinders to compare the results with those in 1D geometries. We demonstrate a possible astrophysical application on a very simple model of circumstellar ring illuminated by a host star where we show that such a disk can introduce a significant amount of scattering polarization in the system. Conclusions: This method is found to converge properly and, apparently, to allow for substantial time saving compared to 3D Cartesian geometry. We also discuss the advantages and disadvantages of this approach in multidimensional radiative transfer modeling.
Molecular coupling of light with plasmonic waveguides
Kuzyk, Anton; Toppari, J Jussi; Hakala, Tommi K; Tikkanen, Hanna; Kunttu, Henrik; Torma, Paivi
2007-01-01
We use molecules to couple light into and out of microscale plasmonic waveguides. Energy transfer, mediated by surface plasmons, from donor molecules to acceptor molecules over ten micrometer distances is demonstrated. Also surface plasmon coupled emission from the donor molecules is observed at similar distances away from the excitation spot. The lithographic fabrication method we use for positioning the dye molecules allows scaling to nanometer dimensions. The use of molecules as couplers between far-field and near-field light offers the advantages that no special excitation geometry is needed, any light source can be used to excite plasmons and the excitation can be localized below the diffraction limit. Moreover, the use of molecules has the potential for integration with molecular electronics and for the use of molecular self-assembly in fabrication. Our results constitute a proof-of-principle demonstration of a plasmonic waveguide where signal in- and outcoupling is done by molecules.
LIMB Demonstration Project Extension and Coolside Demonstration
Energy Technology Data Exchange (ETDEWEB)
Goots, T.R.; DePero, M.J.; Nolan, P.S.
1992-11-10
This report presents results from the limestone Injection Multistage Burner (LIMB) Demonstration Project Extension. LIMB is a furnace sorbent injection technology designed for the reduction of sulfur dioxide (SO[sub 2]) and nitrogen oxides (NO[sub x]) emissions from coal-fired utility boilers. The testing was conducted on the 105 Mwe, coal-fired, Unit 4 boiler at Ohio Edison's Edgewater Station in Lorain, Ohio. In addition to the LIMB Extension activities, the overall project included demonstration of the Coolside process for S0[sub 2] removal for which a separate report has been issued. The primary purpose of the DOE LIMB Extension testing, was to demonstrate the generic applicability of LIMB technology. The program sought to characterize the S0[sub 2] emissions that result when various calcium-based sorbents are injected into the furnace, while burning coals having sulfur content ranging from 1.6 to 3.8 weight percent. The four sorbents used included calcitic limestone, dolomitic hydrated lime, calcitic hydrated lime, and calcitic hydrated lime with a small amount of added calcium lignosulfonate. The results include those obtained for the various coal/sorbent combinations and the effects of the LIMB process on boiler and plant operations.
Adhesion and the Geometry of the Cosmic Web
Hidding, Johan; Vegter, Gert; Jones, Bernard J T
2012-01-01
We present a new way to formulate the geometry of the Cosmic Web in terms of Lagrangian space. The Adhesion model has an ingenious geometric interpretation out of which the spine of the Cosmic Web emerges naturally. Within this context we demonstrate a deep connection of the relation between Eulerian and Lagrangian space with that between Voronoi and Delaunay tessellations.
Application of Analytic Geometry to Ternary and Quaternary Diagrams.
MacCarthy, Patrick
1986-01-01
Advantages of representing ternary and quaternary composition diagrams by means of rectangular coordinates were pointed out in a previous paper (EJ 288 693). A further advantage of that approach is that analytic geometry, based on rectangular coordinates, is directly applicable as demonstrated by the examples presented. (JN)
Satheeshkumar, Rajendran; Sayin, Koray; Kaminsky, Werner; Rajendra Prasad, Karnam Jayarampillai
2017-01-01
7-Chloro-9-(2'-chlorophenyl)-2,3-dihydroacridin-4(1H)-one (3a) and 7-chloro-9-(2'-fluorophenyl)-2,3-dihydroacridin-4-(1H)-one (3b) were synthesized from 2-amino-2‧,5-dichlorobenzophenone (1a) and 2-amino-5-chloro-2'-fluorobenzophenone (1b) respectively with 1,2-cyclohexanedione (2) in the presence of 1-butyl-3-methylimidazolium tetrafluoroborate and InCl3 condition. The synthesized compounds have been recorded of FT-IR, NMR spectra and the structure was further confirmed by using single crystal X-ray diffraction. The synthesized compounds have been further checked the photo physical properties like UV, emission and fluorescent quantum yields were calculated. FT-NMR spectra and 1H and 13C NMR chemical shifts have been measured and computational calculations of compounds 3 are done by using B3LYP method with 6-311G basis set in gas phase. Similarly calculated vibrational frequencies were found in good agreement with experimental findings. The optimized geometry of molecules 3 was compared with experimental XRD values. DFT calculations of the molecular electrostatic potential (MEP) and HOMO - LUMO frontier orbitals identified chemically active sites of compounds 3 responsible for its chemical reactivity.
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)
Generalised Complex Geometry in Thermodynamical Fluctuation Theory
Directory of Open Access Journals (Sweden)
P. Fernández de Córdoba
2015-08-01
Full Text Available We present a brief overview of some key concepts in the theory of generalized complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyze thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalized complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction.
Mesoscopic model for filament orientation in growing actin networks: the role of obstacle geometry
Weichsel, Julian; 10.1088/1367-2630/15/3/035006
2013-01-01
Propulsion by growing actin networks is a universal mechanism used in many different biological systems. Although the core molecular machinery for actin network growth is well preserved in most cases, the geometry of the propelled obstacle can vary considerably. In recent years, filament orientation distribution has emerged as an important observable characterizing the structure and dynamical state of the growing network. Here we derive several continuum equations for the orientation distribution of filaments growing behind stiff obstacles of various shapes and validate the predicted steady state orientation patterns by stochastic computer simulations based on discrete filaments. We use an ordinary differential equation approach to demonstrate that for flat obstacles of finite size, two fundamentally different orientation patterns peaked at either +35/-35 or +70/0/-70 degrees exhibit mutually exclusive stability, in agreement with earlier results for flat obstacles of very large lateral extension. We calculat...
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Students' Misconceptions and Errors in Transformation Geometry
Ada, Tuba; Kurtulus, Aytac
2010-01-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…
Global continuation for distance geometry problems
Energy Technology Data Exchange (ETDEWEB)
More, J.J.; Wu, Zhijun
1995-03-01
Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. The authors formulate the distance geometry problem as a global minimization problem with special structure, and show the global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.
Geometry in the Early Years: A Commentary
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Number Theory, Analysis and Geometry
Goldfeld, Dorian; Jones, Peter
2012-01-01
Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th
Integral geometry and representation theory
Gel'fand, I M; Vilenkin, N Ya
1966-01-01
Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one.This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of comp
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
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.
Adding momentum to supersymmetric geometries
Energy Technology Data Exchange (ETDEWEB)
Lunin, Oleg, E-mail: olunin@albany.edu [Department of Physics, University at Albany (SUNY), Albany, NY 12222 (United States); Mathur, Samir D., E-mail: mathur.16@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States); Turton, David, E-mail: turton.7@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)
2013-03-11
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a traveling wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T{sup 4}. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
Adding momentum to supersymmetric geometries
Lunin, Oleg; Turton, David
2012-01-01
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
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
Generalised geometry for string corrections
Coimbra, André; Triendl, Hagen; Waldram, Daniel
2014-01-01
We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz--Bismut theorem. As examples of this construction we discuss the corrections linear in $\\alpha'$ in heterotic strings and the absence of such corrections for type II theories.
Loop quantum geometry: a primer
Energy Technology Data Exchange (ETDEWEB)
Corichi, Alejandro [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico)
2005-01-15
This is the written version of a lecture given at the 'VI Mexican School of Gravitation and Mathematical Physics' (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate students and non-experts interested in learning the basics of the subject.
Exceptional geometry and Borcherds superalgebras
Palmkvist, Jakob
2015-01-01
We study generalized diffeomorphisms in exceptional geometry with U-duality group E_{n(n)} from an algebraic point of view. By extending the Lie algebra e_n to an infinite-dimensional Borcherds superalgebra, involving also the extension to e_{n+1}, the generalized Lie derivatives can be expressed in a simple way, and the expressions take the same form for any n less than 8. The closure of the transformations then follows from the Jacobi identity and the grading of e_{n+1} with respect to e_n.
Complexity and Shock Wave Geometries
Stanford, Douglas
2014-01-01
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by $G_N l_{AdS}$. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.
Loop Quantum Geometry: A primer
Corichi, Alejandro
2005-01-01
This is the written version of a lecture given at the ``VI Mexican School of Gravitation and Mathematical Physics" (Nov 21-27, 2004, Playa del Carmen, Mexico), introducing the basics of Loop Quantum Geometry. The purpose of the written contribution is to provide a Primer version, that is, a first entry into Loop Quantum Gravity and to present at the same time a friendly guide to the existing pedagogical literature on the subject. This account is geared towards graduate students and non-expert...
Isosurfaces geometry, topology, and algorithms
Wenger, Rephael
2013-01-01
Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. In color throughout, the book covers the Marching Cubes algorithm and variants, dual contouring algorithms, multilinear interpolation, multiresolutio
Quanta of geometry and unification
Chamseddine, Ali H.
2016-11-01
This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Quanta of Geometry and Unification
Chamseddine, Ali H
2016-01-01
This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Numerical shadow and geometry of quantum states
Energy Technology Data Exchange (ETDEWEB)
Dunkl, Charles F [Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137 (United States); Gawron, Piotr; Miszczak, Jaroslaw A; Puchala, Zbigniew [Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Baltycka 5, 44-100 Gliwice (Poland); Holbrook, John A [Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Zyczkowski, Karol, E-mail: cfd5z@virginia.edu, E-mail: gawron@iitis.pl, E-mail: jholbroo@uoguelph.ca, E-mail: miszczak@iitis.pl, E-mail: z.puchala@iitis.pl, E-mail: karol@tatry.if.uj.edu.pl [Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow (Poland)
2011-08-19
The totality of normalized density matrices of dimension N forms a convex set Q{sub N} in R{sup N2-1}. Working with the flat geometry induced by the Hilbert-Schmidt distance, we consider images of orthogonal projections of Q{sub N} onto a two-plane and show that they are similar to the numerical ranges of matrices of dimension N. For a matrix A of dimension N, one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP{sup N-1}. We define generalized, mixed-state shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.
Numerical shadow and geometry of quantum states
Dunkl, Charles F; Holbrook, John A; Miszczak, Jarosław A; Puchała, Zbigniew; Życzkowski, Karol
2011-01-01
The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.
Geometry and stability of dynamical systems
Punzi, Raffaele
2008-01-01
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional geometric structure that is not intrinsic to the dynamical system itself. While global Lyapunov stability is based on the choice of seminorms on the vector bundle of perturbations, we propose a definition of local stability based on the choice of a linear connection. We show how this definition reproduces known stability criteria for second order dynamical systems. In contrast to the general case, the special geometry of Lagrangian systems provides completely intrinsic notions of global and local stability. We demonstrate that these do not suffer from the limitations occurring in the analysis of the Maupertuis-Jacobi geodesics associated to natural Lagrangian systems.
Magnetic geometry and particle source drive of supersonic divertor regimes
Bufferand, H.; Ciraolo, G.; Dif-Pradalier, G.; Ghendrih, P.; Tamain, Ph; Marandet, Y.; Serre, E.
2014-12-01
We present a comprehensive picture of the mechanisms driving the transition from subsonic to supersonic flows in tokamak plasmas. We demonstrate that supersonic parallel flows into the divertor volume are ubiquitous at low density and governed by the divertor magnetic geometry. As the density is increased, subsonic divertor plasmas are recovered. On detachment, we show the change in particle source can also drive the transition to a supersonic regime. The comprehensive theoretical analysis is completed by simulations in ITER geometry. Such results are essential in assessing the divertor performance and when interpreting measurements and experimental evidence.
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)
Laar, P.J.L.J. van de
2013-01-01
In this chapter, we discuss the Poseidon demonstrator: a demonstrator that integrates the individual research results of all partners of the Poseidon project. After describing how the Poseidon demonstrator was built, deployed, and operated, we will not only show many results obtained from the demons
Overhead Projector Demonstrations.
Kolb, Doris, Ed.
1988-01-01
Details two demonstrations for use with an overhead projector in a chemistry lecture. Includes "A Very Rapidly Growing Silicate Crystal" and "A Colorful Demonstration to Simulate Orbital Hybridization." The materials and directions for each demonstration are included as well as a brief explanation of the essential learning involved. (CW)
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.
Quanta of Geometry: Noncommutative Aspects
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
2015-03-01
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.
Warped Geometry of Brane Worlds
Felder, G; Kofman, L A; Felder, Gary; Frolov, Andrei; Kofman, Lev
2002-01-01
We study the dynamical equations for a warp factor and a bulk scalar in 5d brane world scenarios. These equations are similar to those for the time dependence of the scale factor and a scalar field in 4d cosmology, but with the sign of the scalar field potential reversed. Based on this analogy, we introduce two novel methods for studying the warped geometry. First, we construct the full phase portraits of the warp factor/scalar system for several examples of the bulk potential. This allows us to view the global properties of the warped geometry. For flat branes, the phase portrait is two dimensional. Moving along typical phase trajectories, the warp factor is initially increasing and finally decreasing. All trajectories have timelike gradient-dominated singularities at one or both of their ends, which are reachable in a finite distance and must be screened by the branes. For curved branes, the phase portrait is three dimensional. However, as the warp factor increases the phase trajectories tend towards the tw...
Weyl gravity and Cartan geometry
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Geometry and the Quantum: Basics
Chamseddine, Ali H; Mukhanov, Viatcheslav
2014-01-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these represen...
Fuzzy Logic for Incidence Geometry.
Tserkovny, Alex
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.
Toric Geometry and String Theory
Bouchard, Vincent
2006-01-01
In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities. These objects torically encode the local geometry of a degeneration of an elliptic fibration. We classify all tops and give a prescription for assigning an affine, possibly twisted Kac-Moody algebra to any such top. Tops related to twisted Kac-Moody algebras can be used to construct string compactifications with reduced rank of the gauge group. Secondly, we compute all loop closed and open topological string amplitudes on orientifolds of toric Calabi-Yau threefolds, by using geometric transitions involving SO/Sp Chern-Simons theory, localization on the moduli space of holomorphic maps with involution, and the topological vertex. In particular, we count Klein bottles and projective planes with any number of handles in some Calabi-Yau orientifolds. We determine the BPS structure of the amplitudes, and illustrate ou...
Ring polymers in confined geometries
Usatenko, Z; Kuterba, P
2016-01-01
The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interactions (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size were performed. Taking into account the correspondence between the field theoretical $\\phi^4$ $O(n)$-vector model in the limit $n\\to 0$ and the behavior of long-flexible polymer chains in a good solvent the correspondent depletion interaction potentials, depletion forces and the forces which exert phantom ideal ring and ring polymer chains with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions d=3 up to one-loop order. Additionally, the investigation of a dilute solution of phantom ideal ring polymers in a slit geometry of two inert walls and mixed walls with one repulsive and other one inert wall were performed and correspondent depletion interaction potentials and the depletion forces were cal...
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Weyl gravity and Cartan geometry
Attard, Jeremy; Lazzarini, Serge
2015-01-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned by two theories: the first one will be the associated Yang-Mills-like Lagrangian, while the second, inspired by~\\cite{Wheeler2014}, will be a slightly more general one which will relax the conformal Cartan geometry. The corresponding gauge symmetry is treated within the BRST language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the `normal conformal Cartan connection'. Finally, we provide in a Lagrangian framework a justification of the identification, in dimension $4$, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in ...
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.
Coordinated standoff tracking of moving targets using differential geometry
Institute of Scientific and Technical Information of China (English)
Zhi-qiang SONG; Hua-xiong LI; Chun-lin CHEN; Xian-zhong ZHOU; Feng XU
2014-01-01
This research is concerned with coordinated standoff tracking, and a guidance law against a moving target is proposed by using differential geometry. We first present the geometry between the unmanned aircraft (UA) and the target to obtain the convergent solution of standoff tracking when the speed ratio of the UA to the target is larger than one. Then, the convergent solution is used to guide the UA onto the standoff tracking geometry. We propose an improved guidance law by adding a derivative term to the relevant algorithm. To keep the phase angle difference of multiple UAs, we add a second derivative term to the relevant control law. Simulations are done to demonstrate the feasibility and performance of the proposed approach. The proposed algo-rithm can achieve coordinated control of multiple UAs with its simplicity and stability in terms of the standoff distance and phase angle difference.
Extreme localized exhumation at syntaxes initiated by subduction geometry
Bendick, Rebecca; Ehlers, Todd A.
2014-08-01
Some of the highest and most localized rates of lithospheric deformation in the world are observed at the transition between adjacent plate boundary subduction segments. The initiating perturbation of this deformation has long been attributed to vigorous erosional processes as observed at Nanga Parbat and Namche Barwa in the Himalaya and at Mount St. Elias in Alaska. However, an erosion-dominated mechanism ignores the 3-D geometry of curved subducting plates. Here we present an alternative explanation for rapid exhumation at these locations based on the 3-D thermomechanical evolution of collisions between plates with nonplanar geometries. Comparison of model predictions with existing data reproduces the defining characteristics of these mountains and offers an explanation for their spatial correlation with arc termini. These results demonstrate a "bottom-up" tectonic rather than "top-down" erosional initiation of feedbacks between erosion and tectonic deformation; hence, the importance of 3-D subduction geometry.
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.
Cell dipole behaviour revealed by ECM sub-cellular geometry
Mandal, Kalpana; Wang, Irène; Vitiello, Elisa; Orellana, Laura Andreina Chacòn; Balland, Martial
2014-12-01
Cells sense and respond to their mechanical environment by exerting forces on their surroundings. The way forces are modulated by extra-cellular matrix (ECM) properties plays a key role in tissue homoeostasis. Using highly resolved micropatterns that constrain cells into the same square envelope but vary the adhesive geometry, here we investigate how the adhesive micro-environment affects the architecture of actin cytoskeleton and the orientation of traction forces. Our data demonstrate that local adhesive changes can trigger orientational ordering of stress fibres throughout the cell, suggesting that cells are capable of integrating information on ECM geometry at the whole-cell level. Finally, we show that cells tend to generate highly polarized force pattern, that is, unidirectional pinching, in response to adequate adhesive conditions. Hence, the geometry of adhesive environment can induce cellular orientation, a process which may have significant implications for the formation and mechanical properties of tissues.
Efficient road geometry identification from digital vector data
Andrášik, Richard; Bíl, Michal
2016-07-01
A new method for the automatic identification of road geometry from digital vector data is presented. The method is capable of efficiently identifying circular curves with their radii and tangents (straight sections). The average error of identification ranged from 0.01 to 1.30 % for precisely drawn data and 4.81 % in the case of actual road data with noise in the location of vertices. The results demonstrate that the proposed method is faster and more precise than commonly used techniques. This approach can be used by road administrators to complete their databases with information concerning the geometry of roads. It can also be utilized by transport engineers or traffic safety analysts to investigate the possible dependence of traffic accidents on road geometries. The method presented is applicable as well to railroads and rivers or other line features.
Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design
Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian
2012-01-01
We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.
Geometry optimization for micro-pressure sensor considering dynamic interference.
Yu, Zhongliang; Zhao, Yulong; Li, Lili; Tian, Bian; Li, Cun
2014-09-01
Presented is the geometry optimization for piezoresistive absolute micro-pressure sensor. A figure of merit called the performance factor (PF) is defined as a quantitative index to describe the comprehensive performances of a sensor including sensitivity, resonant frequency, and acceleration interference. Three geometries are proposed through introducing islands and sensitive beams into typical flat diaphragm. The stress distributions of sensitive elements are analyzed by finite element method. Multivariate fittings based on ANSYS simulation results are performed to establish the equations about surface stress, deflection, and resonant frequency. Optimization by MATLAB is carried out to determine the dimensions of the geometries. Convex corner undercutting is evaluated. Each PF of the three geometries with the determined dimensions is calculated and compared. Silicon bulk micromachining is utilized to fabricate the prototypes of the sensors. The outputs of the sensors under both static and dynamic conditions are tested. Experimental results demonstrate the rationality of the defined performance factor and reveal that the geometry with quad islands presents the highest PF of 210.947 Hz(1/4). The favorable overall performances enable the sensor more suitable for altimetry.
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.
Reeve, W. D., Ed.
There are a number of recurring topics in the articles that comprise this yearbook, such as the nature of both informal and demonstrative geometry, the reasons for teaching both, and the extent of such courses. Other emphasized topics are use of the analytic method, whether to combine plane and solid geometry, the place of algebra and trigonometry…
Yang, Yi; Mielczarek, Kamil; Zakhidov, Anvar; Hu, Walter
2013-03-01
Among the various organic photovoltaic devices, the conjugated polymer/fullerene approach has drawn the most research interest. The performance of these types of solar cells is greatly determined by the nanoscale morphology of the two components (donor/acceptor) and the molecular orientation/crystallinity in the photoactive layer. This article demonstrates our recent studies on the nanostructure geometry effects on the nanoimprint induced poly(3 hexylthiophene-2,5-diyl) (P3HT) chain alignment and photovoltaic performance. Out-of-plane and in-plane grazing incident X-ray diffractions are employed to characterize the chain orientations in P3HT nanogratings with different widths and heights. It is found that nanoimprint procedure changes the initial edge-on alignment in non-imprinted P3HT thin film to a vertical orientation which favors the hole transport, with an organization height H≥ 170 nm and width in the range of 60 nmImprinted P3HT/[6,6]-penyl-C61-butyric-acid-methyl-ester (PCBM) solar cells show an increase in power conversion efficiency (PCE) with the decrease of nanostructure width, and with the increase of height and junction area. Devices with the highest PCE are made by the fully aligned and highest P3HT nanostructures (width w= 60 nm, height h= 170 nm), allowing for the most efficient charge separation, transport and light absorption. We believe this work will contribute to the optimal geometry design of nanoimprinted polymer solar cells.
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Dijkgraaf, Robbert; Vafa, Cumrun
2002-11-01
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large- N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large- N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun
2002-11-11
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large-N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large-N multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.
Holographic thermalization in noncommutative geometry
Zeng, Xiao-Xiong; Liu, Wen-Biao
2014-01-01
Gravitational collapse of a dust shell in noncommutative geometry is probed by the renormalized geodesic length and minimal area surface, which are dual to the two-point correlation function and expectation value of Wilson loop in the dual conformal field theory. For the spacetime without a horizon, we find the shell will not collapse all the time but will stop in a stable state. For the spacetime with a horizon, we investigate how the noncommutative parameter affects the thermalization process in detail. From the numeric results, we find that larger the noncommutative parameter is, longer the thermalization time is, which implies that the large noncommutative parameter delays the thermalization process. From the fitted functions of the thermalization curve, we find for both thermalization probes, there is a phase transition point during the thermalization process, which divides the thermalization into an acceleration phase and a deceleration phase. During the acceleration phase, the acceleration is found to ...
Interactive graphics for geometry modeling
Wozny, M. J.
1984-01-01
An interactive vector capability to create geometry and a raster color shaded rendering capability to sample and verify interim geometric design steps through color snapshots is described. The development is outlined of the underlying methodology which facilitates computer aided engineering and design. At present, raster systems cannot match the interactivity and line-drawing capability of refresh vector systems. Consequently, an intermediate step in mechanical design is used to create objects interactively on the vector display and then scan convert the wireframe model to render it as a color shaded object on a raster display. Several algorithms are presented for rendering such objects. Superquadric solid primitive extend the class of primitives normally used in solid modelers.
Dialogues about geometry and light
Bermudez, David; Leonhardt, Ulf
2015-01-01
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to what was later known as optics. On the other hand, geometry is a branch of mathematics that was born from practical studies concerning lengths, areas and volumes in the early cultures, although it was not put into axiomatic form until the 3rd century BC. In this work, we will discuss the connection between these two timeless topics and show some new things in old things". There has been several works in this direction, but taking into account the didactic approach of the Enrico Fermi Summer School, we would like to address the subject and our audience in a new light.
Hofstadter's Butterfly in Quantum Geometry
Hatsuda, Yasuyuki; Tachikawa, Yuji
2016-01-01
We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kahler modulus of the Calabi-Yau, can be found explicitly when the quantum parameter $q=e^{i\\hbar}$ is a root of unity, that its branch cuts are given by Hofstadter's butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging $\\hbar$ and $4\\pi^2/\\hbar$, plays an important role.
Hopf algebras in noncommutative geometry
Varilly, J C
2001-01-01
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative 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 noncommutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups.
Walking droplets in confined geometries
Filoux, Boris; Mathieu, Olivier; Vandewalle, Nicolas
2014-11-01
When gently placing a droplet onto a vertically vibrated bath, coalescence may be avoided: the drop bounces permanently. Upon increasing forcing acceleration, a drop interacts with the wave it generates, and becomes a ``walker'' with a well defined velocity. In this work, we investigate the confinement of a walker in a mono-dimensional geometry. The system consists of linear submarine channels used as waveguides for a walker. By studying the dynamics of walkers in those channels, we discover some 1D-2D transition. We also propose a model based on an analogy with ``Quantum Wires.'' Finally, we consider the situation of a walker in a circular submarine channel, and examine the behavior of several walking droplets in this system. We show the quantization of the drop distances, and correlate it to their bouncing modes.
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...
Amoeboid motion in confined geometry
Wu, Hao; Hu, Wei-Fan; Farutin, Alexander; Rafaï, Salima; Lai, Ming-Chih; Peyla, Philippe; Misbah, Chaouqi
2015-01-01
Cells of the immune system, as well as cancer cells, migrating in confined environment of tissues undergo frequent shape changes (described as amoeboid motion) that enable them to move forward through these porous media without the assistance of adhesion sites. In other words, they perform amoeboid swimming (AS) while using extracellular matrices and cells of tissues as support. We introduce a simple model of AS in a confined geometry solved by means of 2D numerical simulations. We find that confinement promotes AS, unless being so strong that it restricts shape change amplitude. A straight AS trajectory in the channel is found to be unstable, and ample lateral excursions of the swimmer prevail. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. This is a spontaneous symmetry-breaking bifurcation. We find that there exists an optimal confinement for migration. We provide numerical results as...
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 ...
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.
Hessian geometry and entanglement thermodynamics
Matsueda, Hiroaki
2015-01-01
We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of ...
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...
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
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 ...
Geometry-dependent distributed polarizability models for the water molecule
Energy Technology Data Exchange (ETDEWEB)
Loboda, Oleksandr; Ingrosso, Francesca; Ruiz-López, Manuel F.; Millot, Claude [Université de Lorraine, SRSMC UMR 7565, Vandoeuvre-les-Nancy F-54506 (France); CNRS, SRSMC UMR 7565, Vandoeuvre-les-Nancy F-54506 (France); Szalewicz, Krzysztof [Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716 (United States)
2016-01-21
Geometry-dependent distributed polarizability models have been constructed by fits to ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set for the water molecule in the field of a point charge. The investigated models include (i) charge-flow polarizabilities between chemically bonded atoms, (ii) isotropic or anisotropic dipolar polarizabilities on oxygen atom or on all atoms, and (iii) combinations of models (i) and (ii). For each model, the polarizability parameters have been optimized to reproduce the induction energy of a water molecule polarized by a point charge successively occupying a grid of points surrounding the molecule. The quality of the models is ascertained by examining their ability to reproduce these induction energies as well as the molecular dipolar and quadrupolar polarizabilities. The geometry dependence of the distributed polarizability models has been explored by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For each considered model, the distributed polarizability components have been fitted as a function of the geometry by a Taylor expansion in monomer coordinate displacements up to the sum of powers equal to 4.
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.
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.
Toy Demonstrator's "VISIT" Handbook.
Levenstein, Phyllis
The role of the toy demonstrator in a home-based, mother-involved intervention effort (Verbal Interaction Project) is presented in this handbook for staff members. It is believed that the prerequisites for functioning in the toy demonstrator's role are a sense of responsibility, patience with the children and their mothers, and willingness to be…
Levitation Kits Demonstrate Superconductivity.
Worthy, Ward
1987-01-01
Describes the "Project 1-2-3" levitation kit used to demonstrate superconductivity. Summarizes the materials included in the kit. Discusses the effect demonstrated and gives details on how to obtain kits. Gives an overview of the documentation that is included. (CW)
Kinetics and Catalysis Demonstrations.
Falconer, John L.; Britten, Jerald A.
1984-01-01
Eleven videotaped kinetics and catalysis demonstrations are described. Demonstrations include the clock reaction, oscillating reaction, hydrogen oxidation in air, hydrogen-oxygen explosion, acid-base properties of solids, high- and low-temperature zeolite reactivity, copper catalysis of ammonia oxidation and sodium peroxide decomposition, ammonia…
Better Ira Remsen Demonstration
Dalby, David K.; Maynard, James H.; Moore, John W.
2011-01-01
Many versions of the classic Ira Remsen experience involving copper and concentrated nitric acid have been used as lecture demonstrations. Remsen's original reminiscence from 150 years ago is included in the Supporting Information, and his biography can be found on the Internet. This article presents a new version that makes the demonstration more…
Levitation Kits Demonstrate Superconductivity.
Worthy, Ward
1987-01-01
Describes the "Project 1-2-3" levitation kit used to demonstrate superconductivity. Summarizes the materials included in the kit. Discusses the effect demonstrated and gives details on how to obtain kits. Gives an overview of the documentation that is included. (CW)
The Silent Guardian Demonstration
2006-01-01
Control Category A biothreat pathogens: B. anthracis (three regions), Variola major virus (two regions), Ebola virus (one region), Lassa fever virus...Lin, and D.A. Stenger Center for Bio/Molecular Science and Engineering introduction During the winter months, runny noses, fevers , and other flu...present clinically with similar symptoms. One approach to surveillance for a bioattack is to monitor for unusual outbreaks of flu-like symptoms
The Geometry of Enhancement in Multiple Regression.
Waller, Niels G
2011-10-01
In linear multiple regression, "enhancement" is said to occur when R (2)=b'r>r'r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R xx≠I, R xx=E[xx']=V Λ V' (where V Λ V' denotes the eigen decomposition of R xx; λ 1>λ 2), the set [Formula: see text] contains four vectors; the set [Formula: see text]; [Formula: see text] contains an infinite number of vectors. When p≥3 (and λ 1>λ 2>⋯>λ p ), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B 1 occurs at the intersection of two hyper-ellipsoids in ℝ (p) . Equations are provided for populating the sets B 1 and B 2 and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included in Appendices A and B.
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. ...
A Relationship between Geometry and Algebra
Bejarano, Jose Ricardo Arteaga
2011-01-01
The three key documents for study geometry are: 1) "The Elements" of Euclid, 2) the lecture by B. Riemann at G\\"ottingen in 1854 entitled "\\"Uber die Hypothesen welche der Geometrie zu Grunde liegen" (On the hypotheses which underlie geometry) and 3) the "Erlangen Program", a document written by F. Klein (1872) on his income as professor at the Faculty of Philosophy and the Senate of the Erlangen University. The latter document F. Klein introduces the concept of group as a tool to study geometry. The concept of a group of transformations of space was known at the time. The purpose of this informative paper is to show a relationship between geometry and algebra through an example, the projective plane. Erlangen program until today continues being a guideline of how to study geometry.
Riemannian geometry of fluctuation theory: An introduction
Velazquez, Luisberis
2016-05-01
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.
A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules
Lu, Shih-I.
2004-01-01
This article describes an approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method based on the floating spherical Gaussians. In conjunction with a projected and renormalized Hellmann-Feynman gradient and an electronic energy at variational Monte Carlo and diffusion quantum Monte Carlo, respectively, the quasi-Newton algorithm implemented with the Broyden-Fletcher-Goldfarb-Shanno updated Hessian was used to find the optimized molecular geometry. We applied this approach to N2 and H2O molecules. The geometry and harmonic frequencies calculated were consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.
Recent developments and some open problems in Finsler geometry
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open problems in Finsler geometry.
Good Codes From Generalised Algebraic Geometry Codes
Jibril, Mubarak; Ahmed, Mohammed Zaki; Tjhai, Cen
2010-01-01
Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used. In this paper we present 41 new codes over GF(16) which improve on the best known codes of the same length and rate. The construction method uses places of small degree with a technique originally published over 10 years ago for the construction of generalised algebraic geometry codes.
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
Generalized Kahler Geometry from supersymmetric sigma models
Bredthauer, A; Persson, J; Zabzine, M; Bredthauer, Andreas; Lindstrom, Ulf; Persson, Jonas; Zabzine, Maxim
2006-01-01
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
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.
Geometry of solar coronal rays
Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.
2016-02-01
Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field
Methanol Cannon Demonstrations Revisited.
Dolson, David A.; And Others
1995-01-01
Describes two variations on the traditional methanol cannon demonstration. The first variation is a chain reaction using real metal chains. The second example involves using easily available components to produce sequential explosions that can be musical in nature. (AIM)
TENCompetence tool demonstration
Kluijfhout, Eric
2010-01-01
Kluijfhout, E. (2009). TENCompetence tool demonstration. Presented at Zorgacademie Parkstad (Health Academy Parkstad), Limburg Leisure Academy, Life Long Learning Limburg and a number of regional educational institutions. May, 18, 2009, Heerlen, The Netherlands: Open University of the Netherlands, T
Land Management Research Demonstration
US Fish and Wildlife Service, Department of the Interior — In 2002, Neal Smith National Wildlife Refuge became one of the first Land Management and Research Demonstration (LMRD) sites. These sites are intended to serve as...
Pancreaticopleural fistula : CT demonstration
Energy Technology Data Exchange (ETDEWEB)
Hahm, Jin Kyeung [Chuncheon Medical Center, ChunChon (Korea, Republic of)
1997-03-01
In patients with chronic pancreatitis, the pancreaticopleural fistula is known to cause recurrent exudative or hemorrhagic pleural effusions. These are often large in volume and require treatment, unlike the effusions in acute pancreatitis. Diagnosis can be made either by the finding of elevated pleural fluid amylase level or, using imaging studies, by the direct demonstration of the fistulous tract. We report two cases of pancreaticopleural fistula demonstrated by computed tomography.