twistors and gauge fields

Directory of Open Access Journals (Sweden)

A. G. Sergeev

1986-01-01

Full Text Available We describe briefly the basic ideas and results of the twistor theory. The main points: twistor representation of Minkowsky space, Penrose correspondence and its geometrical properties, twistor interpretation of linear massless fields, Yang-Mills fields (including instantons and monopoles and Einstein-Hilbert equations.

The development of ideas in twistor theory

International Nuclear Information System (INIS)

Huggett, S.A.

1985-01-01

This paper presents a review of the main concepts of twistor theory. The emphasis is on the evolution of the subject from the original motivating ideas to the more recent work. In particular the physical and philosophical reasoning behind the use of the various mathematical structure is discussed. (author)

Worldsheet factorization for twistor-strings

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim [Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)

2014-04-10

We study the multiparticle factorization properties of two worldsheet theories which — at tree-level — describe the scattering of massless particles in four dimensions: the Berkovits-Witten twistor-string for N=4 super-Yang-Mills coupled to N=4 conformal supergravity, and the Skinner twistor-string for N=8 supergravity. By considering these string-like theories, we can study factorization at the level of the worldsheet before any Wick contractions or integrals have been performed; this is much simpler than considering the factorization properties of the amplitudes themselves. In Skinner’s twistor-string this entails the addition of worldsheet gravity as well as a formalism that represents all external states in a manifestly symmetric way, which we develop explicitly at genus zero. We confirm that the scattering amplitudes of Skinner’s theory, as well as the gauge theory amplitudes for the planar sector of the Berkovits-Witten theory, factorize appropriately at genus zero. In the non-planar sector, we find behavior indicative of conformal gravity in the Berkovits-Witten twistor-string. We contrast factorization in twistor-strings with the story in ordinary string theory, and also make some remarks on higher genus factorization and disconnected prescriptions.

Worldsheet factorization for twistor-strings

International Nuclear Information System (INIS)

Adamo, Tim

2014-01-01

We study the multiparticle factorization properties of two worldsheet theories which — at tree-level — describe the scattering of massless particles in four dimensions: the Berkovits-Witten twistor-string for N=4 super-Yang-Mills coupled to N=4 conformal supergravity, and the Skinner twistor-string for N=8 supergravity. By considering these string-like theories, we can study factorization at the level of the worldsheet before any Wick contractions or integrals have been performed; this is much simpler than considering the factorization properties of the amplitudes themselves. In Skinner’s twistor-string this entails the addition of worldsheet gravity as well as a formalism that represents all external states in a manifestly symmetric way, which we develop explicitly at genus zero. We confirm that the scattering amplitudes of Skinner’s theory, as well as the gauge theory amplitudes for the planar sector of the Berkovits-Witten theory, factorize appropriately at genus zero. In the non-planar sector, we find behavior indicative of conformal gravity in the Berkovits-Witten twistor-string. We contrast factorization in twistor-strings with the story in ordinary string theory, and also make some remarks on higher genus factorization and disconnected prescriptions

Some dual relations in twistor theory

International Nuclear Information System (INIS)

Tarski, J.

1983-08-01

The option of employing twistors or dual twistors in integral representations, etc., is considered. In particular, dual-space analyses are presented which relate to the problem of background electromagnetic fields, and to the inverse transformation. (author)

Twistor Spinoffs for Collider Physics

International Nuclear Information System (INIS)

Dixon, Lance

2006-01-01

In the coming decade, the search for the Higgs boson, and for new particles representing physics beyond the Standard Model, will be carried out by colliding protons at the Tevatron and the Large Hadron Collider. A collision of two protons, each of which is made out of quarks and gluons, is inherently messy. Feynman likened it to smashing two Swiss watches together to figure out how they work. In recent decades, we have learned better how the Swiss watches work, using the theory of quark-gluon interactions, quantum chromodynamics. Armed with this knowledge, we can better predict the results of collisions at the Tevatron and the LHC, to see whether the Standard Model holds up or fails, or whether new particles are in the data. But a major bottleneck is simply in adding up Feynman diagrams, for which the rules are well known, yet there can be thousands of extremely complicated diagrams. In fact, the sum of all diagrams is often much simpler than the typical one, suggesting hidden symmetries and better ways to compute. In the past two years, spinoffs from a new theory, 'twistor string theory', have led to very efficient alternatives to Feynman diagrams for making such predictions, as I will explain.

Twistor methods for AdS{sub 5}

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim; Skinner, David; Williams, Jack [Department of Applied Mathematics & Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA United Kingdom (United Kingdom)

2016-08-30

We consider the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS{sub 5} is the same as the ambitwistor space of the four-dimensional conformal boundary; the geometry of this correspondence is reviewed for both the bulk and boundary. A Penrose transform allows us to describe free bulk fields, with or without mass, in terms of data on twistor space. Explicit representatives for the bulk-to-boundary propagators of scalars and spinors are constructed, along with twistor action functionals for the free theories. Evaluating these twistor actions on bulk-to-boundary propagators is shown to produce the correct two-point functions.

Conformal higher-spin symmetries in twistor string theory

Directory of Open Access Journals (Sweden)

D.V. Uvarov

2014-12-01

Full Text Available It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to SL(4|4,R one.

Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Science.gov (United States)

Herfray, Yannick

2017-11-01

This paper establishes the relation between traditional results from the (Euclidean) twistor theory and chiral formulations of general relativity (GR), especially the pure connection formulation. Starting from an SU(2)-connection only, we show how to construct natural complex data on twistor space, mainly an almost Hermitian structure and a connection on some complex line bundle. Only when this almost Hermitian structure is integrable is the connection related to an anti-self-dual-Einstein metric and makes contact with the usual results. This leads to a new proof of the non-linear graviton theorem. Finally, we discuss what new strategies this "connection approach" to twistors suggests for constructing a twistor action for gravity. In Appendix A, we also review all known chiral Lagrangians for GR.

Structure of twistor and H-spaces

International Nuclear Information System (INIS)

Lugo, G.G.

1979-01-01

In chapter one, we review briefly the spinor and twistor formalisms in general relativity. Following some suggestions of A.H. Taub, we show that the local twistor structure of a general curved space-time is closely related to the conformal structure used by B.G. Schmidt to define conformal infinity. In particular, we prove that the normal Cartan connection of the conformal bundle coincides with the connection which gives the covariant derivative of local twistors. In chapter two, we use the results of E.T. Newman and J. Plebanski to construct some explicit self-dual metrics. These solutions are of interest because they are good candidates for what we would like to call asymptotically flat H-spaces. Furthermore, by a closer look at these metrics, we may gain more insight into the behavior of twistor spaces near the boundary. In chapter three, we study the geometric structure of twistor spaces associated with asymptotically flat space-times. We show that the space of asymptotic projective twistors, PT + , is an Einstein Kaehler manifold of constant holomorphic sectional curvature. We also give a brief description of the twistor space construction of the metrics in chapter two. In chapter four, we apply the Chern-Moser theory of the pseudoconformal geometry of real hypersurfaces in complex manifolds to study the structure of the boundary PN of PT + . Using some ideas due to S. Webster, we show that the Chern-Moser curvature invariants of PN coincide with the Kaehler curvature invariants of PT + . From the results of chapter three, we deduce that the pseudoconformal geodesics (chains) of the boundary are nicely behaved

General split helicity gluon tree amplitudes in open twistor string theory

Science.gov (United States)

Dolan, Louise; Goddard, Peter

2010-05-01

We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al. [25].

BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors

Science.gov (United States)

Witt, Donald M.

2011-04-01

Solitons and instantons play important roles both in pure and applied mathematics as well as in theoretical physics where they are related to the topological structure of the vacuum. Twistors are a useful tool for solving nonlinear differential equations and are useful for the study of the antiself-dual Yang-Mills equations and the Einstein equations. Many books and more advanced monographs have been written on these topics. However, this new book by Maciej Dunajski is a complete first introduction to all of the topics in the title. Moreover, it covers them in a very unique way, through integrable systems. The approach taken in this book is that of mathematical physics à la field theory. The book starts by giving an introduction to integrable systems of ordinary and partial differential equations and proceeds from there. Gauge theories are not covered until chapter 6 which means the reader learning the material for the first time can build up confidence with simpler models of solitons and instantons before encountering them in gauge theories. The book also has an extremely clear introduction to twistor theory useful to both mathematicians and physicists. In particular, the twistor theory presentation may be of interest to string theorists wanting understand twistors. There are many useful connections to research into general relativity. Chapter 9 on gravitational instantons is great treatment useful to anyone doing research in classical or quantum gravity. There is also a nice discussion of Kaluza-Klein monopoles. The three appendices A-C cover the necessary background material of basic differential geometry, complex manifolds, and partial differential equations needed to fully understand the subject. The reader who has some level of expertise in any of the topics covered can jump right into that material without necessarily reading all of the earlier chapters because of the extremely clear writing style of the author. This makes the book an excellent reference on

Twistors in general relativity

International Nuclear Information System (INIS)

Penrose, R.

1987-01-01

The two most significant definitions of a twistor in (conformally) flat space-time are that given by solutions of the twistor equation and that given by α-planes in the complexification of the space-time. It is shown that these concepts are naturally dual to one another, and that they give rise to various different twistor concepts in curved space-time when referred to submanifolds of differing dimension. One of these concepts, that of 2-surface twistors, gives rise to a quasi-local definition of mass (and angular momentum). The status of this definition is explored in relation to various examples. (author)

Twistor Transform for Spinning Particle

International Nuclear Information System (INIS)

Fedoruk, S.

2005-01-01

Twistorial formulation of a particle of arbitrary spin has been constructed. The twistor formulation is deduced from a space-time formulation of the spinning particle by introducing pure gauge Lorentz harmonics in this system. Canonical transformations and gauge fixing conditions, excluding space-time variables, produce the fundamental conditions of twistor transform relating the space-time formulation and twistor one. Integral transformations, relating massive twistor fields with usual space-time fields, have been constructed

Curved twistor spaces and H-space

International Nuclear Information System (INIS)

Tod, K.P.

1980-01-01

The curved twistor space construction of Penrose for anti-self-dual solutions to the Einstein vacuum equations is described. Curved twistor spaces are defined and it is shown with the aid of an example how to obtain them by deforming the complex structure of regions of flat twistor space. The connection of this procedure with Newman's H-space construction via asymptotic twistor space is outlined. (Auth.)

Twistor description of spinning particles in AdS

Science.gov (United States)

Arvanitakis, Alex S.; Barns-Graham, Alec E.; Townsend, Paul K.

2018-01-01

The two-twistor formulation of particle mechanics in D-dimensional anti-de Sitter space for D = 4 , 5 , 7, which linearises invariance under the AdS isometry group Sp(4; K ) for K=R,C,H, is generalized to the massless N -extended "spinning particle". The twistor variables are gauge invariant with respect to the initial N local worldline supersymmetries; this simplifies aspects of the quantum theory such as implications of global gauge anomalies. We also give details of the two-supertwistor form of the superparticle, in particular the massive superparticle on AdS5.

An off-shell formulation of N=4 supersymmetric Yang-Mills theory in twistor harmonic superspace

International Nuclear Information System (INIS)

Sokatchev, E.

1989-01-01

Twistor-like harmonic variables which parametrize the coset space SO(1, 4)/SO(1, 2)xSO(2) are introduced. With their help the on-shell constraints for N=4, d=5 supersymmetric Yang-Mills theory are rewritten as conditions for flatness in the harmonic directions of superspace. A Chern-Simons off-shell action leading to those equations is proposed. There are indications that the off-shell theory might be finite, despite the fact that the on-shell one seems non-renormalizable. (orig.)

Twistor connection and the Palatini method

International Nuclear Information System (INIS)

Merkulov, S.A.

1988-01-01

For the Yang-Mills Lagrangian of the twistor connection, an analog of the Palatini variational method is considered, in which the variations of the twistor connection A m and metric g ab are taken to be independent. It is shown that varying the Lagrangian with respect to the connection establishes a relation between A m and g ab (i.e., defines a standard twistor connection, postulated earlier), while varying with respect to the metric with a subsequent substitution of explicit expressions of the standard twistor connection leads to the Bach vacuum equations, describing the dynamics of conformal gravity

Structure of three-twistor particles

International Nuclear Information System (INIS)

Lukacs, B.; Perjes, Z.; Sebestyen, A.; Newman, E.T.; Porter, J.

1981-11-01

The simplest physical system to have a non-trivial intrinsic structure in Minkowski space-time is a three-twistor particle. The authors investigate this structure and the two pictures of the particle as an extended object in space-time and as a point in unitary space. The effect of twistor translations on the mass triangle defined by the partial centre of mass points in space-time as well as the connections between twistor rotations and the spin are considered and the spin deficiency formula is established. (author)

Twistor quantisation of open strings in three dimensions

International Nuclear Information System (INIS)

Shaw, W.T.

1987-01-01

The paper treats the first quantisation of loops in real four-dimensional twistor space. Such loops correspond to open strings in three-dimensional spacetime. The geometry and reality structures pertaining to twistors in three dimensions are reviewed and the twistor description of null geodesics is presented as a prototype for the discussion of null curves. The classical twistor structure of null curves is then described. The symplectic structure is exhibited and used to investigate the constraint algebra. Expressions for the momentum operators are found. The symplectic structure defines natural canonical variables for covariant twistor quantisation and the consequences of carrying this out are described. A twistor representation of the Virasoro algebra with central charge 2 is found and some solutions of the quantum constraints are exhibited. (author)

All tree-level MHV form factors in N=4 SYM from twistor space

Energy Technology Data Exchange (ETDEWEB)

Koster, Laura [Institut für Mathematik, Institut für Physik und IRIS Adlershof,Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin (Germany); Mitev, Vladimir [Institut für Mathematik, Institut für Physik und IRIS Adlershof,Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin (Germany); PRISMA Cluster of Excellence, Institut für Physik, WA THEP,Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128 Mainz (Germany); Staudacher, Matthias [Institut für Mathematik, Institut für Physik und IRIS Adlershof,Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin (Germany); Wilhelm, Matthias [Institut für Mathematik, Institut für Physik und IRIS Adlershof,Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, 12489 Berlin (Germany); Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, 2100 Copenhagen (Denmark)

2016-06-28

We incorporate all gauge-invariant local composite operators into the twistor-space formulation of N=4 SYM theory, detailing and expanding on ideas we presented recently in http://arxiv.org/abs/1603.04471. The vertices for these operators contain infinitely many terms and we show how they can be constructed by taking suitable derivatives of a light-like Wilson loop in twistor space and shrinking it down to a point. In particular, these vertices directly yield the tree-level MHV super form factors of all composite operators in N=4 SYM theory.

2-surface twistors, embeddings and symmetries

International Nuclear Information System (INIS)

Jeffryes, B.P.

1987-01-01

2-Surface twistor space was introduced in connection with a proposal for a quasi-local definition of mass and angular momentum within general relativity. Properties of the 2-surface twistor space are related to the possibilities for embedding the 2-surface in real and complex conformally flat spaces. The additional properties of the twistor space resulting from symmetries of the 2-surface are discussed, with particular detail on axisymmetric 2-surfaces. (author)

First-Order Twistor Lifts

Directory of Open Access Journals (Sweden)

Simões BrunoAscenso

2010-01-01

Full Text Available The use of twistor methods in the study of Jacobi fields has proved quite fruitful, leading to a series of results. L. Lemaire and J. C. Wood proved several properties of Jacobi fields along harmonic maps from the two-sphere to the complex projective plane and to the three- and four-dimensional spheres, by carefully relating the infinitesimal deformations of the harmonic maps to those of the holomorphic data describing them. In order to advance this programme, we prove a series of relations between infinitesimal properties of the map and those of its twistor lift. Namely, we prove that isotropy and harmonicity to first order of the map correspond to holomorphicity to first order of its lift into the twistor space, relatively to the standard almost complex structures and . This is done by obtaining first-order analogues of classical twistorial constructions.

First-Order Twistor Lifts

Directory of Open Access Journals (Sweden)

Bruno Ascenso Simões

2010-01-01

Full Text Available The use of twistor methods in the study of Jacobi fields has proved quite fruitful, leading to a series of results. L. Lemaire and J. C. Wood proved several properties of Jacobi fields along harmonic maps from the two-sphere to the complex projective plane and to the three- and four-dimensional spheres, by carefully relating the infinitesimal deformations of the harmonic maps to those of the holomorphic data describing them. In order to advance this programme, we prove a series of relations between infinitesimal properties of the map and those of its twistor lift. Namely, we prove that isotropy and harmonicity to first order of the map correspond to holomorphicity to first order of its lift into the twistor space, relatively to the standard almost complex structures J1 and J2. This is done by obtaining first-order analogues of classical twistorial constructions.

Twistor space, Minkowski space and the conformal group

International Nuclear Information System (INIS)

Broek, P.M. van den

1983-01-01

It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the transformation of twistor space under space inversion and time inversion. (orig.)

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

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

Twistor theory and the energy-momentum and angular momentum of the gravitational field at spatial infinity

International Nuclear Information System (INIS)

Shaw, W.T.

1983-01-01

Penrose's 'quasi-local mass and angular momentum' is investigated for 2-surfaces near spatial infinity in both linearized theory on Minkowski space and full general relativity. It is shown that for space-times that are radially smooth of order one in the sense of Beig and Schmidt with asymptotically electric Weyl curvature, there exists a global concept of a twistor space at spatial infinity. Global conservation laws for the energy-momentum and angular momentum are obtained, and the ten conserved quantities are shown to be invariant under asymptotic coordinate transformations. The relation to other definitions is discussed briefly. (author)

Single twistor description of massless, massive, AdS, and other interacting particles

International Nuclear Information System (INIS)

Bars, Itzhak; Picon, Moises

2006-01-01

The Penrose transform between twistors and the phase space of massless particles is generalized from the massless case to an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or nonrelativistic, interacting or noninteracting, in flat space or curved spaces. Our unified construction involves always the same twistor Z A with only four complex degrees of freedom and subject to the same helicity constraint. Only the twistor to phase space transform differs from one case to another. Hence, a unification of diverse particle dynamical systems is displayed by the fact that they all share the same twistor description. Our single twistor approach seems to be rather different and a strikingly economical construction of twistors compared to other past approaches that introduced multiple twistors to represent some similar but far more limited set of particle phase space systems

Quaternionic Kaehler and hyperkaehler manifolds with torsion and twistor spaces

International Nuclear Information System (INIS)

Ivanov, Stefan; Minchev, Ivan

2001-12-01

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(l) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle of a QKT manifold admits a HKT structure with special symmetry if and only if the twistor space of the QKT manifold admits an almost hermitian structure with totally skew-symmetric Nijenhuis tensor, thus connecting two structures arising from quantum field theories and supersymmetric sigma models with Wess- Zumino term. We discovered that a HKT manifold has always co-closed Lee form. Applying this property to compact HKT manifold we get information about the plurigenera. (author)

Twistor space, Minkowski space and the conformal group

NARCIS (Netherlands)

van den Broek, P.M.

1983-01-01

It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

Energy Technology Data Exchange (ETDEWEB)

Burinskii, Alexander, E-mail: bur@ibrae.ac.r [Laboratory of Theoretical Physics, NSI Russian Academy of Sciences, B.Tulskaya 52, Moscow, 115191 (Russian Federation)

2010-04-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

International Nuclear Information System (INIS)

Burinskii, Alexander

2010-01-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

S-duality in Twistor Space

CERN Document Server

Alexandrov, Sergei

2012-01-01

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.

S-duality in twistor space

Science.gov (United States)

Alexandrov, Sergei; Pioline, Boris

2012-08-01

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space {{M}_H} must carry an isometric action of the modular group SL(2 , {Z} ), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of {{M}_H} , and construct a general class of SL(2 , {Z} )-invariant quaternion-Kähler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include {{M}_H} corrected by D3-D1-D(-1)-instantons (with five-brane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional {N} = {2} gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.

Conformal higher spin scattering amplitudes from twistor space

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim [Blackett Laboratory, Imperial College, London, SW7 2AZ (United Kingdom); Hähnel, Philipp; McLoughlin, Tristan [School of Mathematics, Trinity College Dublin, College Green, Dublin 2 (Ireland)

2017-04-04

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.

Conformal higher spin scattering amplitudes from twistor space

International Nuclear Information System (INIS)

Adamo, Tim; Hähnel, Philipp; McLoughlin, Tristan

2017-01-01

We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.

Perspectives of Penrose theory in particle physics

International Nuclear Information System (INIS)

Perjes, Z.

1976-09-01

Existing results and some conjectures in the flat-space twistor approach to fundamental particles are reviewed. A consice introduction into the twistor description of dynamical systems with rest-mass is given (both classical and quantum). The Hamiltonian structure inherent to the angular momentum twistor is analyzed. The following discussion outlines the properties of n-twistor systems, the Penrose classification of particles, the Isup(10)SU(3) group and the problem of its twistor representations. Finally, speculative arguments are propounded as to the possible bearings of hadronic quark model to twistor theory. (Sz.N.Z.)

Hermitian Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds

International Nuclear Information System (INIS)

Popov, Alexander D.

2010-01-01

We consider the Hermitian Yang-Mills (HYM) equations for gauge potentials on a complex vector bundle E over an almost complex manifold X 6 which is the twistor space of an oriented Riemannian manifold M 4 . Each solution of the HYM equations on such X 6 defines a pseudo-holomorphic structure on the bundle E. It is shown that the pull-back to X 6 of any anti-self-dual gauge field on M 4 is a solution of the HYM equations on X 6 . This correspondence allows us to introduce new twistor actions for bosonic and supersymmetric Yang-Mills theories. As examples of X 6 we consider homogeneous nearly Kaehler and nearly Calabi-Yau manifolds which are twistor spaces of S 4 , CP 2 and B 4 , CB 2 (real 4-ball and complex 2-ball), respectively. Various explicit examples of solutions to the HYM equations on these spaces are provided. Applications in flux compactifications of heterotic strings are briefly discussed.

New constructions of twistor lifts for harmonic maps

DEFF Research Database (Denmark)

Svensson, Martin; C. Wood, John

2014-01-01

We show that given a harmonic map \\varphi from a Riemann surface into a classical simply connected compact inner symmetric space, there is a J_2-holomorphic twistor lift of \\varphi (or its negative) if and only if it is nilconformal. In the case of harmonic maps of finite uniton number, we give...... algebraic formulae in terms of holomorphic data which describes their extended solutions. In particular, this gives explicit formulae for the twistor lifts of all harmonic maps of finite uniton number from a surface to the above symmetric spaces....

Twistor Interpretation of Harmonic Spheres and Yang–Mills Fields

Directory of Open Access Journals (Sweden)

Armen Sergeev

2015-03-01

Full Text Available We consider the twistor descriptions of harmonic maps of the Riemann sphere into Kähler manifolds and Yang–Mills fields on four-dimensional Euclidean space. The motivation to study twistor interpretations of these objects comes from the harmonic spheres conjecture stating the existence of the bijective correspondence between based harmonic spheres in the loop space \\(\\Omega G\\ of a compact Lie group \\(G\\ and the moduli space of Yang–Mills \\(G\\-fields on \\(\\mathbb R^4\\.

Differential calculus for q-deformed twistors

International Nuclear Information System (INIS)

Akulov, V.P.; Duplij, S.A.; Chitov, V.V.

1998-01-01

Brief type of q-deformed differential calculus at light cone with using of twistor representation is suggested. Commutative relations between coordinates and moments are obtained. Considered quasiclassical limit gives exact form of vanish from mass shell

Superstrings and the search for the theory of everything

International Nuclear Information System (INIS)

Peat, D.

1988-01-01

This book contains the following chapters: A Crisis in Physics; From Points to Strings; Nambu's String Theory; Grand Unification; Superstrings; Heterotic Strings: Two Dimensions in One; From Spinors to Twistors; Twistor Space; Twistor Gravity; and Into Deep Waters

Drawing Euler Diagrams with Circles: The Theory of Piercings.

Science.gov (United States)

Stapleton, Gem; Leishi Zhang; Howse, John; Rodgers, Peter

2011-07-01

Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less comprehensible. In this paper, we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints, then it can be drawn with circles, which are more esthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.

Phase Diagrams of Strongly Interacting Theories

DEFF Research Database (Denmark)

Sannino, Francesco

2010-01-01

We summarize the phase diagrams of SU, SO and Sp gauge theories as function of the number of flavors, colors, and matter representation as well as the ones of phenomenologically relevant chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. We finally report...

The Penrose transform its interaction with representation theory

CERN Document Server

Baston, Robert J

1989-01-01

This advanced text explores the Penrose transform, a major component of classical twistor theory. Geared toward students of physics and mathematics, the treatment presupposes no familiarity with twistor theory and a minimum of representation theory. "Brings to the reader a huge amount of information, well organized and condensed into less than 200 pages." — Mathematical Reviews.

On superwistor geometry and integrability in super gauge theory

International Nuclear Information System (INIS)

Wolf, M.

2006-01-01

In this thesis, we report on different aspects of intgrability in supersymmetric gauge theories. Our main tool of investigation is supertwistor geometry. In the first chapter, we briefly review the basics of twistor geometry. Afterwards, we discuss self-dual super Yang-Mills (SYM) theory and some of its relatives. In particular, a detailed twistor description of self-dual SYM theory is presented. Furthermore, we introduce certain self-dual models which are, in fact, obtainable from self-dual SYM theory by a suitable reduction. Some of them can be interpreted within the context of topological field theories. To provide a twistor description of these models, we propose weighted projective superspaces as twistor space. These spaces turn out to be Calabi-Yau supermanifolds. Therefore, it is possible to write down approriate action princuples, as well. In chapter three, we then deal with the twistor formulation of a certain supersymmetric Bogomolnyi model in three space-time dimensions. The nonsupersymmetric version of this model describes static Yang-Mills-Higgs monopoles in the Prasad-Sommerfield limit. In particular, we consider a supersymmetric extension of mini-twistor space. This space is in turn a part of a certain doubble fibration. It is then possible to formulate a Chern-Simons type theory on the correspondence space of this fibration. As we explain, this theory describes partially holomorphic vector bundles. It should be noticed that the correspondence space can be equipped with a Cauchy-Riemann structure. Moreover, we formulate holomorphic BF theory on mini-supertwistor space. e then prove that the moduli spaces of all three theories are bijective. In addition, complex structure deformations on mini-supertwistor space are investigated eventually resulting in a twistor correspondence involving a supersymmetric Bogomolnyi model with massive fields. In chapter four, we review the twistor formulation of non-self-dual SYM theories. The remaining chapter is

Untwisting the pure spinor formalism to the RNS and twistor string in a flat and AdS{sub 5}×S{sup 5} background

Energy Technology Data Exchange (ETDEWEB)

Berkovits, Nathan [ICTP South American Institute for Fundamental Research,Instituto de Física Teórica, UNESP - Universidade Estadual Paulista,Rua Dr. Bento T. Ferraz 271, 01140-070, São Paulo, SP (Brazil)

2016-06-21

The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators j{sub BRST} and composite b ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor j{sub BRST}+b, the worldsheet variables combine into N=1 worldsheet superfields X{sup m} and Θ{sup α} together with a superfield constraint relating DX{sup m} and DΘ{sup α}. The constraint implies that the worldsheet superpartner of θ{sup α} is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formalisms, as well as a new twistor-string formalism with manifest N=1 worldsheet supersymmetry. These N=1 worldsheet methods generalize in curved Ramond-Ramond backgrounds, and a manifestly N=1 worldsheet supersymmetric action is proposed for the superstring in an AdS{sub 5}×S{sup 5} background in terms of the twistor superfields. This AdS{sub 5}×S{sup 5} worldsheet action is a remarkably simple fermionic coset model with manifest PSU(2,2|4) symmetry and might be useful for computing AdS{sub 5}×S{sup 5} superstring scattering amplitudes.

Advanced quantum theory and its applications through Feynman diagrams

International Nuclear Information System (INIS)

Scadron, M.D.

1979-01-01

The two themes of scattering diagrams and the fundamental forces characterize this book. Transformation theory is developed to review the concepts of nonrelativistic quantum mechanics and to formulate the relativistic Klein-Gordon, Maxwell, and Dirac wave equations for relativistic spin-0, massless spin-1, and spin-1/2 particles, respectively. The language of group theory is used to write relativistic Lorentz transformations in a form similar to ordinary rotations and to describe the important discrete symmetries of C, P, and T. Then quantum mechanics is reformulated in the language of scattering theory, with the momentum-space S matrix replacing the coordinate-space hamiltonian as the central dynamical operator. Nonrelativistic perturbation scattering diagrams are then developed, and simple applications given for nuclear, atomic, and solid-state scattering problems. Next, relativistic scattering diagrams built up from covariant Feynman propagators and vertices in a manner consistent with the CPT theorem are considered. The theory is systematically applied to the lowest-order fundamental electromagnetic, strong, weak, and gravitational interactions. Finally, the use of higher-order Feynman diagrams to explain more detailed aspects of quantum electrodynamics (QED) and strong-interaction elementary-particle physics is surveyed. Throughout, the notion of currents is used to exploit the underlying symmetries and dynamical interactions of the various quantum forces. 258 references, 77 figures, 1 table

Homotopy theory of modules over diagrams of rings

Directory of Open Access Journals (Sweden)

J. P. C. Greenlees

2014-09-01

Full Text Available Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories ℳ( (as runs through the diagram, we consider the category of diagrams where the object ( at comes from ℳ(. We develop model structures on such categories of diagrams and Quillen adjunctions that relate categories based on different diagram shapes. Under certain conditions, cellularizations (or right Bousfield localizations of these adjunctions induce Quillen equivalences. As an application we show that a cellularization of a category of modules over a diagram of ring spectra (or differential graded rings is Quillen equivalent to modules over the associated inverse limit of the rings. Another application of the general machinery here is given in work by the authors on algebraic models of rational equivariant spectra. Some of this material originally appeared in the preprint “An algebraic model for rational torus-equivariant stable homotopy theory”, arXiv:1101.2511, but has been generalized here.

Criteria for evaluating programme theory diagrams in quality improvement initiatives: a structured method for appraisal.

Science.gov (United States)

Issen, Laurel; Woodcock, Thomas; McNicholas, Christopher; Lennox, Laura; Reed, Julie E

2018-04-09

Despite criticisms that many quality improvement (QI) initiatives fail due to incomplete programme theory, there is no defined way to evaluate how programme theory has been articulated. The objective of this research was to develop, and assess the usability and reliability of scoring criteria to evaluate programme theory diagrams. Criteria development was informed by published literature and QI experts. Inter-rater reliability was tested between two evaluators. About 63 programme theory diagrams (42 driver diagrams and 21 action-effect diagrams) were reviewed to establish whether the criteria could support comparative analysis of different approaches to constructing diagrams. Components of the scoring criteria include: assessment of overall aim, logical overview, clarity of components, cause-effect relationships, evidence and measurement. Independent reviewers had 78% inter-rater reliability. Scoring enabled direct comparison of different approaches to developing programme theory; action-effect diagrams were found to have had a statistically significant but moderate improvement in programme theory quality over driver diagrams; no significant differences were observed based on the setting in which driver diagrams were developed. The scoring criteria summarise the necessary components of programme theory that are thought to contribute to successful QI projects. The viability of the scoring criteria for practical application was demonstrated. Future uses include assessment of individual programme theory diagrams and comparison of different approaches (e.g. methodological, teaching or other QI support) to produce programme theory. The criteria can be used as a tool to guide the production of better programme theory diagrams, and also highlights where additional support for QI teams could be needed.

Perturbation theory via Feynman diagrams in classical mechanics

OpenAIRE

Penco, R.; Mauro, D.

2006-01-01

In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

The classification of diagrams in perturbation theory

International Nuclear Information System (INIS)

Phillips, D.R.; Afnan, I.R.

1995-01-01

The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. First, it is not clear whether Taylor's original method is equivlant to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Second, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. In then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method and derives corrections which compensate for this double-counting. copyright 1995 Academic Press, Inc

Matrix model approximations of fuzzy scalar field theories and their phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)

2015-12-29

We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.

Drawing theories apart the dispersion of Feynman diagrams in postwar physics

CERN Document Server

Kaiser, David

2005-01-01

Winner of the 2007 Pfizer Prize from the History of Science Society. Feynman diagrams have revolutionized nearly every aspect of theoretical physics since the middle of the twentieth century. Introduced by the American physicist Richard Feynman (1918-88) soon after World War II as a means of simplifying lengthy calculations in quantum electrodynamics, they soon gained adherents in many branches of the discipline. Yet as new physicists adopted the tiny line drawings, they also adapted the diagrams and introduced their own interpretations. Drawing Theories Apart traces how generations of young theorists learned to frame their research in terms of the diagrams—and how both the diagrams and their users were molded in the process.Drawing on rich archival materials, interviews, and more than five hundred scientific articles from the period, Drawing Theories Apart uses the Feynman diagrams as a means to explore the development of American postwar physics. By focusing on the ways young physicists learned new calcul...

Quaternionic six-dimensional (super)twistor formalism and composite (super)spaces

International Nuclear Information System (INIS)

Lukierski, J.; Nowicki, A.

1990-06-01

We extend by real quaternions the D=4 twistor and supertwistor formalism. The notion of quaternionic D=4 composite superspaces is considered. It is shown how to construct D=6 real composite space-time variables as well as D=6 real composite superspaces. (author). 21 refs

From chaos to unification: U theory vs. M theory

International Nuclear Information System (INIS)

Ye, Fred Y.

2009-01-01

A unified physical theory called U theory, that is different from M theory, is defined and characterized. U theory, which includes spinor and twistor theory, loop quantum gravity, causal dynamical triangulations, E-infinity unification theory, and Clifford-Finslerian unifications, is based on physical tradition and experimental foundations. In contrast, M theory pays more attention to mathematical forms. While M theory is characterized by supersymmetry string theory, U theory is characterized by non-supersymmetry unified field theory.

Phase diagram of N = 2 superconformal field theories and bifurcation sets in catastrophe theory

International Nuclear Information System (INIS)

Kei Ito.

1989-08-01

Phase diagrams of N=2 superconformal field theories are mapped out. It is shown that they coincide with bifurcation sets in catastrophe theory. The results are applied to the determination of renormalization group flows triggered by a combination of two or more relevant operators. (author). 13 refs, 2 figs

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in φ4-Theory

International Nuclear Information System (INIS)

Finster, Felix; Tolksdorf, Juergen

2012-01-01

Solutions of the classical φ 4 -theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a ''classical measurement process'' in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

Science.gov (United States)

Finster, Felix; Tolksdorf, Jürgen

2012-05-01

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

Irreducible diagrams in Landau-Ginzburg field theory

Energy Technology Data Exchange (ETDEWEB)

Witten, Jr, T A [Michigan Univ., Ann Arbor (USA). Dept. of Psychology

1981-10-19

It is shown that the free energy W of a Landau-Ginzburg-Wilson field theory with O(n) symmetry may be written in terms of the generating function V of diagrams irreducible in both propagator and interaction lines. This generalizes and simplifies a recent result of Des Cloizeaux. The functions W and V are related by a type of Legendre transformation on the bare mass variable.

On the twistor representation of Siegel transformation for superparticles

International Nuclear Information System (INIS)

Volkov, D.V.; Sorokin, D.P.; Tkach, V.I.

1988-01-01

It is shown that an explicit incorporation of twistor variables into the Lagrangian of a massless relativistic particle together with the local supersymmetrization of its proper time leads to a Lagrangian which is invariant under the space-time global supersymmetry. The equivalence of the Siegel symmetry and the local proper-time supersymmetry with a complexified grassmanian parameter is established. The Siegel algebra is formed by an irreducible set of covariant constraints and is closed off shell. 20 refs

Integrable systems twistors, loop groups, and Riemann surfaces

CERN Document Server

Hitchin, NJ; Ward, RS

2013-01-01

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors. It is written in an accessible and informal style, and fills a gap in the existing literature. The introduction by Nigel Hitchin addresses the meaning of integrability: how do werecognize an integrable system? His own contribution then develops connections with algebraic geometry, and inclu

Block diagrams and the cancellation of divergencies in energy-level perturbation theory

International Nuclear Information System (INIS)

Michels, M.A.J.; Suttorp, L.G.

1979-01-01

The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no divergencies are encountered. The resummed form of the effective Hamiltonian is used to establish a connexion with the S matrix. (Auth.)

Aspects of some dualities in string theory

Science.gov (United States)

Kim, Bom Soo

AdS/CFT correspondence in string theory has changed landscape of the theoretical physics. Through this celebrated duality between gravity theory and field theory, one can investigate analytically strongly coupled gauge theories such as Quantum Chromodynamics (QCD) in terms of weakly coupled string theory such as supergravity theory and vice versa. In the first part of this thesis we used this duality to construct a new type of nonlocal field theory, called Puff Field Theory, in terms of D3 branes in type IIB string theory with a geometric twist. In addition to the strong-weak duality of AdS/CFT, there also exists a weak-weak duality, called Twistor String Theory. Twistor technique is successfully used to calculate the SYM scattering amplitude in an elegant fashion. Yet, the progress in the string theory side was hindered by a non-unitary conformal gravity. We extend the Twistor string theory by introducing mass terms, in the second part of the thesis. A chiral mass term is identified as a vacuum expectation value of a conformal supergravity field and is tied with the breaking of the conformal symmetry of gravity. As a prime candidate for a quantum theory of gravity, string theory revealed many promising successes such as counting the number of microstates in supersymmetric Black Holes thermodynamics and resolution of timelike and null singularities, to name a few. Yet, the fundamental string and M-theroy formulations are not yet available. Various string theories without gravity, such as Non-Commutative Open String (NCOS) and Open Membrane (OM) theories, are very nice playground to investigate the fundamental structure of string and M-theory without the complication of gravity. In the last part of the thesis, simpler Non-Relativistic String Theories are constructed and investigated. One important motivation for those theories is related to the connection between Non-Relativistic String Theories and Non-critical String Theories through the bosonization of betagamma

Chiral symmetry breaking in gauge theories from Reggeon diagram analysis

International Nuclear Information System (INIS)

White, A.R.

1991-01-01

It is argued that reggeon diagrams can be used to study dynamical properties of gauge theories containing a large number of massless fermions. SU(2) gauge theory is studied in detail and it is argued that there is a high energy solution which is analogous to the solution of the massless Schwinger model. A generalized winding-number condensate produces the massless pseudoscalar spectrum associated with chiral symmetry breaking and a ''trivial'' S-Matrix

Analytic properties of Feynman diagrams in quantum field theory

CERN Document Server

Todorov, I T

1971-01-01

Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with a

High-energy, large-momentum-transfer processes: Ladder diagrams in φ3 theory. Pt. 1

International Nuclear Information System (INIS)

Osland, P.; Wu, T.T.; Harvard Univ., Cambridge, MA

1987-01-01

Relativistic quantum field theories may give us useful guidance to understanding high-energy, large-momentum-transfer processes, where the center-of-mass energy is much larger than the transverse momentum transfers, which are in turn much larger than the masses of the participating particles. With this possibility in mind, we study the ladder diagrams in φ 3 theory. In this paper, some of the necessary techniques are developed and applied to the simplest cases of the fourth- and sixth-order ladder diagrams. (orig.)

High-energy, large-momentum-transfer processes: Ladder diagrams in var-phi 3 theory

International Nuclear Information System (INIS)

Newton, C.L.J.

1990-01-01

Relativistic quantum field theories may help one to understand high-energy, large-momentum-transfer processes, where the center-of-mass energy is much larger than the transverse momentum transfers, which are in turn much larger than the masses of the participating particles. With this possibility in mind, the author studies ladder diagrams in var-phi 3 theory. He shows that in the limit s much-gt |t| much-gt m 2 , the scattering amplitude for the N-rung ladder diagram takes the form s -1 |t| -N+1 times a homogeneous polynomial of degree 2N - 2 and ln s and ln |t|. This polynomial takes different forms depending on the relation of ln |t| to ln s. More precisely, the asymptotic formula for the N-rung ladder diagram has points of non-analytically when ln |t| = γ ln s for γ = 1/2, 1/3, hor-ellipsis, 1/N-2

Diagram Techniques in Group Theory

Science.gov (United States)

Stedman, Geoffrey E.

2009-09-01

Preface; 1. Elementary examples; 2. Angular momentum coupling diagram techniques; 3. Extension to compact simple phase groups; 4. Symmetric and unitary groups; 5. Lie groups and Lie algebras; 6. Polarisation dependence of multiphoton processes; 7. Quantum field theoretic diagram techniques for atomic systems; 8. Applications; Appendix; References; Indexes.

Renormalization of modular invariant Coulomb gas and Sine-Gordon theories, and quantum Hall flow diagram

OpenAIRE

Carpentier, David

1998-01-01

Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive the critical behaviour at the various transition points of the diagram. Following proposal for a SL(2,Z) duality between different quantum Hall fluids, we discuss the analogy between this flow and the global quantum Hall phase diagram.

Magnetic phase diagrams from non-collinear canonical band theory

DEFF Research Database (Denmark)

Shallcross, Sam; Nordstrom, L.; Sharma, S.

2007-01-01

A canonical band theory of non-collinear magnetism is developed and applied to the close packed fcc and bcc crystal structures. This is a parameter-free theory where the crystal and magnetic symmetry and exchange splitting uniquely determine the electronic bands. In this way, we are able...... hybridization, and on this basis we are able to analyze the microscopic reasons behind the occurrence of non-collinear magnetism in the elemental itinerant magnets....... to construct phase diagrams of magnetic order for the fcc and bcc lattices. Several examples of non-collinear magnetism are seen to be canonical in origin, in particular, that of gamma-Fe. In this approach, the determination of magnetic stability results solely from changes in kinetic energy due to spin...

Do we need Feynman diagrams for higher order perturbation theory?

International Nuclear Information System (INIS)

Jora, Renata

2012-01-01

We compute the two loop and three loop corrections to the beta function for Yang-Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.

One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

Science.gov (United States)

Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V

2017-07-28

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

Non-supersymmetric loop amplitudes and MHV vertices

International Nuclear Information System (INIS)

Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele

2005-01-01

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes-the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result

The connected prescription for form factors in twistor space

Energy Technology Data Exchange (ETDEWEB)

Brandhuber, A.; Hughes, E.; Panerai, R.; Spence, B.; Travaglini, G. [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)

2016-11-23

We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in N=4 super Yang-Mills, which is a generalisation of the expression of Roiban, Spradlin and Volovich for superamplitudes. By introducing link variables, we show that our formula is identical to the recently proposed four-dimensional scattering equations for form factors. Similarly to the case of amplitudes, the link representation of form factors is shown to be directly related to BCFW recursion relations, and is considerably more tractable than the scattering equations. We also discuss how our results are related to a recent Grassmannian formulation of form factors, and comment on a possible derivation of our formula from ambitwistor strings.

Introduction to Feynman diagrams

CERN Document Server

Bilenky, Samoil Mikhelevich

1974-01-01

Introduction to Feynman Diagrams provides Feynman diagram techniques and methods for calculating quantities measured experimentally. The book discusses topics Feynman diagrams intended for experimental physicists. Topics presented include methods for calculating the matrix elements (by perturbation theory) and the basic rules for constructing Feynman diagrams; techniques for calculating cross sections and polarizations; processes in which both leptons and hadrons take part; and the electromagnetic and weak form factors of nucleons. Experimental physicists and graduate students of physics will

An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

Energy Technology Data Exchange (ETDEWEB)

Ananthanarayan, B.; Ghosh, Shayan [Indian Institute of Science, Centre for High Energy Physics, Karnataka (India); Bijnens, Johan [Lund University, Department of Astronomy and Theoretical Physics, Lund (Sweden); Hebbar, Aditya [Indian Institute of Science, Centre for High Energy Physics, Karnataka (India); University of Delaware, Department of Physics and Astronomy, Newark, DE (United States)

2016-12-15

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper. (orig.)

An analytic approach to sunset diagrams in chiral perturbation theory: Theory and practice

International Nuclear Information System (INIS)

Ananthanarayan, B.; Ghosh, Shayan; Bijnens, Johan; Hebbar, Aditya

2016-01-01

We demonstrate the use of several code implementations of the Mellin-Barnes method available in the public domain to derive analytic expressions for the sunset diagrams that arise in the two-loop contribution to the pion mass and decay constant in three-flavoured chiral perturbation theory. We also provide results for all possible two mass configurations of the sunset integral, and derive a new one-dimensional integral representation for the one mass sunset integral with arbitrary external momentum. Thoroughly annotated Mathematica notebooks are provided as ancillary files in the Electronic Supplementary Material to this paper, which may serve as pedagogical supplements to the methods described in this paper. (orig.)

Actuality of the Einstein theory of gravitation

International Nuclear Information System (INIS)

Ivanenko, D.D.

1982-01-01

Problems of actuality of the Einstein theory of gravitation are lightened. The great Einstein theory of gravitation is shown to remain a reliable base of understanding of modern physical world pattern and its inevitable further inexhaustible precising. The main GRT difficulties are enumirated: determination of reference systems, presence of singularities in the theory, absence of consistent determination of the gravity energy, impossibility of accounting the relations between atomic, gravitational and cosmological characteristics. The attention is paid to gauge, twistor problems and to unified interaction theory. The great contribution of the soviet science in the theory of gravitation is stressed

Alternative approaches to maximally supersymmetric field theories

International Nuclear Information System (INIS)

Broedel, Johannes

2010-01-01

The central objective of this work is the exploration and application of alternative possibilities to describe maximally supersymmetric field theories in four dimensions: N=4 super Yang-Mills theory and N=8 supergravity. While twistor string theory has been proven very useful in the context of N=4 SYM, no analogous formulation for N=8 supergravity is available. In addition to the part describing N=4 SYM theory, twistor string theory contains vertex operators corresponding to the states of N=4 conformal supergravity. Those vertex operators have to be altered in order to describe (non-conformal) Einstein supergravity. A modified version of the known open twistor string theory, including a term which breaks the conformal symmetry for the gravitational vertex operators, has been proposed recently. In a first part of the thesis structural aspects and consistency of the modified theory are discussed. Unfortunately, the majority of amplitudes can not be constructed, which can be traced back to the fact that the dimension of the moduli space of algebraic curves in twistor space is reduced in an inconsistent manner. The issue of a possible finiteness of N=8 supergravity is closely related to the question of the existence of valid counterterms in the perturbation expansion of the theory. In particular, the coefficient in front of the so-called R 4 counterterm candidate has been shown to vanish by explicit calculation. This behavior points into the direction of a symmetry not taken into account, for which the hidden on-shell E 7(7) symmetry is the prime candidate. The validity of the so-called double-soft scalar limit relation is a necessary condition for a theory exhibiting E 7(7) symmetry. By calculating the double-soft scalar limit for amplitudes derived from an N=8 supergravity action modified by an additional R 4 counterterm, one can test for possible constraints originating in the E 7(7) symmetry. In a second part of the thesis, the appropriate amplitudes are calculated

Unified-field theory: yesterday, today, tomorrow

International Nuclear Information System (INIS)

Bergman, P.G.

1982-01-01

Beginning with the expounding of Einstein understanding of advantages and disadvantages of general relativity theory, the authors proceed to consideration of what the complete unified theory have to be according to Einstein. The four theories which can be considered as ''unified'', namely weyl and Calutsa ones, worked out a half of century ago, and twistor twisting and supersymmetry theories, nowadays attracting attention, are briefly described and discussed. The authors come to a conclusion that achievements in elementary-particle physics have to affect any future theory, that this theory has to explain the principle contradictions between classical and quantum field theories, and that finally it can lead to change of the modern space-time model as a four-dimensional variety

Effective-field theory for dynamic phase diagrams of the kinetic spin-3/2 Blume–Capel model under a time oscillating longitudinal field

Energy Technology Data Exchange (ETDEWEB)

Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Kocakaplan, Yusuf [Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)

2013-12-15

Dynamic phase diagrams are presented for the kinetic spin-3/2 Blume–Capel model under a time oscillating longitudinal field by use of the effective-field theory with correlations. The dynamic equation of the average magnetization is obtained for the square lattice by utilizing the Glauber-type stochastic process. Dynamic phase diagrams are presented in the reduced temperature and the magnetic field amplitude plane. We also investigated the effect of longitudinal field frequency. Finally, the discussion and comparison of the phase diagrams are given. - Highlights: • Dynamic behaviors in the spin-3/2 Blume–Capel system is investigated by the effective-field theory based on the Glauber-type stochastic dynamics. • The dynamic phase transitions and dynamic phase diagrams are obtained. • The effects of the longitudinal field frequency on the dynamic phase diagrams of the system are investigated. • Dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and several critical points as well as a re-entrant behavior.

Effective-field theory for dynamic phase diagrams of the kinetic spin-3/2 Blume–Capel model under a time oscillating longitudinal field

International Nuclear Information System (INIS)

Ertaş, Mehmet; Kocakaplan, Yusuf; Keskin, Mustafa

2013-01-01

Dynamic phase diagrams are presented for the kinetic spin-3/2 Blume–Capel model under a time oscillating longitudinal field by use of the effective-field theory with correlations. The dynamic equation of the average magnetization is obtained for the square lattice by utilizing the Glauber-type stochastic process. Dynamic phase diagrams are presented in the reduced temperature and the magnetic field amplitude plane. We also investigated the effect of longitudinal field frequency. Finally, the discussion and comparison of the phase diagrams are given. - Highlights: • Dynamic behaviors in the spin-3/2 Blume–Capel system is investigated by the effective-field theory based on the Glauber-type stochastic dynamics. • The dynamic phase transitions and dynamic phase diagrams are obtained. • The effects of the longitudinal field frequency on the dynamic phase diagrams of the system are investigated. • Dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and several critical points as well as a re-entrant behavior

The phase diagram of scalar field theory on the fuzzy disc

Energy Technology Data Exchange (ETDEWEB)

Rea, Simone; Sämann, Christian [Maxwell Institute for Mathematical Sciences, Department of Mathematics,Heriot-Watt University,Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)

2015-11-17

Using a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second and third order phase transitions between them. In particular, we find that the second order phase transition happens approximately at a fixed ratio of the two coupling constants defining the potential. We compute this ratio analytically in the limit of large coupling constants. Our results qualitatively agree with previously obtained numerical results.

MHV Vertices And Tree Amplitudes In Gauge Theory

International Nuclear Information System (INIS)

Cachazo, Freddy; Svrcek, Peter; Witten, Edward

2004-01-01

As an alternative to the usual Feynman graphs, tree amplitudes in Yang-Mills theory can be constructed from tree graphs in which the vertices are tree level MHV scattering amplitudes, continued off shell in a particular fashion. The formalism leads to new and relatively simple formulas for many amplitudes, and can be heuristically derived from twistor space. (author)

Feynman diagrams sampling for quantum field theories on the QPACE 2 supercomputer

Energy Technology Data Exchange (ETDEWEB)

Rappl, Florian

2016-08-01

This work discusses the application of Feynman diagram sampling in quantum field theories. The method uses a computer simulation to sample the diagrammatic space obtained in a series expansion. For running large physical simulations powerful computers are obligatory, effectively splitting the thesis in two parts. The first part deals with the method of Feynman diagram sampling. Here the theoretical background of the method itself is discussed. Additionally, important statistical concepts and the theory of the strong force, quantum chromodynamics, are introduced. This sets the context of the simulations. We create and evaluate a variety of models to estimate the applicability of diagrammatic methods. The method is then applied to sample the perturbative expansion of the vertex correction. In the end we obtain the value for the anomalous magnetic moment of the electron. The second part looks at the QPACE 2 supercomputer. This includes a short introduction to supercomputers in general, as well as a closer look at the architecture and the cooling system of QPACE 2. Guiding benchmarks of the InfiniBand network are presented. At the core of this part, a collection of best practices and useful programming concepts are outlined, which enables the development of efficient, yet easily portable, applications for the QPACE 2 system.

Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram

DEFF Research Database (Denmark)

Codello, Alessandro; Tonero, Alberto

2016-01-01

We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2-scalar theories. The idea is to perform the path integral by weighting...... the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we...

Phase diagrams of exceptional and supersymmetric lattice gauge theories

Energy Technology Data Exchange (ETDEWEB)

Wellegehausen, Bjoern-Hendrik

2012-07-10

In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G{sub 2}, that has a trivial centre. To investigate G{sub 2} gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

Phase diagrams of exceptional and supersymmetric lattice gauge theories

International Nuclear Information System (INIS)

Wellegehausen, Bjoern-Hendrik

2012-01-01

In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G 2 , that has a trivial centre. To investigate G 2 gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

On-shell diagrams for N=8 supergravity amplitudes

Energy Technology Data Exchange (ETDEWEB)

Heslop, Paul; Lipstein, Arthur E. [Department of Mathematical Sciences, Durham University,Lower Mountjoy, Stockton Road, Durham, DH1 3LE (United Kingdom)

2016-06-10

We define recursion relations for N=8 supergravity amplitudes using a generalization of the on-shell diagrams developed for planar N=4 super-Yang-Mills. Although the recursion relations generically give rise to non-planar on-shell diagrams, we show that at tree-level the recursion can be chosen to yield only planar diagrams, the same diagrams occurring in the planar N=4 theory. This implies non-trivial identities for non-planar diagrams as well as interesting relations between the N=4 and N=8 theories. We show that the on-shell diagrams of N=8 supergravity obey equivalence relations analogous to those of N=4 super-Yang-Mills, and we develop a systematic algorithm for reading off Grassmannian integral formulae directly from the on-shell diagrams. We also show that the 1-loop 4-point amplitude of N=8 supergravity can be obtained from on-shell diagrams.

Strings on AdS2 and the high-energy limit of noncritical M-theory

International Nuclear Information System (INIS)

Horava, Petr; Horava, Petr; Keeler, Cynthia A.

2007-01-01

Noncritical M-theory in 2+1 dimensions has been defined as a double-scaling limit of a nonrelativistic Fermi liquid on a flat two-dimensional plane. Here we study this noncritical M-theory in the limit of high energies, analogous to the alpha(prime) → ∞ limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal alpha(prime) → ∞ limit leads to AdS 2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the high-energy limit, the natural ground state of noncritical M-theory similarly describes the AdS 2 x S 1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higher-spin extension of conformal Chern-Simons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the two-dimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS 2 x S 1 spacetime; thus, at least in the high-energy limit, noncritical M-theory can be nonperturbatively described as a 'Fermi liquid on twistor space'

Pure spinors as auxiliary fields in the ten-dimensional supersymmetric Yang-Mills theory

International Nuclear Information System (INIS)

Nilsson, B.E.W.

1986-01-01

A new way of introducing auxiliary fields into the ten-dimensional supersymmetric Yang-Mills theory is proposed. The auxiliary fields are commuting 'pure spinors' and constitute a non-linear realisation of the Lorentz group. This invalidates previous no-go theorems concerning the possibility of going off-shell in this theory. There seems to be a close relation between pure spinors and the concepts usually used in twistor theory. The non-Abelian theory can be constructed for all groups having pseudo-real representations. (author)

The mean squared writhe of alternating random knot diagrams

Energy Technology Data Exchange (ETDEWEB)

Diao, Y; Hinson, K [Department of Mathematics and Statistics University of North Carolina at Charlotte, NC 28223 (United States); Ernst, C; Ziegler, U, E-mail: ydiao@uncc.ed [Department of Mathematics and Computer Science, Western Kentucky University, Bowling Green, KY 42101 (United States)

2010-12-10

The writhe of a knot diagram is a simple geometric measure of the complexity of the knot diagram. It plays an important role not only in knot theory itself, but also in various applications of knot theory to fields such as molecular biology and polymer physics. The mean squared writhe of any sample of knot diagrams with n crossings is n when for each diagram at each crossing one of the two strands is chosen as the overpass at random with probability one-half. However, such a diagram is usually not minimal. If we restrict ourselves to a minimal knot diagram, then the choice of which strand is the over- or under-strand at each crossing is no longer independent of the neighboring crossings and a larger mean squared writhe is expected for minimal diagrams. This paper explores the effect on the correlation between the mean squared writhe and the diagrams imposed by the condition that diagrams are minimal by studying the writhe of classes of reduced, alternating knot diagrams. We demonstrate that the behavior of the mean squared writhe heavily depends on the underlying space of diagram templates. In particular this is true when the sample space contains only diagrams of a special structure. When the sample space is large enough to contain not only diagrams of a special type, then the mean squared writhe for n crossing diagrams tends to grow linearly with n, but at a faster rate than n, indicating an intrinsic property of alternating knot diagrams. Studying the mean squared writhe of alternating random knot diagrams also provides some insight into the properties of the diagram generating methods used, which is an important area of study in the applications of random knot theory.

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2016-10-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Center for Theoretical Physics (MCTP), University of Michigan,450 Church Street, Ann Arbor, MI 48109 (United States); Deutsches Elektronen-Synchrotron (DESY),Notkestraße 85, 22607 Hamburg (Germany)

2017-05-30

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

Energy Technology Data Exchange (ETDEWEB)

Zhang, Zhengkang [Michigan Univ., Ann Arbor, MI (United States). Michigan Center for Theoretical Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2016-10-15

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gaugecovariant quantities and are thus dubbed ''covariant diagrams.'' The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Covariant diagrams for one-loop matching

International Nuclear Information System (INIS)

Zhang, Zhengkang

2017-01-01

We present a diagrammatic formulation of recently-revived covariant functional approaches to one-loop matching from an ultraviolet (UV) theory to a low-energy effective field theory. Various terms following from a covariant derivative expansion (CDE) are represented by diagrams which, unlike conventional Feynman diagrams, involve gauge-covariant quantities and are thus dubbed “covariant diagrams.” The use of covariant diagrams helps organize and simplify one-loop matching calculations, which we illustrate with examples. Of particular interest is the derivation of UV model-independent universal results, which reduce matching calculations of specific UV models to applications of master formulas. We show how such derivation can be done in a more concise manner than the previous literature, and discuss how additional structures that are not directly captured by existing universal results, including mixed heavy-light loops, open covariant derivatives, and mixed statistics, can be easily accounted for.

Diagrams for symmetric product orbifolds

International Nuclear Information System (INIS)

Pakman, Ari; Rastelli, Leonardo; Razamat, Shlomo S.

2009-01-01

We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.

On E(11) of M-theory: 1. Hidden Symmetries of Maximal Supergravities and Lego of Dynkin Diagrams

International Nuclear Information System (INIS)

Nurmagambetov, A.J.

2007-01-01

We review a graphical way of classifying hidden symmetry algebras and groups of D=11, 10 maximal supergravities in terms of Dynkin diagrams, the shapes of which are determined by the bosonic field content of supergravities supermultiplets. The approach we follow is tightly related to the West's conjecture on a hidden symmetry of M-theory, and we discuss benefits of the approach in compare to other ways of searching for hidden symmetries of String Theory

Electron band theory predictions and the construction of phase diagrams

International Nuclear Information System (INIS)

Watson, R.E.; Bennett, L.H.; Davenport, J.W.; Weinert, M.

1985-01-01

The a priori theory of metals is yielding energy results which are relevant to the construction of phase diagrams - to the solution phases as well as to line compounds. There is a wide range in the rigor of the calculations currently being done and this is discussed. Calculations for the structural stabilities (fcc vs bcc vs hcp) of the elemental metals, quantities which are employed in the constructs of the terminal phases, are reviewed and shown to be inconsistent with the values currently employed in such constructs (also see Miodownik elsewhere in this volume). Finally, as an example, the calculated heats of formation are compared with experiment for PtHf, IrTa and OsW, three compounds with the same electron to atom ratio but different bonding properties

CERPHASE: Computer-generated phase diagrams

International Nuclear Information System (INIS)

Ruys, A.J.; Sorrell, C.C.; Scott, F.H.

1990-01-01

CERPHASE is a collection of computer programs written in the programming language basic and developed for the purpose of teaching the principles of phase diagram generation from the ideal solution model of thermodynamics. Two approaches are used in the generation of the phase diagrams: freezing point depression and minimization of the free energy of mixing. Binary and ternary phase diagrams can be generated as can diagrams containing the ideal solution parameters used to generate the actual phase diagrams. Since the diagrams generated utilize the ideal solution model, data input required from the operator is minimal: only the heat of fusion and melting point of each component. CERPHASE is menu-driven and user-friendly, containing simple instructions in the form of screen prompts as well as a HELP file to guide the operator. A second purpose of CERPHASE is in the prediction of phase diagrams in systems for which no experimentally determined phase diagrams are available, enabling the estimation of suitable firing or sintering temperatures for otherwise unknown systems. Since CERPHASE utilizes ideal solution theory, there are certain limitations imposed on the types of systems that can be predicted reliably. 6 refs., 13 refs

Selected topics on the nonrelativistic diagram technique

International Nuclear Information System (INIS)

Blokhintsev, L.D.; Narodetskij, I.M.

1983-01-01

The construction of the diagrams describing various processes in the four-particle systems is considered. It is shown that these diagrams, in particular the diagrams corresponding to the simple mechanisms often used in nuclear and atomic reaction theory, are readily obtained from the Faddeev-Yakubovsky equations. The covariant four-dimensional formalism of nonrelativistic Feynman graphs and its connection to the three-dimensional graph technique are briefly discussed

Indefinite harmonic forms and gauge theory

International Nuclear Information System (INIS)

Nakashima, M.

1988-01-01

Indecomposable representations have been extensively used in the construction of conformal and de Sitter gauge theories. It is thus noteworthy that certain unitary highest weight representations have been given a geometric realization as the unitary quotient of an indecomposable representation using indefinite harmonic forms [RSW]. We apply this construction to SU(2,2) and the de Sitter group. The relation is established between these representations and the massless, positive energy representations of SU(2,2) obtained in the physics literature. We investigate the extent to which this construction allows twistors to be viewed as a gauge theory of SU(2,2). For the de Sitter group, on which the gauge theory of singletons is based, we find that this construction is not directly applicable. (orig.)

Satake diagrams of affine Kac-Moody algebras

Energy Technology Data Exchange (ETDEWEB)

Tripathy, L K [S B R Government Womens' College, Berhampur, Orissa 760 001 (India); Pati, K C [Department of Physics, Khallikote College, Berhampur, Orissa 760 001 (India)

2006-02-10

Satake diagrams of affine Kac-Moody algebras (untwisted and twisted) are obtained from their Dynkin diagrams. These diagrams give a classification of restricted root systems associated with these algebras. In the case of simple Lie algebras, these root systems and Satake diagrams correspond to symmetric spaces which have recently found many physical applications in quantum integrable systems, quantum transport problems, random matrix theories etc. We hope these types of root systems may have similar applications in theoretical physics in future and may correspond to symmetric spaces analogue of affine Kac-Moody algebras if they exist.

Basics of introduction to Feynman diagrams and electroweak interactions physics

International Nuclear Information System (INIS)

Bilenky, S.M.; Mikhov, S.G.

1994-01-01

The Feynman diagrams are the main computational method for the evaluation of the matrix elements of different processes. Although it is a perturbative method, its significance is not restricted to perturbation theory only. In this book, the elements of quantum field theory, the Feynman diagram method, the theory of electroweak interactions and other topics are discussed. A number of classical weak and electroweak processes are considered in details. This involves, first of all, the construction of the matrix elements of the process using both the Feynman diagram method (when perturbation theory can be applied) and the invariance principles (when perturbation theory fails). Then the cross sections and the decay probabilities are computed. The text is providing widely used computational techniques and some experimental data. (A.B.). 32 refs., 7 appendix

Spin wave Feynman diagram vertex computation package

Science.gov (United States)

Price, Alexander; Javernick, Philip; Datta, Trinanjan

Spin wave theory is a well-established theoretical technique that can correctly predict the physical behavior of ordered magnetic states. However, computing the effects of an interacting spin wave theory incorporating magnons involve a laborious by hand derivation of Feynman diagram vertices. The process is tedious and time consuming. Hence, to improve productivity and have another means to check the analytical calculations, we have devised a Feynman Diagram Vertex Computation package. In this talk, we will describe our research group's effort to implement a Mathematica based symbolic Feynman diagram vertex computation package that computes spin wave vertices. Utilizing the non-commutative algebra package NCAlgebra as an add-on to Mathematica, symbolic expressions for the Feynman diagram vertices of a Heisenberg quantum antiferromagnet are obtained. Our existing code reproduces the well-known expressions of a nearest neighbor square lattice Heisenberg model. We also discuss the case of a triangular lattice Heisenberg model where non collinear terms contribute to the vertex interactions.

A twistor-like D=10 superparticle action with manifest N=8 world-line supersymmetry

International Nuclear Information System (INIS)

Galperin, A.; Sokatchev, E.

1992-03-01

We propose a new formulation of the D = 10 Brink-Schwarz superparticle which is manifestly invariant under both the target-space super-Poincare group and the world-line local N = 8 superconformal group. This twistor-like construction naturally involves the sphere S 8 as a coset space of the D = 10 Lorentz group. The action contains only a finite set of auxiliary fields, but they appear in unusual trilinear combinations. The origin of the on-shell D = 10 fermionic Κ symmetry of the standard Brink-Schwarz formulation is explained. The coupling to a D = 10 super-Maxwell background requires a new mechanism, in which the electric charge appears only on shell as an integration constant. (orig.)

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

International Nuclear Information System (INIS)

Weingarten, D.

1980-01-01

It is shown that the limit as N → infinitely with g 2 N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft. (orig.)

Correlation functions of the chiral stress-tensor multiplet in $ \\mathcal{N}=4 $ SYM

CERN Document Server

Chicherin, Dmitry; Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Mason, Lionel; Sokatchev, Emery

2015-01-01

We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N=4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N=4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N=4 SYM.

Gluing Ladder Feynman Diagrams into Fishnets

International Nuclear Information System (INIS)

Basso, Benjamin; Dixon, Lance J.; Stanford University, CA; University of California, Santa Barbara, CA

2017-01-01

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar Φ "4 theory. Our results are always multilinear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, which leads to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

An ambitwistor Yang-Mills Lagrangian

International Nuclear Information System (INIS)

Mason, L.J.; Skinner, D.

2006-01-01

We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory

Partition functions of web diagrams with an O7{sup −}-plane

Energy Technology Data Exchange (ETDEWEB)

Hayashi, Hirotaka [Tokai University, 4-1-1 Kitakaname,Hiratsuka, Kanagawa 259-1292 (Japan); Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Zoccarato, Gianluca [Departamento de Física Teórica and Instituto de Física Teórica UAM/CSIC,Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid (Spain)

2017-03-22

We consider the computation of the topological string partition function for 5-brane web diagrams with an O7{sup −}-plane. Since upon quantum resolution of the orientifold plane these diagrams become non-toric web diagrams without the orientifold we are able to apply the topological vertex to obtain the Nekrasov partition function of the corresponding 5d theory. We apply this procedure to the case of 5d SU(N) theories with one hypermultiplet in the antisymmetric representation and to the case of 5d pure USp(2N) theories. For these cases we discuss the dictionary between parameters and moduli of the 5d gauge theory and lengths of 5-branes in the web diagram and moreover we perform comparison of the results obtained via application of the topological vertex and the one obtained via localisation techniques, finding in all instances we consider perfect agreement.

Folded diagram theory, time-dependent approach of Johnson and Baranger

International Nuclear Information System (INIS)

Johnson, M.B.

1975-01-01

The folded diagram expansion of Brandow and extensively developed by Johnson and Baranger is discussed in detail. The time-dependent approach is reviewed through Feynman-Goldstone diagrams to establish the conventions used. The problem of calculating the effective interaction for nuclei beyond 208 Pb is then considered as an example. Finally, examples are given which show how to do the time integrations. (17 figures) (SDF)

Comparisons between observational color-magnitude diagrams and synthetic cluster diagrams for young star clusters in the Magellanic Clouds

International Nuclear Information System (INIS)

Recker, S.A.; Brunish, W.M.; Mathews, G.J.

1984-01-01

Young star clusters ( 8 yr) in the Magellanic Clouds (MC) can be used to test the current status of the theory of stellar evolution as applied to intermediate and massive stars. The color-magnitude diagram of many young clusters in the MC shows large numbers of stars in both the main sequence and post main sequence evolutionary phases. Using a grid of stellar evolution models, synthetic cluster H-R diagrams are constructed and compared to observed color-magnitude diagrams to determine the age, age spread, and composition for any given cluster. In addition, for those cases where the data is of high quality, detailed comparisons between theory and observation can provide a diagnostic of the accuracy of the stellar evolution models. Initial indications of these comparisons suggest that the theoretical models should be altered to include: a larger value for the mixing length parameter, a larger rate of mass loss during the asymptotic giant branch phase, and possibly convective overshoot during the core burning phases. (Auth.)

Field theory

CERN Multimedia

1999-11-08

In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

Pembuatan Kakas Bantu untuk Mendeteksi Ketidaksesuaian Diagram Urutan (Sequence Diagram dengan Diagram Kasus Penggunaan (Use Case Diagram

Directory of Open Access Journals (Sweden)

Andrias Meisyal Yuwantoko

2017-03-01

Full Text Available Sebuah diagram urutan dibuat  berdasarkan alur yang ada pada deskripsi kasus penggunaan. Alur tersebut dire- presentasikan dalam  bentuk  interaksi antara aktor  dan  sistem. Pemeriksaan rancangan diagram urutan perlu dilakukan untuk mengetahui ketidaksesuaian urutan alur  kasus penggunaan dengan urutan pesan yang dikirimkan oleh objek-objek pada diagram urutan. Rancangan diagram yang sesuai merupakan kunci ketepatan (correctness implementasi  perangkat lunak. Namun, pemeriksaan ketidaksesuaian masih dilakukan secara manual. Hal ini menjadi masalah apabila sebuah proyek perangkat lunak memiliki banyak  rancangan diagram dan sumber daya manusia tidak  mencukupi. Pemeriksaan membutuhkan waktu yang lama dan memiliki dampak pada waktu pengembangan perangkat lunak. Penelitian ini mengusulkan pembuatan kakas bantu  untuk mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Ketidaksesuaian dilihat dari kemiripan semantik kalimat antara alur pada deskripsi kasus penggunaan dan triplet. Dari hasil pembuatan kakas bantu, kakas bantu yang dibuat dapat mendeteksi ketidaksesuaian diagram urutan dengan diagram kasus penggunaan. Kakas  bantu ini diharapkan tidak hanya membantu pemeriksaan rancangan diagram akan tetapi mempercepat waktu pengembangan perangkat lunak.

The phase diagram and transport properties of MgO from theory and experiment

Science.gov (United States)

Shulenburger, Luke

2013-06-01

Planetary structure and the formation of terrestrial planets have received tremendous interest due to the discovery of so called super-earth exoplanets. MgO is a major constituent of Earth's mantle, the rocky cores of gas giants and is a likely component of the interiors of many of these exoplanets. The high pressure - high temperature behavior of MgO directly affects equation of state models for planetary structure and formation. In this work, we examine MgO under extreme conditions using experimental and theoretical methods to determine its phase diagram and transport properties. Using plate impact experiments on Sandia's Z facility the solid-solid phase transition from B1 to B2 is clearly determined. The melting transition, on the other hand, is subtle, involving little to no signal in us-up space. Theoretical work utilizing density functional theory (DFT) provides a complementary picture of the phase diagram. The solid-solid phase transition is identified through a series of quasi-harmonic phonon calculations and thermodynamic integration, while the melt boundary is found using phase coexistence calculations. One issue of particular import is the calculation of reflectivity along the Hugoniot and the influence of the ionic structure on the transport properties. Particular care is necessary because of the underestimation of the band gap and attendant overestimation of transport properties due to the use of semi-local density functional theory. We will explore the impact of this theoretical challenge and its potential solutions in this talk. The integrated use of DFT simulations and high-accuracy shock experiments together provide a comprehensive understanding of MgO under extreme conditions. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.

From State Diagram to Class Diagram

DEFF Research Database (Denmark)

Borch, Ole; Madsen, Per Printz

2009-01-01

UML class diagram and Java source code are interrelated and Java code is a kind of interchange format. Working with UML state diagram in CASE tools, a corresponding xml file is maintained. Designing state diagrams is mostly performed manually using design patterns and coding templates - a time...... consuming process. This article demonstrates how to compile such a diagram into Java code and later, by reverse engineering, produce a class diagram. The process from state diagram via intermediate SAX parsed xml file to Apache Velocity generated Java code is described. The result is a fast reproducible...

Conformal description of spinning particles

International Nuclear Information System (INIS)

Todorov, I.T.

1986-01-01

This book is an introduction to the application of the conformal group to quantum field theory of particles with spin. After an introduction to the twistor representations of the conformal group of a conformally flat space-time and twistor flag manifolds with Su(2,2) orbits the classical phase space of conformal spinning particles is described. Thereafter the twistor description of classical zero mass fields is considered together with the quantization. (HSI)

High-energy, large-momentum-transfer processes: Ladder diagrams in φ3 theory. Pt. 2

International Nuclear Information System (INIS)

Osland, P.; Wu, T.T.; Harvard Univ., Cambridge, MA

1987-01-01

The scattering amplitude for the four-rung ladder diagram in φ 3 theory is evaluated at high energies and for large momentum transfers. The result takes the form of s -1 vertical stroketvertical stroke -3 multiplied by a homogeneous sixth-order polynomial in ln s and 1nvertical stroketvertical stroke. The novel and unexpected feature is that this polynomial is different depending on whether 1n vertical stroketvertical stroke is larger or less than 1/2 1n s. Thus the asymptotic formula is not analytic at 1n vertical stroketvertical stroke=1/2 1n s, although the first five derivatives are continuous. (orig.)

The Coulomb Branch of 3d N= 4 Theories

Science.gov (United States)

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide

2017-09-01

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.

[Identification of meridian-acupoint diagrams and meridian diagrams].

Science.gov (United States)

Shen, Wei-hong

2008-08-01

In acu-moxibustion literature, there are two kinds of diagrams, meridian-acupoint diagrams and meridian diagrams. Because they are very similar in outline, and people now have seldom seen the typical ancient meridian diagrams, meridian-acupoint diagrams have been being incorrectly considered to be the meridian diagrams for a long time. It results in confusion in acu-moxibustion academia. The present paper stresses its importance in academic research and introduces some methods for identifying them correctly. The key points for identification of meridian-acupoint diagrams and meridian diagrams are: the legend of diagrams and the drawing style of the ancient charts. In addition, the author makes a detailed explanation about some acu-moxibustion charts which are easily confused. In order to distinguish meridian-acupoint diagrams and meridian diagrams correctly, he or she shoulnd understand the diagrams' intrinsic information as much as possible and make a comprehensive analysis about them.

Is the string theory doomed?

International Nuclear Information System (INIS)

Le Meur, H.; Daninos, F.; Bachas, C.

2007-01-01

Since its beginning, in the sixties, the string theory has succeeded in overcoming a lot of theoretical difficulties but now the complete absence of experimental validation entertains doubts about its ability to represent the real world and questions its hegemony in today's theoretical physics. Other space-time theories like the twistors, or the non-commutative geometry, or the loop quantum gravity, or the causal dynamics triangulation might begin receiving more attention. Despite all that, the string theory can be given credit for 4 achievements. First, the string theory has provided a consistent quantum description of gravity. Secondly, the string theory has built a theoretical frame that has allowed the unification of the 4 basic interactions. Thirdly, the string theory applied to astrophysics issues has demonstrated that the evaporation of a black hole does not necessarily lead to a loss of information which comforts the universality of the conservation of the quantity of information in any system and as a consequence put a fatal blow to the so-called paradox observed in black holes. Fourthly, the string theory has given a new and original meaning on the true nature of space-time. (A.C.)

Dynamic phase diagrams of the Ising metamagnet in an oscillating magnetic field within the effective-field theory

Energy Technology Data Exchange (ETDEWEB)

Deviren, Bayram [Department of Physics, Nevsehir University, 50300 Nevsehir (Turkey); Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.t [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)

2010-07-12

Dynamic aspects of a two-sublattice Ising metamagnet on honeycomb, square and hexagonal lattices under the presence of a time-dependent oscillating external magnetic field are studied by using the effective-field theory with correlations. The set of effective-field dynamic equations is derived by employing Glauber transition rates. The phases in the system are obtained by solving these dynamic equations. The thermal behavior of the dynamic staggered magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. The phase diagrams are constructed in two different planes, and exhibit dynamic tricritical behavior, which strongly depends on interaction parameters. In order to investigate the spin correlation effect on the dynamic phase diagrams of the system, the results are also given within the framework of the dynamic mean-field approximation.

Dynamic phase diagrams of the Ising metamagnet in an oscillating magnetic field within the effective-field theory

International Nuclear Information System (INIS)

Deviren, Bayram; Keskin, Mustafa

2010-01-01

Dynamic aspects of a two-sublattice Ising metamagnet on honeycomb, square and hexagonal lattices under the presence of a time-dependent oscillating external magnetic field are studied by using the effective-field theory with correlations. The set of effective-field dynamic equations is derived by employing Glauber transition rates. The phases in the system are obtained by solving these dynamic equations. The thermal behavior of the dynamic staggered magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. The phase diagrams are constructed in two different planes, and exhibit dynamic tricritical behavior, which strongly depends on interaction parameters. In order to investigate the spin correlation effect on the dynamic phase diagrams of the system, the results are also given within the framework of the dynamic mean-field approximation.

Random matrix models for phase diagrams

International Nuclear Information System (INIS)

Vanderheyden, B; Jackson, A D

2011-01-01

We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from quantum chromodynamics to high-T c materials. Instead of working from specific models, phase diagrams are constructed by averaging over the ensemble of theories that possesses the relevant symmetries of the problem. Although approximate in nature, this approach has a number of advantages. First, it can be useful in distinguishing generic features from model-dependent details. Second, it can help in understanding the 'minimal' number of symmetry constraints required to reproduce specific phase structures. Third, the robustness of predictions can be checked with respect to variations in the detailed description of the interactions. Finally, near critical points, random matrix models bear strong similarities to Ginsburg-Landau theories with the advantage of additional constraints inherited from the symmetries of the underlying interaction. These constraints can be helpful in ruling out certain topologies in the phase diagram. In this Key Issues Review, we illustrate the basic structure of random matrix models, discuss their strengths and weaknesses, and consider the kinds of system to which they can be applied.

Algorithmic approach to diagram techniques

International Nuclear Information System (INIS)

Ponticopoulos, L.

1980-10-01

An algorithmic approach to diagram techniques of elementary particles is proposed. The definition and axiomatics of the theory of algorithms are presented, followed by the list of instructions of an algorithm formalizing the construction of graphs and the assignment of mathematical objects to them. (T.A.)

Diagrams in the polaron model

International Nuclear Information System (INIS)

Smondyrev, M.A.

1985-01-01

The perturbation theory for the polaron energy is systematically treated on the diagrammatic basis. Feynman diagrams being constructed allow to calculate the polaron energy up to the third order in powers of the coupling constant. Similar calculations are performed for the average number of virtual phonons

Reading fitness landscape diagrams through HSAB concepts

Energy Technology Data Exchange (ETDEWEB)

Vigneresse, Jean-Louis, E-mail: jean-louis.vigneresse@univ-lorraine.fr

2014-10-31

Highlights: • Qualitative information from HSAB descriptors. • 2D–3D diagrams using chemical descriptors (χ, η, ω, α) and principles (MHP, mEP, mPP). • Estimate of the energy exchange during reaction paths. • Examples from complex systems (geochemistry). - Abstract: Fitness landscapes are conceived as range of mountains, with local peaks and valleys. In terms of potential, such topographic variations indicate places of local instability or stability. The chemical potential, or electronegativity, its value changed of sign, carries similar information. In addition to chemical descriptors defined through hard-soft acid-base (HSAB) concepts and computed through density functional theory (DFT), the principles that rule chemical reactions allow the design of such landscape diagrams. The simplest diagram uses electrophilicity and hardness as coordinates. It allows examining the influence of maximum hardness or minimum electrophilicity principles. A third dimension is introduced within such a diagram by mapping the topography of electronegativity, polarizability or charge exchange. Introducing charge exchange during chemical reactions, or mapping a third parameter (f.i. polarizability) reinforces the information carried by a simple binary diagram. Examples of such diagrams are provided, using data from Earth Sciences, simple oxides or ligands.

Yank-Mills fields and hypersurface twistors

International Nuclear Information System (INIS)

Fioravanti, M.A.

1989-01-01

The author establishes a one-to-one correspondence between (not necessarily self-dual) solutions of the non-abelian source-free Yang-Mills equations on Minkowski space, and pairs of cohomology classes [γ], [φ]. If O(n) is the sheaf of holomorphic sections of the n th tensor power of the hyperplane line bundle over C P 1 , and g is the Lie algebra of the gauge group, [γ] var-epsilon H CR 1 (PN circumflex,g) and defines a deformation C-R(γ) of the canonical C-R structure on a principal bundle over PN circumflex, the subset of null twistor space PN, representing unscaled null geodesics in Minkowski space. [φ] var-epsilon H CR(γ) 1 (PN,O(-4) direct-product g). The spin-bundle over Minkowski space is used in the construction. This bundle is foliated by a congruence of lines; each of these lines projects into a null geodesic in Minkowski space, and corresponds to a point in N. The restriction S of the spin-bundle to a spacelike hyperplane in Minkowski space is transversal to this foliation, and PN is identified with S. [γ] encodes certain components of the Yang-Mills connection on S, and [φ] encodes the self-dual part of the field on S. They give initial values for a system of evolution equations in the spin-bundle. This system is composed by four first order ordinary differential equations along the lines in the foliation of the spin-bundle, with some of the right-hand sides given by integrals on the fiber over a point in Minkowski space, and a partial differential equation on this fiber. The evolution equations simplify largely in the case of an abelian gauge group. In the case of anti-self-dual fields, the system reduces to two ordinary differential equations along the lines in the foliation of the spin-bundle, and the differential equation on the fiber over each point in Minkowski space. He studies the modifications in the construction when sources are present

A Three-dimensional Topological Model of Ternary Phase Diagram

International Nuclear Information System (INIS)

Mu, Yingxue; Bao, Hong

2017-01-01

In order to obtain a visualization of the complex internal structure of ternary phase diagram, the paper realized a three-dimensional topology model of ternary phase diagram with the designed data structure and improved algorithm, under the guidance of relevant theories of computer graphics. The purpose of the model is mainly to analyze the relationship between each phase region of a ternary phase diagram. The model not only obtain isothermal section graph at any temperature, but also extract a particular phase region in which users are interested. (paper)

Quantum MHV Diagrams

OpenAIRE

Brandhuber, Andreas; Travaglini, Gabriele

2006-01-01

Over the past two years, the use of on-shell techniques has deepened our understanding of the S-matrix of gauge theories and led to the calculation of many new scattering amplitudes. In these notes we review a particular on-shell method developed recently, the quantum MHV diagrams, and discuss applications to one-loop amplitudes. Furthermore, we briefly discuss the application of D-dimensional generalised unitarity to the calculation of scattering amplitudes in non-supersymmetric Yang-Mills.

Gravity with a cosmological constant from rational curves

Science.gov (United States)

Adamo, Tim

2015-11-01

We give a new formula for all tree-level correlators of boundary field insertions in gauged N=8 supergravity in AdS4; this is an analogue of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann sphere to twistor space, with no reference to bulk perturbation theory. It is polynomial in the cosmological constant, and equal to the classical scattering amplitudes of supergravity in the flat space limit. The formula is manifestly supersymmetric, independent of gauge choices on twistor space, and equivalent to expressions computed via perturbation theory at 3-point overline{MHV} and n-point MHV. We also show that the formula factorizes and obeys BCFW recursion in twistor space.

Gravity with a cosmological constant from rational curves

International Nuclear Information System (INIS)

Adamo, Tim

2015-01-01

We give a new formula for all tree-level correlators of boundary field insertions in gauged N=8 supergravity in AdS_4; this is an analogue of the tree-level S-matrix in anti-de Sitter space. The formula is written in terms of rational maps from the Riemann sphere to twistor space, with no reference to bulk perturbation theory. It is polynomial in the cosmological constant, and equal to the classical scattering amplitudes of supergravity in the flat space limit. The formula is manifestly supersymmetric, independent of gauge choices on twistor space, and equivalent to expressions computed via perturbation theory at 3-point (MHV)-bar and n-point MHV. We also show that the formula factorizes and obeys BCFW recursion in twistor space.

Macroscopic Fundamental Diagram for pedestrian networks : Theory and applications

NARCIS (Netherlands)

Hoogendoorn, S.P.; Daamen, W.; Knoop, V.L.; Steenbakkers, Jeroen; Sarvi, Majid

2017-01-01

The Macroscopic Fundamental diagram (MFD) has proven to be a powerful concept in understanding and managing vehicular network dynamics, both from a theoretical angle and from a more application-oriented perspective. In this contribution, we explore the existence and the characteristics of the

Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

KAUST Repository

Zuberi, M. A. H.; Alkhalifah, Tariq Ali

2014-01-01

Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

The limit shape problem for ensembles of Young diagrams

CERN Document Server

Hora, Akihito

2016-01-01

This book treats ensembles of Young diagrams originating from group-theoretical contexts and investigates what statistical properties are observed there in a large-scale limit. The focus is mainly on analyzing the interesting phenomenon that specific curves appear in the appropriate scaling limit for the profiles of Young diagrams. This problem is regarded as an important origin of recent vital studies on harmonic analysis of huge symmetry structures. As mathematics, an asymptotic theory of representations is developed of the symmetric groups of degree n as n goes to infinity. The framework of rigorous limit theorems (especially the law of large numbers) in probability theory is employed as well as combinatorial analysis of group characters of symmetric groups and applications of Voiculescu's free probability. The central destination here is a clear description of the asymptotic behavior of rescaled profiles of Young diagrams in the Plancherel ensemble from both static and dynamic points of view.

Generalized internal multiple imaging (GIMI) using Feynman-like diagrams

KAUST Repository

Zuberi, M. A. H.

2014-05-19

Single scattering events recorded in surface seismic data do not fully illuminate the subsurface structure, especially if it is complicated. In such cases, multiple internal scatterings (internal multiples) can help improve the illumination. We devise a generalized internal multiple imaging (GIMI) procedure that maps internal multiple energy to their true location with a relatively mild addition to the computational cost. GIMI theory relies heavily on seismic interferometry, which often involves cumbersome algebra, especially when one is dealing with high-order terms in the perturbation series. To make the derivations, and inference of the results easier, we introduce Feynman-like diagrams to represent different terms of the perturbation series (solution to the Lippman–Schwinger equation). The rules we define for the diagrams allow operations like convolution and cross-correlation in the series to be compressed in diagram form. The application of the theory to a double scattering example demonstrates the power of the method.

The geometry of on-shell diagrams

Science.gov (United States)

Franco, Sebastián; Galloni, Daniele; Mariotti, Alberto

2014-08-01

The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such as the Grassmannian. We perform a detailed investigation of the combinatorial and geometric objects associated to these graphs. We mainly focus on their relation to polytopes and toric geometry, the Grassmannian and its stratification. Our work extends the current understanding of these connections along several important fronts, most notably eliminating restrictions imposed by planarity, positivity, reducibility and edge removability. We illustrate our ideas with several explicit examples and introduce concrete methods that considerably simplify computations. We consider it highly likely that the structures unveiled in this article will arise in the on-shell study of scattering amplitudes beyond the planar limit. Our results can be conversely regarded as an expansion in the understanding of the Grassmannian in terms of bipartite graphs.

On tree amplitudes of supersymmetric Einstein-Yang-Mills theory

Energy Technology Data Exchange (ETDEWEB)

Adamo, Tim; Casali, Eduardo; Roehrig, Kai A.; Skinner, David [Department of Applied Mathematics & Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA United Kingdom (United Kingdom)

2015-12-29

We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization and sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.

A diagram approach to character formulae for finite and compact groups

International Nuclear Information System (INIS)

Kibler, M.; Elbaz, E.

1978-06-01

Some basic relations for the representation theory and the Wigner-Racah algebra of a finite or compact continuous group are discussed and transcribed in terms of diagrams. Special emphasis is placed on the case of a simply reducible group and all the diagrams are applicable to SU 2 without any change

Phase diagram of a Lennard-Jones solid

International Nuclear Information System (INIS)

Choi, Y.; Ree, T.; Ree, F.H.

1993-01-01

A phase diagram of a Lennard-Jones solid at kT/ε≥0.8 is constructed by our recent perturbation theory. It shows the stability of the face-centered-cubic phase except within a small pressure and temperature domain, where the hexagonal-close packed phase may occur. The theory predicts anharmonic contributions to the Helmholtz free energy (important to the crystal stability) in good agreement with Monte Carlo data

The unitary space of particle internal states

International Nuclear Information System (INIS)

Perjes, Z.

1978-09-01

A relativistic theory of particle internal properties has been developed. Suppressing space-time information, internal wave functions and -observables are constructed in a 3-complex-dimensional space. The quantum numbers of a spinning point particle in this unitary space correspond with those of a low-mass hadron. Unitary space physics is linked with space-time notions via the Penrose theory of twistors, where new flavors may be represented by many-twistor systems. It is shown here that a four-twistor particle fits into the unitary space picture as a system of two points with equal masses and oppositely pointing unitary spins. Quantum states fall into the ISU(3) irreducible representations discovered by Sparling and the author. Full details of the computation involving SU(3) recoupling techniques are given. (author)

Use of Influence Diagrams and Fuzzy Theory to Develop Assessment Method of Organizational Influences on Component Maintenance

International Nuclear Information System (INIS)

Yoonik Kim; Kwang-Won Ahn; Chang-Hyun Chung; Kil Yoo Kim; Joon-Eon Yang

2002-01-01

Organization can make influences on all the systems. Especially in case of nuclear power plants in which safety is established to be one of the most important operating goals, there have been a lot of research efforts for the hardware advancement. However in recent years, it has been widely recognized that organizational factors in nuclear power plants have an important influence on the safety attitudes and the safe behavior of individuals. Until now, any means to include assessments of organizational structure in probabilistic risk assessments have not been universally accepted. The objective of this work is to develop a method to assess organizational influences on component maintenance. Influence diagrams are introduced in this method as a decision making tool and fuzzy theory is used to reflect the vagueness in considering relevance of human activities in maintenance tasks. Introducing fuzzy theory to assess the organizational factors is deemed to a somewhat new trial, which makes it possible to convert linguistic vague descriptions into mathematical ones. Fuzzy linguistic descriptions offer an alternative and often complementary language to conventional, i.e., analytic approaches to modeling systems. Among the existing methodologies to assess organizational factors, the concept of the ω-factor model is utilized and the mechanism that organizational factors have influences on component maintenance is evaluated through composing influence diagrams. These influences go to failure rates and eventually affect component unavailability. Further study will make it possible that the influences of organizational factors on human error probabilities are incorporated into human reliability analysis and furthermore probabilistic safety assessment. (authors)

Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams

International Nuclear Information System (INIS)

Willow, Soohaeng Yoo; Hirata, So

2014-01-01

A new, alternative set of interpretation rules of Feynman–Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE h after 10 6 Monte Carlo steps

Stochastic, real-space, imaginary-time evaluation of third-order Feynman–Goldstone diagrams

Energy Technology Data Exchange (ETDEWEB)

Willow, Soohaeng Yoo [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Center for Superfunctional Materials, Department of Chemistry, Pohang University of Science and Technology, San 31, Hyojadong, Namgu, Pohang 790-784 (Korea, Republic of); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, Saitama 332-0012 (Japan)

2014-01-14

A new, alternative set of interpretation rules of Feynman–Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mE{sub h} after 10{sup 6} Monte Carlo steps.

Phase diagrams of diluted transverse Ising nanowire

International Nuclear Information System (INIS)

Bouhou, S.; Essaoudi, I.; Ainane, A.; Saber, M.; Ahuja, R.; Dujardin, F.

2013-01-01

In this paper, the phase diagrams of diluted Ising nanowire consisting of core and surface shell coupling by J cs exchange interaction are studied using the effective field theory with a probability distribution technique, in the presence of transverse fields in the core and in the surface shell. We find a number of characteristic phenomena. In particular, the effect of concentration c of magnetic atoms, the exchange interaction core/shell, the exchange in surface and the transverse fields in core and in surface shell of phase diagrams are investigated. - Highlights: ► We use the EFT to investigate the phase diagrams of Ising transverse nanowire. ► Ferrimagnetic and ferromagnetic cases are investigated. ► The effects of the dilution and the transverse fields in core and shell are studied. ► Behavior of the transition temperature with the exchange interaction is given

Synthetic H-R diagrams as an observational test of stellar evolution theory

International Nuclear Information System (INIS)

Mathews, G.J.; Becker, S.A.; Brunish, W.M.

1983-07-01

Synthetic H-R diagrams are constructed from a grid of stellar models. These are compared directly with observations of young clusters in the LMC and SMC as a test of the models and as a means to determine the age, age dispersion, and composition of the clusters. Significant discrepancies between the observed and model H-R diagrams indicate the possible influences of convective overshoot, large AGB mass-loss rates, and the best value for the mixing length parameter

The interface of mathematics and particle physics

Energy Technology Data Exchange (ETDEWEB)

Quillen, D.G.; Segal, G.B.; Tsousheung Tsun (Oxford Univ. (UK). Mathematical Inst.) (eds.)

1990-01-01

This collection of papers is based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on the Interface of Mathematics and Particle Physics held at Oxford University in September 1988. There are twenty-five papers, all of which are indexed separately. Many contribute to the search for an understanding of how gravity can be unified with other interactions in one field theory. String and twistor theories are important in this search and many of the papers refer to strings, superstrings or twistor. All the papers seek a physical interpretation of theories and elementary particles. (author).

The Traders' Cross: Identifying Traders' Surpluses in the Traditional Edgeworth Exchange Diagram

Science.gov (United States)

Beaulier, Scott A.; Prychitko, David L.

2010-01-01

The Edgeworth exchange diagram is a traditional tool of undergraduate microeconomic theory that depicts the mutually beneficial gains from voluntary trade. The authors take the analysis one step further. They identify the buyer's and seller's surpluses that accrue to both trading parties in the Edgeworth diagram. This is a straightforward exercise…

Sedimentation stacking diagram of binary colloidal mixtures and bulk phases in the plane of chemical potentials

International Nuclear Information System (INIS)

Heras, Daniel de las; Schmidt, Matthias

2015-01-01

We give a full account of a recently proposed theory that explicitly relates the bulk phase diagram of a binary colloidal mixture to its phase stacking phenomenology under gravity (de las Heras and Schmidt 2013 Soft Matter 9 8636). As we demonstrate, the full set of possible phase stacking sequences in sedimentation-diffusion equilibrium originates from straight lines (sedimentation paths) in the chemical potential representation of the bulk phase diagram. From the analysis of various standard topologies of bulk phase diagrams, we conclude that the corresponding sedimentation stacking diagrams can be very rich, even more so when finite sample height is taken into account. We apply the theory to obtain the stacking diagram of a mixture of nonadsorbing polymers and colloids. We also present a catalog of generic phase diagrams in the plane of chemical potentials in order to facilitate the practical application of our concept, which also generalizes to multi-component mixtures. (paper)

Feynman diagrams coupled to three-dimensional quantum gravity

International Nuclear Information System (INIS)

Barrett, John W

2006-01-01

A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological constant tends to zero

Phase diagrams of diluted transverse Ising nanowire

Energy Technology Data Exchange (ETDEWEB)

Bouhou, S.; Essaoudi, I. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Ainane, A., E-mail: ainane@pks.mpg.de [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Saber, M. [Laboratoire de Physique des Matériaux et Modélisation, des Systèmes, (LP2MS), Unité Associée au CNRST-URAC 08, University of Moulay Ismail, Physics Department, Faculty of Sciences, B.P. 11201 Meknes (Morocco); Max-Planck-Institut für Physik Complexer Systeme, Nöthnitzer Str. 38 D-01187 Dresden (Germany); Ahuja, R. [Condensed Matter Theory Group, Department of Physics and Astronomy, Uppsala University, 75120 Uppsala (Sweden); Dujardin, F. [Laboratoire de Chimie et Physique des Milieux Complexes (LCPMC), Institut de Chimie, Physique et Matériaux (ICPM), 1 Bd. Arago, 57070 Metz (France)

2013-06-15

In this paper, the phase diagrams of diluted Ising nanowire consisting of core and surface shell coupling by J{sub cs} exchange interaction are studied using the effective field theory with a probability distribution technique, in the presence of transverse fields in the core and in the surface shell. We find a number of characteristic phenomena. In particular, the effect of concentration c of magnetic atoms, the exchange interaction core/shell, the exchange in surface and the transverse fields in core and in surface shell of phase diagrams are investigated. - Highlights: ► We use the EFT to investigate the phase diagrams of Ising transverse nanowire. ► Ferrimagnetic and ferromagnetic cases are investigated. ► The effects of the dilution and the transverse fields in core and shell are studied. ► Behavior of the transition temperature with the exchange interaction is given.

Diagram Size vs. Layout Flaws: Understanding Quality Factors of UML Diagrams

DEFF Research Database (Denmark)

Störrle, Harald

2016-01-01

, though, is our third goal of extending our analysis aspects of diagram quality. Method: We improve our definition of diagram size and add a (provisional) definition of diagram quality as the number of topographic layout flaws. We apply these metrics on 60 diagrams of the five most commonly used types...... of UML diagram. We carefully analyze the structure of our diagram samples to ensure representativeness. We correlate diagram size and layout quality with modeler performance data obtained in previous experiments. The data set is the largest of its kind (n-156). Results: We replicate earlier findings......, and extend them to two new diagram types. We provide an improved definition of diagram size, and provide a definition of topographic layout quality, which is one more step towards a comprehensive definition of diagram quality as such. Both metrics are shown to be objectively applicable. We quantify...

Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo

Energy Technology Data Exchange (ETDEWEB)

Azadi, Sam, E-mail: s.azadi@ucl.ac.uk [Departments of Physics and Astronomy, University College London, Thomas Young Center, London Centre for Nanotechnology, London WC1E 6BT (United Kingdom); Cohen, R. E. [Extreme Materials Initiative, Geophysical Laboratory, Carnegie Institution for Science, Washington, DC 20015 (United States); Department of Earth- and Environmental Sciences, Ludwig Maximilians Universität, Munich 80333 (Germany); Department of Physics and Astronomy, University College London, London WC1E 6BT (United Kingdom)

2016-08-14

We studied the low-pressure (0–10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo and density functional theory (DFT) methods. We performed diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. Using density functional perturbation theory, we computed the phonon contributions to the free energies. Our DFT enthalpy-pressure phase diagrams indicate that the Pbca and P2{sub 1}/c structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature Pbca to P2{sub 1}/c phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations give 50.6 ± 0.5 kJ/mol for crystalline benzene lattice energy.

Heuristic Diagrams as a Tool to Teach History of Science

Science.gov (United States)

Chamizo, José A.

2012-05-01

The graphic organizer called here heuristic diagram as an improvement of Gowin's Vee heuristic is proposed as a tool to teach history of science. Heuristic diagrams have the purpose of helping students (or teachers, or researchers) to understand their own research considering that asks and problem-solving are central to scientific activity. The left side originally related in Gowin's Vee with philosophies, theories, models, laws or regularities now agrees with Toulmin's concepts (language, models as representation techniques and application procedures). Mexican science teachers without experience in science education research used the heuristic diagram to learn about the history of chemistry considering also in the left side two different historical times: past and present. Through a semantic differential scale teachers' attitude to the heuristic diagram was evaluated and its usefulness was demonstrated.

Gravity on-shell diagrams

Energy Technology Data Exchange (ETDEWEB)

Herrmann, Enrico [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Trnka, Jaroslav [Center for Quantum Mathematics and Physics (QMAP),Department of Physics, University of California,Davis, CA 95616 (United States)

2016-11-22

We study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only dlog-factors, in gravity there is a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for N=8 supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present, in complete agreement with the conjecture presented in http://dx.doi.org/10.1007/JHEP06(2015)202.

Roundhouse Diagrams.

Science.gov (United States)

Ward, Robin E.; Wandersee, James

2000-01-01

Students must understand key concepts through reasoning, searching out related concepts, and making connections within multiple systems to learn science. The Roundhouse diagram was developed to be a concise, holistic, graphic representation of a science topic, process, or activity. Includes sample Roundhouse diagrams, a diagram checklist, and…

Safety- barrier diagrams

DEFF Research Database (Denmark)

Duijm, Nijs Jan

2008-01-01

Safety-barrier diagrams and the related so-called 'bow-tie' diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation of safety-barrier diagrams to other methods such as fault...... trees and Bayesian networks is discussed. A simple method for quantification of safety-barrier diagrams is proposed. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk analysis with operational safety management....

Basic principles of Hasse diagram technique in chemistry.

Science.gov (United States)

Brüggemann, Rainer; Voigt, Kristina

2008-11-01

Principles of partial order applied to ranking are explained. The Hasse diagram technique (HDT) is the application of partial order theory based on a data matrix. In this paper, HDT is introduced in a stepwise procedure, and some elementary theorems are exemplified. The focus is to show how the multivariate character of a data matrix is realized by HDT and in which cases one should apply other mathematical or statistical methods. Many simple examples illustrate the basic theoretical ideas. Finally, it is shown that HDT is a useful alternative for the evaluation of antifouling agents, which was originally performed by amoeba diagrams.

The phase diagram of water at negative pressures: virtual ices.

Science.gov (United States)

Conde, M M; Vega, C; Tribello, G A; Slater, B

2009-07-21

The phase diagram of water at negative pressures as obtained from computer simulations for two models of water, TIP4P/2005 and TIP5P is presented. Several solid structures with lower densities than ice Ih, so-called virtual ices, were considered as possible candidates to occupy the negative pressure region of the phase diagram of water. In particular the empty hydrate structures sI, sII, and sH and another, recently proposed, low-density ice structure. The relative stabilities of these structures at 0 K was determined using empirical water potentials and density functional theory calculations. By performing free energy calculations and Gibbs-Duhem integration the phase diagram of TIP4P/2005 was determined at negative pressures. The empty hydrates sII and sH appear to be the stable solid phases of water at negative pressures. The phase boundary between ice Ih and sII clathrate occurs at moderate negative pressures, while at large negative pressures sH becomes the most stable phase. This behavior is in reasonable agreement with what is observed in density functional theory calculations.

T-duality diagram for a weakly curved background

International Nuclear Information System (INIS)

Davidovic, Ljubica; Nikolic, Bojan; Sazdovic, Branislav

2015-01-01

In one of our previous papers we generalized the Buscher T-dualization procedure. Here we will investigate the application of this procedure to the theory of a bosonic string moving in the weakly curved background. We obtain the complete T-dualization diagram, connecting the theories which are the result of the T-dualizations over all possible choices of the coordinates. We distinguish three forms of the T-dual theories: the initial theory, the theory obtained T-dualizing some of the coordinates of the initial theory and the theory obtained T-dualizing all of the initial coordinates. While the initial theory is geometric, all the other theories are non-geometric and additionally non-local. We find the T-dual coordinate transformation laws connecting these theories and show that the set of all T-dualizations forms an Abelian group. (orig.)

Conformal techniques in string theory and string field theory

International Nuclear Information System (INIS)

Giddings, S.B.

1987-01-01

The application of some conformal and Riemann surface techniques to string theory and string field theory is described. First a brief review of Riemann surface techniques and of the Polyakov approach to string theory is presented. This is followed by a discussion of some features of string field theory and of its Feynman rules. Specifically, it is shown that the Feynman diagrams for Witten's string field theory respect modular invariance, and in particular give a triangulation of moduli space. The Polyakov formalism is then used to derive the Feynman rules that should follow from this theory upon gauge-fixing. It should also be possible to apply this derivation to deduce the Feynman rules for other gauge-fixed string field theories. Following this, Riemann surface techniques are turned to the problem of proving the equivalence of the Polyakov and light-cone formalisms. It is first shown that the light-cone diagrams triangulate moduli space. Then the Polyakov measure is worked out for these diagrams, and shown to equal that deduced from the light-cone gauge fixed formalism. Also presented is a short description of the comparison of physical states in the two formalisms. The equivalence of the two formalisms in particular constitutes a proof of the unitarity of the Polyakov framework for the closed bosonic string

Integrable systems and quantum field theory. Works in progress Nr 75

International Nuclear Information System (INIS)

Baird, Paul; Helein, Frederic; Kouneiher, Joseph; Roubtsov, Volodya; Antunes, Paulo; Banos, Bertrand; Barbachoux, Cecile; Desideri, Laura; Kahouadji, Nabil; Gerding, Aaron; Heller, Sebastian; Schmitt, Nicholas; Harrivel, Dikanaina; Hoevenaars, Luuk K.; Iftime, Mihaela; Levy, Thierry; Lisovyy, Oleg; Masson, Thierry; Skrypnyk, Taras; Pedit, Franz; Egeileh, Michel

2009-01-01

The contributions of this collective book address the quantum field theory (integrable systems and quantum field theory, introduction to supermanifolds and supersymmetry, beyond geometric quantification, Gaussian measurements and Fock spaces), differential geometry and physics (gravitation and geometry, physical events and the superspace about the hole argument, the Cartan-Kaehler theory and applications to local isometric and conformal embedding, calibrations, Cabal-Yau structures and Monge-Ampere structures, Hamiltonian multi-symplectic formalism and Monge-Ampere equations, big bracket, derivations and derivative multi-brackets), integrable system, geometry and physics (finite-volume correlation functions of monodromy fields on the lattice with the Toeplitz representation, Frobenius manifolds and algebraic integrability, an introduction to twistors, Hamiltonian systems on the 'coupled' curves, Nambu-Poisson mechanics and Fairlie-type integrable systems, minimal surfaces with polygonal boundary and Fuchsian equations, global aspects of integrable surface geometry), and non commutative geometry (an informal introduction to the ideas and concepts of non commutative geometry)

Adaptive Diagrams: Handing Control over to the Learner to Manage Split-Attention Online

Science.gov (United States)

Agostinho, Shirley; Tindall-Ford, Sharon; Roodenrys, Kylie

2013-01-01

Based on cognitive load theory, it is well known that when studying a diagram that includes explanatory text, optimal learning occurs when the text is physically positioned close to the diagram as it eliminates the need for learners to split their attention between the two sources of information. What is not known is the effect on learning when…

Safety-barrier diagrams

DEFF Research Database (Denmark)

Duijm, Nijs Jan

2007-01-01

Safety-barrier diagrams and the related so-called "bow-tie" diagrams have become popular methods in risk analysis. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The relation with other methods such as fault trees and Bayesian networks...... are discussed. A simple method for quantification of safety-barrier diagrams is proposed, including situations where safety barriers depend on shared common elements. It is concluded that safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk...... analysis with operational safety management....

The holographic dual of the Penrose transform

Science.gov (United States)

Neiman, Yasha

2018-01-01

We consider the holographic duality between type-A higher-spin gravity in AdS4 and the free U( N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these "square root" spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a "square root" of CPT.

Worldline Green functions for multiloop diagrams

International Nuclear Information System (INIS)

Schmidt, M.G.; Heidelberg Univ.; Schubert, C.

1994-03-01

We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions. (orig.)

Counting loop diagrams: computational complexity of higher-order amplitude evaluation

International Nuclear Information System (INIS)

Eijk, E. van; Kleiss, R.; Lazopoulos, A.

2004-01-01

We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we determine the complexity as a function of the number of external legs. We describe a method for obtaining the number of topologically inequivalent Feynman graphs containing closed loops, and apply this to 1- and 2-loop amplitudes. We also compute the number of graphs weighted by their symmetry factors, thus arriving at exact and asymptotic estimates for the average symmetry factor of diagrams. We present results for the asymptotic number of diagrams up to 10 loops, and prove that the average symmetry factor approaches unity as the number of external legs becomes large. (orig.)

N=4 super-Yang-Mills in LHC superspace part I: classical and quantum theory

Energy Technology Data Exchange (ETDEWEB)

Chicherin, Dmitry [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Sokatchev, Emery [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Theoretical Physics Department, CERN,CH -1211, Geneva 23 (Switzerland)

2017-02-10

We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper https://arxiv.org/abs/1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.

More on boundary holographic Witten diagrams

Science.gov (United States)

Sato, Yoshiki

2018-01-01

In this paper we discuss geodesic Witten diagrams in general holographic conformal field theories with boundary or defect. In boundary or defect conformal field theory, two-point functions are nontrivial and can be decomposed into conformal blocks in two distinct ways; ambient channel decomposition and boundary channel decomposition. In our previous work [A. Karch and Y. Sato, J. High Energy Phys. 09 (2017) 121., 10.1007/JHEP09(2017)121] we only consider two-point functions of same operators. We generalize our previous work to a situation where operators in two-point functions are different. We obtain two distinct decomposition for two-point functions of different operators.

Quark disconnected diagrams in chiral perturbation theory

CERN Document Server

Della Morte, Michele

2010-01-01

We show how quark-disconnected and quark-connected contributions to hadronic n-point functions can be written as independent correlators for which one can derive expressions in partially quenched chiral effective theory. As an example we apply the idea to the case of the hadronic vacuum polarisation. In particular, we consider the cases of the Nf = 2 theory without and with a partially quenched strange quark and also the Nf = 2 + 1 theory. In the latter two cases a parameter-free prediction for the disconnected contribution at NLO in the effective theory is given. Finally we show how twisted boundary conditions can then be used in lattice QCD to improve the q^2 resolution in the connected contributions even when flavour singlet operators are considered.

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

Energy Technology Data Exchange (ETDEWEB)

Ertas, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Institute of Science, Erciyes University, 38039 Kayseri (Turkey); Deviren, Bayram [Department of Physics, Nevsehir University, 50300 Nevsehir (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)

2012-03-15

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F{sub 2}) and three coexistence or mixed phase regions, namely the F{sub 2}+P, F{sub 1}+P and F{sub 2}+F{sub 1}+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior. - Highlights: Black-Right-Pointing-Pointer Dynamic phase transitions are studied in spin-2 BC model using EFT. Black-Right-Pointing-Pointer Dynamic phase diagrams are constructed in (T/zJ, h/zJ) plane. Black-Right-Pointing-Pointer Seven fundamental types of dynamic phase diagrams are found in the system. Black-Right-Pointing-Pointer System exhibits dynamic tricritical behavior.

The Eh-pH Diagram and Its Advances

Directory of Open Access Journals (Sweden)

Hsin-Hsiung Huang

2016-01-01

Full Text Available Since Pourbaix presented Eh versus pH diagrams in his “Atlas of Electrochemical Equilibria in Aqueous Solution”, diagrams have become extremely popular and are now used in almost every scientific area related to aqueous chemistry. Due to advances in personal computers, such diagrams can now show effects not only of Eh and pH, but also of variables, including ligand(s, temperature and pressure. Examples from various fields are illustrated in this paper. Examples include geochemical formation, corrosion and passivation, precipitation and adsorption for water treatment and leaching and metal recovery for hydrometallurgy. Two basic methods were developed to construct an Eh-pH diagram concerning the ligand component(s. The first method calculates and draws a line between two adjacent species based on their given activities. The second method performs equilibrium calculations over an array of points (500 × 800 or higher are preferred, each representing one Eh and one pH value for the whole system, then combines areas of each dominant species for the diagram. These two methods may produce different diagrams. The fundamental theories, illustrated results, comparison and required conditions behind these two methods are presented and discussed in this paper. The Gibbs phase rule equation for an Eh-pH diagram was derived and verified from actual plots. Besides indicating the stability area of water, an Eh-pH diagram normally shows only half of an overall reaction. However, merging two or more related diagrams together reveals more clearly the possibility of the reactions involved. For instance, leaching of Au with cyanide followed by cementing Au with Zn (Merrill-Crowe process can be illustrated by combining Au-CN and Zn-CN diagrams together. A second example of the galvanic conversion of chalcopyrite can be explained by merging S, Fe–S and Cu–Fe–S diagrams. The calculation of an Eh-pH diagram can be extended easily into another dimension, such

Relation of a unified quantum field theory of spinors to the structure of general relativity

International Nuclear Information System (INIS)

Kober, Martin

2009-01-01

Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space-time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space-time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space-time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space-time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.

Application of laws of diagramic logic to calculation of middle coefficient of friction for turbulent boundary layer

International Nuclear Information System (INIS)

Denisov, A.S.

1994-01-01

Canonical formalization of an phenomenon of reasoning by images consists of eight laws of diagramic logic, providing an structural diagram of exploring object as main unit of operating. That laws are divided into three groups: (1) The first channel of application for structural diagrams is the deduction of necessary result from previous theorems of author. (2) The second channel of application for structural diagrams is the deduction of necessary result from parallel theorems of other author. (3) The third channel of application for structural diagrams is the deduction of necessary result by means of modification of nuclear theory

Algorithmic phase diagrams

Science.gov (United States)

Hockney, Roger

1987-01-01

Algorithmic phase diagrams are a neat and compact representation of the results of comparing the execution time of several algorithms for the solution of the same problem. As an example, the recent results are shown of Gannon and Van Rosendale on the solution of multiple tridiagonal systems of equations in the form of such diagrams. The act of preparing these diagrams has revealed an unexpectedly complex relationship between the best algorithm and the number and size of the tridiagonal systems, which was not evident from the algebraic formulae in the original paper. Even so, for a particular computer, one diagram suffices to predict the best algorithm for all problems that are likely to be encountered the prediction being read directly from the diagram without complex calculation.

Generalized string theory mapping relations between gravity and gauge theory

International Nuclear Information System (INIS)

Bjerrum-Bohr, N.E.J.

2003-01-01

A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang-Mills theory, as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings

Phase diagrams for surface alloys

DEFF Research Database (Denmark)

Christensen, Asbjørn; Ruban, Andrei; Stoltze, Per

1997-01-01

We discuss surface alloy phases and their stability based on surface phase diagrams constructed from the surface energy as a function of the surface composition. We show that in the simplest cases of pseudomorphic overlayers there are four generic classes of systems, characterized by the sign...... is based on density-functional calculations using the coherent-potential approximation and on effective-medium theory. We give self-consistent density-functional results for the segregation energy and surface mixing energy for all combinations of the transition and noble metals. Finally we discuss...

Three-body crystallization diagrams and the cooling of white dwarfs.

Science.gov (United States)

Segretain, L.

1996-06-01

The 3-body crystallization diagrams of C/O/Ne ionic mixtures characteristic of white dwarf interiors are examined within the framework of the density-functional theory of freezing. The crystallization process is described more accurately than in former calculations where the three-component system was treated as an effective two-component mixture (Segretain et al. 1994). The distillation process due to neon-crystallization is found to occur only for the late stages of crystallization. At the beginning, the presence of neon plays only a minor role and the phase diagram resembles a pure carbon-oxygen diagram. The final phase diagram is found to exhibit an azeotropic point with a neon concentration x_Ne_=0.22, a carbon concentration x_C_=0.78 and an oxygen concentration x_O_=0, so that during the distillation process, the fluid crystallizes into a pure neon-carbon solid. The critical temperature is T_A_=0.85T_C_, where T_C_ is the pure carbon crystallization temperature. We use this accurate phase diagram to calculate the total gravitational energy released during white dwarf crystallization and the related time delay. The final result yields {DELTA}τ=~2.6Gyr, among which about 20% are due to the neon-distillation process.

Electronic diagrams

CERN Document Server

Colwell, Morris A

1976-01-01

Electronic Diagrams is a ready reference and general guide to systems and circuit planning and in the preparation of diagrams for both newcomers and the more experienced. This book presents guidelines and logical procedures that the reader can follow and then be equipped to tackle large complex diagrams by recognition of characteristic 'building blocks' or 'black boxes'. The goal is to break down many of the barriers that often seem to deter students and laymen in learning the art of electronics, especially when they take up electronics as a spare time occupation. This text is comprised of nin

Calculations in perturbative string field theory

International Nuclear Information System (INIS)

Thorn, C.B.

1987-01-01

The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules

The Use of Kruskal-Newton Diagrams for Differential Equations

International Nuclear Information System (INIS)

Fishaleck, T.; White, R.B.

2008-01-01

The method of Kruskal-Newton diagrams for the solution of differential equations with boundary layers is shown to provide rapid intuitive understanding of layer scaling and can result in the conceptual simplification of some problems. The method is illustrated using equations arising in the theory of pattern formation and in plasma physics.

The relationship between the Johnson-Baranger time-dependent folded diagram expansion and the time-independent methods of perturbation theory

International Nuclear Information System (INIS)

Passos, E.M.J. de

1976-01-01

The relationship between the Johnson-Baranger time-dependent folded diagram (JBFD) expansion, and the time independent methods of perturbation theory, are investigated. In the nondegenerate case, the JBFD expansion and the Rayleigh-Schroedinger perturbation expansion, for the ground state energy, are identical. On the other hand, in the degenerate case, for the nonhermitian effective interaction considered, the JBFD expansion, of the effective interaction, is equal to the perturbative expansion of the effective interaction of the nonhermitian eigenvalue problem of Bloch and Brandow-Des Cloizeaux. For the two hermitian effective interactions, the JBFD expansion of the effective interaction differs from the perturbation expansion of the effective interaction of the hermitian eigenvalue problem of Des Cloizeaux [pt

Viral pathogenesis in diagrams

National Research Council Canada - National Science Library

Tremblay, Michel; Berthiaume, Laurent; Ackermann, Hans-Wolfgang

2001-01-01

.... The 268 diagrams in Viral Pathogenesis in Diagrams were selected from over 800 diagrams of English and French virological literature, including one derived from a famous drawing by Leonardo da Vinci...

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards' field theory

International Nuclear Information System (INIS)

Morse, David C.

2006-01-01

Edwards' functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules, and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of

Summation of Parquet diagrams as an ab initio method in nuclear structure calculations

International Nuclear Information System (INIS)

Bergli, Elise; Hjorth-Jensen, Morten

2011-01-01

Research highlights: → We present a Green's function based approach for doing ab initio nuclear structure calculations. → In particular the sum the subset of so-called Parquet diagrams. → Applying the theory to a simple but realistic model, results in good agreement with other ab initio methods. → This opens up for ab initio calculations for medium-heavy nuclei. - Abstract: In this work we discuss the summation of the Parquet class of diagrams within Green's function theory as a possible framework for ab initio nuclear structure calculations. The theory is presented and some numerical details are discussed, in particular the approximations employed. We apply the Parquet method to a simple model, and compare our results with those from an exact solution. The main conclusion is that even at the level of approximation presented here, the results shows good agreement with other comparable ab initio approaches.

Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams

Science.gov (United States)

Py, Dominique; Auxepaules, Ludovic; Alonso, Mathilde

2013-01-01

This paper presents Diagram, a learning environment for object-oriented modelling (OOM) with UML class diagrams. Diagram an open environment, in which the teacher can add new exercises without constraints on the vocabulary or the size of the diagram. The interface includes methodological help, encourages self-correcting and self-monitoring, and…

Phase stabilities at a glance: Stability diagrams of nickel dipnictides

International Nuclear Information System (INIS)

Bachhuber, F.; Rothballer, J.; Weihrich, R.; Söhnel, T.

2013-01-01

In the course of the recent advances in chemical structure prediction, a straightforward type of diagram to evaluate phase stabilities is presented based on an expedient example. Crystal structures and energetic stabilities of dipnictides NiPn 2 (Pn = N, P, As, Sb, Bi) are systematically investigated by first principles calculations within the framework of density functional theory using the generalized gradient approximation to treat exchange and correlation. These dipnictides show remarkable polymorphism that is not yet understood systematically and offers room for the discovery of new phases. Relationships between the concerned structures including the marcasite, the pyrite, the arsenopyrite/CoSb 2 , and the NiAs 2 types are highlighted by means of common structural fragments. Electronic stabilities of experimentally known and related AB 2 structure types are presented graphically in so-called stability diagrams. Additionally, competing binary phases are taken into consideration in the diagrams to evaluate the stabilities of the title compounds with respect to decomposition. The main purpose of the stability diagrams is the introduction of an image that enables the estimation of phase stabilities at a single glance. Beyond that, some of the energetically favored structure types can be identified as potential new phases

The phase diagram of solid hydrogen at high pressure: A challenge for first principles calculations

Science.gov (United States)

Azadi, Sam; Foulkes, Matthew

2015-03-01

We present comprehensive results for the high-pressure phase diagram of solid hydrogen. We focus on the energetically most favorable molecular and atomic crystal structures. To obtain the ground-state static enthalpy and phase diagram, we use semi-local and hybrid density functional theory (DFT) as well as diffusion quantum Monte Carlo (DMC) methods. The closure of the band gap with increasing pressure is investigated utilizing quasi-particle many-body calculations within the GW approximation. The dynamical phase diagram is calculated by adding proton zero-point energies (ZPE) to static enthalpies. Density functional perturbation theory is employed to calculate the proton ZPE and the infra-red and Raman spectra. Our results clearly demonstrate the failure of DFT-based methods to provide an accurate static phase diagram, especially when comparing insulating and metallic phases. Our dynamical phase diagram obtained using fully many-body DMC calculations shows that the molecular-to-atomic phase transition happens at the experimentally accessible pressure of 374 GPa. We claim that going beyond mean-field schemes to obtain derivatives of the total energy and optimize crystal structures at the many-body level is crucial. This work was supported by the UK engineering and physics science research council under Grant EP/I030190/1, and made use of computing facilities provided by HECTOR, and by the Imperial College London high performance computing centre.

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R

Directory of Open Access Journals (Sweden)

Boutros Paul C

2011-01-01

Full Text Available Abstract Background Visualization of orthogonal (disjoint or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. Results The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. Conclusions The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

VennDiagram: a package for the generation of highly-customizable Venn and Euler diagrams in R.

Science.gov (United States)

Chen, Hanbo; Boutros, Paul C

2011-01-26

Visualization of orthogonal (disjoint) or overlapping datasets is a common task in bioinformatics. Few tools exist to automate the generation of extensively-customizable, high-resolution Venn and Euler diagrams in the R statistical environment. To fill this gap we introduce VennDiagram, an R package that enables the automated generation of highly-customizable, high-resolution Venn diagrams with up to four sets and Euler diagrams with up to three sets. The VennDiagram package offers the user the ability to customize essentially all aspects of the generated diagrams, including font sizes, label styles and locations, and the overall rotation of the diagram. We have implemented scaled Venn and Euler diagrams, which increase graphical accuracy and visual appeal. Diagrams are generated as high-definition TIFF files, simplifying the process of creating publication-quality figures and easing integration with established analysis pipelines. The VennDiagram package allows the creation of high quality Venn and Euler diagrams in the R statistical environment.

Scalar-flat Kaehler metrics with conformal Bianchi V symmetry

Energy Technology Data Exchange (ETDEWEB)

Dunajski, Maciej [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Plansangkate, Prim, E-mail: M.Dunajski@damtp.cam.ac.uk, E-mail: plansang@CRM.UMontreal.ca [Centre de Recherches Mathematiques (CRM), Universite de Montreal, CP 6128, Montreal (Quebec) H3C 3J7 (Canada)

2011-06-21

We provide an affirmative answer to a question posed by Tod (1995, Twistor Theory (New York: Dekker)), and construct all four-dimensional Kaehler metrics with vanishing scalar curvature which are invariant under the conformal action of the Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterize the associated solutions of the SU({infinity}) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

The effect of the vertical part of the path on the real time Feynman rules in finite temperature field theory 2-point functions and vacuum diagrams

International Nuclear Information System (INIS)

Gelis, F.

1996-01-01

The effect of the contribution of the vertical part of the real time path is studied completely in the case of two points functions and vacuum diagrams. Indeed, this vertical part generally contributes in the calculation of a given graph. Moreover, this contribution is essential in order to have a consistent equilibrium theory: thanks to this contribution, the Green functions are effectively invariant by time translation, as they should be. As a by product, it is shown that the perturbative calculations give a result which does not depend on the initial time t I and final time t F of the path. The property of independence with respect to t I is closely related to the KMS conditions, i.e. to the fact the system is in thermal equilibrium. In the case of two point functions and vacuum diagrams, the contribution of the vertical part can be taken into account by the n(vertical stroke k 0 vertical stroke) prescription in the usual RTF Feynman rules. The extra Feynman rule needed for vacuum diagrams is shown not to be related directly to the contribution of the vertical part of the path. (orig.). With 4 figs

Interaction diagrams for composite columns exposed to fire

Directory of Open Access Journals (Sweden)

Milanović Milivoje

2014-01-01

Full Text Available The bearing capacity of the cross section of composite column in fire conditions through changes in the interaction diagram 'bending moment-axialforce' were analyzed in this paper. The M-N interaction diagram presents the relationship between the intensities of the bending moment and the axial force as actions on the column cross section, or the relationship between the design value of the plastic resistance to axial compression of the total cross-section Npl, Rd and the design value of the bending moment resistance Mpl, Rd. It is well known that the temperature increase causes decrease of the load-bearing characteristics of the constitutive materials. This effect directly reflects on the reduction of the axial force and the bending moment that could be accepted by the column cross section. Interaction diagrams for three different types of column cross sections for five different maximal temperatures developed during the fire action were defined. For that purpose the software package SAFIR was used. The columns, materials and load characteristics, as well as all other terms and conditions, were taken in accordance with the relevant Eurocodes and the theory of composite columns.

Diagrams benefit symbolic problem-solving.

Science.gov (United States)

Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R

2017-06-01

The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equations can benefit problem-solving performance as well. We tested the impact of diagram presence on students' performance on algebra equation problems to determine whether diagrams increase problem-solving success. We also examined the influence of item- and student-level factors to test the robustness of the diagram effect. We worked with 61 seventh-grade students who had received 2 months of pre-algebra instruction. Students participated in an experimenter-led classroom session. Using a within-subjects design, students solved algebra problems in two matched formats (equation and equation-with-diagram). The presence of diagrams increased equation-solving accuracy and the use of informal strategies. This diagram benefit was independent of student ability and item complexity. The benefits of diagrams found previously for story problems generalized to symbolic problems. The findings are consistent with cognitive models of problem-solving and suggest that diagrams may be a useful additional representation of symbolic problems. © 2017 The British Psychological Society.

The phase diagram of KNO3-KClO3

International Nuclear Information System (INIS)

Zhang Xuejun; Tian Jun; Xu Kangcheng; Gao Yici

2004-01-01

The binary phase diagram of KNO 3 -KClO 3 is studied by means of differential scanning calorimetry (DSC) and high-temperature X-ray diffraction. The limited solid solutions, K(NO 3 ) 1-x (ClO 3 ) x (0 3 ) 1-x (ClO 3 ) x (0.90 3 -based solid solutions and KClO 3 -based solid solutions phase, respectively. For KNO 3 -based solid solutions, KNO 3 ferroelectric phase can be stable from 423 to 223 K as a result of substituting of NO 3 by ClO 3 -radicals. The temperatures for solidus and liquidus have been determined based on limited solid solutions. Two models, Henrian solution and regular solution theory for KNO 3 -based (α) phase and KClO 3 -based (β) phase, respectively, are employed to reproduce solidus and liquidus of the phase diagram. The results are in good agreement with the DSC data. The thermodynamic properties for α and β solid solutions have been derived from an optimization procedure using the experimental data. The calculated phase diagram and optimized thermodynamic parameters are thermodynamically self-consistent

Phase diagrams of the ternary alloy with a single-ion anisotropy in the mean-field approximation

International Nuclear Information System (INIS)

Dely, J.; Bobak, A.

2006-01-01

The phase diagram of the AB p C 1-p ternary alloy consisting of Ising spins S A =32, S B =2, and S C =52 is investigated by the use of a mean-field theory based on the Bogoliubov inequality for the Gibbs free energy. The effect of the single-ion anisotropy on the phase diagrams is discussed by changing values of the parameters in the model Hamiltonian and comparison is made with the recently reported finite-temperature phase diagrams for the ternary alloy having spin S B =1

Optimizing UML Class Diagrams

Directory of Open Access Journals (Sweden)

Sergievskiy Maxim

2018-01-01

Full Text Available Most of object-oriented development technologies rely on the use of the universal modeling language UML; class diagrams play a very important role in the design process play, used to build a software system model. Modern CASE tools, which are the basic tools for object-oriented development, can’t be used to optimize UML diagrams. In this manuscript we will explain how, based on the use of design patterns and anti-patterns, class diagrams could be verified and optimized. Certain transformations can be carried out automatically; in other cases, potential inefficiencies will be indicated and recommendations given. This study also discusses additional CASE tools for validating and optimizing of UML class diagrams. For this purpose, a plugin has been developed that analyzes an XMI file containing a description of class diagrams.

Ideal related K-theory with coefficients

DEFF Research Database (Denmark)

Eilers, Soren; Restorff, Gunnar; Ruiz, Efren

2017-01-01

In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with coefficients are constructed. These diagrams will in most cases help...... to determine the new groups, and will in a companion paper be used to prove a universal multi-coefficient theorem for the one distinguished ideal case for a large class of algebras......In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with coefficients are constructed. These diagrams will in most cases help...

Berry Fermi liquid theory

Energy Technology Data Exchange (ETDEWEB)

Chen, Jing-Yuan, E-mail: chjy@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States); Stanford Institute for Theoretical Physics, Stanford University, CA 94305 (United States); Son, Dam Thanh, E-mail: dtson@uchicago.edu [Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637 (United States)

2017-02-15

We develop an extension of the Landau Fermi liquid theory to systems of interacting fermions with non-trivial Berry curvature. We propose a kinetic equation and a constitutive relation for the electromagnetic current that together encode the linear response of such systems to external electromagnetic perturbations, to leading and next-to-leading orders in the expansion over the frequency and wave number of the perturbations. We analyze the Feynman diagrams in a large class of interacting quantum field theories and show that, after summing up all orders in perturbation theory, the current–current correlator exactly matches with the result obtained from the kinetic theory. - Highlights: • We extend Landau’s kinetic theory of Fermi liquid to incorporate Berry phase. • Berry phase effects in Fermi liquid take exactly the same form as in Fermi gas. • There is a new “emergent electric dipole” contribution to the anomalous Hall effect. • Our kinetic theory is matched to field theory to all orders in Feynman diagrams.

Infrared equivalence of strongly and weakly coupled gauge theories

International Nuclear Information System (INIS)

Olesen, P.

1975-10-01

Using the decoupling theorem of Apelquist and Carazzone, it is shown that in terms of Feynman diagrams the pure Yang-Mills theory is equivalent in the infrared limit to a theory (zero-mass renormalized), where the vector mesons are coupled fo fermions, and where the fermions do not decouple. By taking enough fermions it is then shown that even though the pure Yang-Mills theory is characterized by the lack of applicability of perturbation theory, nevertheless the effective coupling in the equivalent fermion description is very weak. The effective mass in the zero-mass renormalization blows up. In the fermion description, diagrams involving only vector mesons are suppressed relative to diagrams containing at least one fermion loop. (Auth.)

Group theory for chemists fundamental theory and applications

CERN Document Server

Molloy, K C

2010-01-01

The basics of group theory and its applications to themes such as the analysis of vibrational spectra and molecular orbital theory are essential knowledge for the undergraduate student of inorganic chemistry. The second edition of Group Theory for Chemists uses diagrams and problem-solving to help students test and improve their understanding, including a new section on the application of group theory to electronic spectroscopy.Part one covers the essentials of symmetry and group theory, including symmetry, point groups and representations. Part two deals with the application of group theory t

Stage line diagram: An age-conditional reference diagram for tracking development

NARCIS (Netherlands)

Buuren, S. van; Ooms, J.C.L.

2009-01-01

This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and

Stage line diagram: an age-conditional reference diagram for tracking development.

NARCIS (Netherlands)

Van Buuren, S.; Ooms, J.C.L.

2009-01-01

This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and

Deformation of the cubic open string field theory

Energy Technology Data Exchange (ETDEWEB)

Lee, Taejin, E-mail: taejin@kangwon.ac.kr

2017-05-10

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Deformation of the cubic open string field theory

International Nuclear Information System (INIS)

Lee, Taejin

2017-01-01

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Deformation of the cubic open string field theory

Directory of Open Access Journals (Sweden)

Taejin Lee

2017-05-01

Full Text Available We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

International Nuclear Information System (INIS)

Deviren, Bayram; Polat, Yasin; Keskin, Mustafa

2011-01-01

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point (TP), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Néel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions. (general)

Electrodynamic metaphors: communicating particle physics with Feynman diagrams

Directory of Open Access Journals (Sweden)

Pietroni Massimo

2002-03-01

Full Text Available The aim of this project is to communicate the basic laws of particle physics with Feynman diagrams - visual tools which represent elementary particle processes. They were originally developed as a code to be used by physicists and are still used today for calculations and elaborations of theoretical nature. The technical and mathematical rules of Feynman diagrams are obviously the exclusive concern of physicists, but on a pictorial level they can help to popularize many concepts, ranging from matter and the antimatter; the creation, destruction and transformation of particles; the role of ‘virtual’ particles in interactions; the conservation laws, symmetries, etc. Unlike the metaphors often used to describe the microcosm, these graphic representations provide an unequivocal translation of the physical content of the underlying quantum theory. As such they are perfect metaphors, not misleading constructions. A brief introduction on Feynman diagrams will be followed by the practical realization of this project, which will be carried out with the help of an experiment based on three-dimensional manipulable objects. The Feynman rules are expressed in terms of mechanical constraints on the possible conjuctions among the various elements of the experiment. The final part of the project will present the results of this experiment, which has been conducted among high-school students.

Para-equilibrium phase diagrams

International Nuclear Information System (INIS)

Pelton, Arthur D.; Koukkari, Pertti; Pajarre, Risto; Eriksson, Gunnar

2014-01-01

Highlights: • A rapidly cooled system may attain a state of para-equilibrium. • In this state rapidly diffusing elements reach equilibrium but others are immobile. • Application of the Phase Rule to para-equilibrium phase diagrams is discussed. • A general algorithm to calculate para-equilibrium phase diagrams is described. - Abstract: If an initially homogeneous system at high temperature is rapidly cooled, a temporary para-equilibrium state may result in which rapidly diffusing elements have reached equilibrium but more slowly diffusing elements have remained essentially immobile. The best known example occurs when homogeneous austenite is quenched. A para-equilibrium phase assemblage may be calculated thermodynamically by Gibbs free energy minimization under the constraint that the ratios of the slowly diffusing elements are the same in all phases. Several examples of calculated para-equilibrium phase diagram sections are presented and the application of the Phase Rule is discussed. Although the rules governing the geometry of these diagrams may appear at first to be somewhat different from those for full equilibrium phase diagrams, it is shown that in fact they obey exactly the same rules with the following provision. Since the molar ratios of non-diffusing elements are the same in all phases at para-equilibrium, these ratios act, as far as the geometry of the diagram is concerned, like “potential” variables (such as T, pressure or chemical potentials) rather than like “normal” composition variables which need not be the same in all phases. A general algorithm to calculate para-equilibrium phase diagrams is presented. In the limit, if a para-equilibrium calculation is performed under the constraint that no elements diffuse, then the resultant phase diagram shows the single phase with the minimum Gibbs free energy at any point on the diagram; such calculations are of interest in physical vapor deposition when deposition is so rapid that phase

Quantum corrections for the phase diagram of systems with competing order

Science.gov (United States)

Silva, N. L., Jr.; Continentino, Mucio A.; Barci, Daniel G.

2018-06-01

We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios: regions of the phase diagram where there is a bicritical point, at which both phases vanish continuously, and the case where both phases coexist homogeneously. We consider different types of couplings between the order parameters, including a bilinear one. This kind of coupling breaks time-reversal symmetry and it is only allowed if both order parameters transform according to the same irreducible representation. This occurs in many physical systems of actual interest like competing spin density waves, different types of orbital antiferromagnetism, elastic instabilities of crystal lattices, vortices in a multigap SC and also applies to describe the unusual magnetism of the heavy fermion compound URu2Si2. Our results show that quantum corrections have an important effect on the phase diagram of systems with competing orders.

Quantum corrections for the phase diagram of systems with competing order.

Science.gov (United States)

Silva, N L; Continentino, Mucio A; Barci, Daniel G

2018-06-06

We use the effective potential method of quantum field theory to obtain the quantum corrections to the zero temperature phase diagram of systems with competing order parameters. We are particularly interested in two different scenarios: regions of the phase diagram where there is a bicritical point, at which both phases vanish continuously, and the case where both phases coexist homogeneously. We consider different types of couplings between the order parameters, including a bilinear one. This kind of coupling breaks time-reversal symmetry and it is only allowed if both order parameters transform according to the same irreducible representation. This occurs in many physical systems of actual interest like competing spin density waves, different types of orbital antiferromagnetism, elastic instabilities of crystal lattices, vortices in a multigap SC and also applies to describe the unusual magnetism of the heavy fermion compound URu 2 Si 2 . Our results show that quantum corrections have an important effect on the phase diagram of systems with competing orders.

Sintering diagrams of UO2

International Nuclear Information System (INIS)

Mohan, A.; Soni, N.C.; Moorthy, V.K.

1979-01-01

Ashby's method (see Acta Met., vol. 22, p. 275, 1974) of constructing sintering diagrams has been modified to obtain contribution diagrams directly from the computer. The interplay of sintering variables and mechanisms are studied and the factors that affect the participation of mechanisms in UO 2 are determined. By studying the physical properties, it emerges that the order of inaccuracies is small in most cases and do not affect the diagrams. On the other hand, even a 10% error in activation energies, which is quite plausible, would make a significant difference to the diagram. The main criticism of Ashby's approach is that the numerous properties and equations used, communicate their inaccuracies to the diagrams and make them unreliable. The present study has considerably reduced the number of factors that need to be refined to make the sintering diagrams more meaningful. (Auth.)

Feynman diagram drawing made easy

International Nuclear Information System (INIS)

Baillargeon, M.

1997-01-01

We present a drawing package optimised for Feynman diagrams. These can be constructed interactively with a mouse-driven graphical interface or from a script file, more suitable to work with a diagram generator. It provides most features encountered in Feynman diagrams and allows to modify every part of a diagram after its creation. Special attention has been paid to obtain a high quality printout as easily as possible. This package is written in Tcl/Tk and in C. (orig.)

Formal verification of Simulink/Stateflow diagrams a deductive approach

CERN Document Server

Zhan, Naijun; Zhao, Hengjun

2017-01-01

This book presents a state-of-the-art technique for formal verification of continuous-time Simulink/Stateflow diagrams, featuring an expressive hybrid system modelling language, a powerful specification logic and deduction-based verification approach, and some impressive, realistic case studies. Readers will learn the HCSP/HHL-based deductive method and the use of corresponding tools for formal verification of Simulink/Stateflow diagrams. They will also gain some basic ideas about fundamental elements of formal methods such as formal syntax and semantics, and especially the common techniques applied in formal modelling and verification of hybrid systems. By investigating the successful case studies, readers will realize how to apply the pure theory and techniques to real applications, and hopefully will be inspired to start to use the proposed approach, or even develop their own formal methods in their future work.

The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning

Science.gov (United States)

Dimmel, Justin K.; Herbst, Patricio G.

2015-01-01

Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two,…

The origins of Penrose diagrams in physics, art, and the psychology of perception, 1958-62.

Science.gov (United States)

Wright, Aaron Sidney

2013-09-01

Penrose diagrams gave mid-twentieth century physicists studying General Relativity (GR) a new tool for understanding Einstein's theory of gravity. Starting in 1962 they allowed new understandings and conceptualizations of the mathematical objects of theoretical physics. One origin of the diagrams is found in Roger Penrose's engagement with the art of "impossible objects". These new understandings contributed to the "renaissance" GR experienced starting in the late 1950s. By following the diagrams through the GR community, the interrelation of research and pedagogy is explicated. This interrelation rapidly disseminated the tools to new workers in the field, further amplifying the effect of this new theoretical tool on disciplinary growth. Copyright © 2013 Elsevier Ltd. All rights reserved.

Stage line diagram: an age-conditional reference diagram for tracking development.

Science.gov (United States)

van Buuren, Stef; Ooms, Jeroen C L

2009-05-15

This paper presents a method for calculating stage line diagrams, a novel type of reference diagram useful for tracking developmental processes over time. Potential fields of applications include: dentistry (tooth eruption), oncology (tumor grading, cancer staging), virology (HIV infection and disease staging), psychology (stages of cognitive development), human development (pubertal stages) and chronic diseases (stages of dementia). Transition probabilities between successive stages are modeled as smoothly varying functions of age. Age-conditional references are calculated from the modeled probabilities by the mid-P value. It is possible to eliminate the influence of age by calculating standard deviation scores (SDS). The method is applied to the empirical data to produce reference charts on secondary sexual maturation. The mean of the empirical SDS in the reference population is close to zero, whereas the variance depends on age. The stage line diagram provides quick insight into both status (in SDS) and tempo (in SDS/year) of development of an individual child. Other measures (e.g. height SDS, body mass index SDS) from the same child can be added to the chart. Diagrams for sexual maturation are available as a web application at http://vps.stefvanbuuren.nl/puberty. The stage line diagram expresses status and tempo of discrete changes on a continuous scale. Wider application of these measures scores opens up new analytic possibilities. (c) 2009 John Wiley & Sons, Ltd.

(α,η) phase diagrams in tilted chiral smectics

International Nuclear Information System (INIS)

Rjili, M.; Marcerou, J.P.; Gharbi, A.; Othman, T.

2013-01-01

The polymorphism of tilted chiral smectics liquid crystals is incredibly rich and encompasses many subphases such as SmC A ⁎ ; SmC Fi1 ⁎ ; SmC Fi2 ⁎ ; SmC ⁎ ; SmC α ⁎ . The continuum theory established by Marcerou (2010) is used to derive an expression for the free energy density of those subphases. The minimization of this free energy is obtained through a combination of analytical and numerical methods. It leads to a phase diagram built in the (α,η) plane where α is local angular parameter and η describes the variation of the temperature. From this graphical representation, many experimentally observed phase sequences of ferroelectric liquid crystals can be explained, even them including subphases which were recently observed like the SmC 5 ⁎ and the SmC 6 ⁎ ones. However, it should be emphasized that the details of predicted phase diagram are strongly dependent on the compound studied.

Ring diagrams and phase transitions

International Nuclear Information System (INIS)

Takahashi, K.

1986-01-01

Ring diagrams at finite temperatures carry most infrared-singular parts among Feynman diagrams. Their effect to effective potentials are in general so significant that one must incorporate them as well as 1-loop diagrams. The author expresses these circumstances in some examples of supercooled phase transitions

Two loop diagrams in Yang Mills theory

International Nuclear Information System (INIS)

Jones, D.R.T.

1974-01-01

A calculation of the renormalization constants of the Yang Mills field to 0(g 4 ) is presented. The function β(g) is hence evaluated to 0(g 5 ) and possible implications for gauge theories of the strong interactions discussed

Highly Accurate Calculations of the Phase Diagram of Cold Lithium

Science.gov (United States)

Shulenburger, Luke; Baczewski, Andrew

The phase diagram of lithium is particularly complicated, exhibiting many different solid phases under the modest application of pressure. Experimental efforts to identify these phases using diamond anvil cells have been complemented by ab initio theory, primarily using density functional theory (DFT). Due to the multiplicity of crystal structures whose enthalpy is nearly degenerate and the uncertainty introduced by density functional approximations, we apply the highly accurate many-body diffusion Monte Carlo (DMC) method to the study of the solid phases at low temperature. These calculations span many different phases, including several with low symmetry, demonstrating the viability of DMC as a method for calculating phase diagrams for complex solids. Our results can be used as a benchmark to test the accuracy of various density functionals. This can strengthen confidence in DFT based predictions of more complex phenomena such as the anomalous melting behavior predicted for lithium at high pressures. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Stereo 3D spatial phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Kang, Jinwu, E-mail: kangjw@tsinghua.edu.cn; Liu, Baicheng, E-mail: liubc@tsinghua.edu.cn

2016-07-15

Phase diagrams serve as the fundamental guidance in materials science and engineering. Binary P-T-X (pressure–temperature–composition) and multi-component phase diagrams are of complex spatial geometry, which brings difficulty for understanding. The authors constructed 3D stereo binary P-T-X, typical ternary and some quaternary phase diagrams. A phase diagram construction algorithm based on the calculated phase reaction data in PandaT was developed. And the 3D stereo phase diagram of Al-Cu-Mg ternary system is presented. These phase diagrams can be illustrated by wireframe, surface, solid or their mixture, isotherms and isopleths can be generated. All of these can be displayed by the three typical display ways: electronic shutter, polarization and anaglyph (for example red-cyan glasses). Especially, they can be printed out with 3D stereo effect on paper, and watched by the aid of anaglyph glasses, which makes 3D stereo book of phase diagrams come to reality. Compared with the traditional illustration way, the front of phase diagrams protrude from the screen and the back stretches far behind of the screen under 3D stereo display, the spatial structure can be clearly and immediately perceived. These 3D stereo phase diagrams are useful in teaching and research. - Highlights: • Stereo 3D phase diagram database was constructed, including binary P-T-X, ternary, some quaternary and real ternary systems. • The phase diagrams can be watched by active shutter or polarized or anaglyph glasses. • The print phase diagrams retains 3D stereo effect which can be achieved by the aid of anaglyph glasses.

Asymptotic behaviour in field theory

Energy Technology Data Exchange (ETDEWEB)

Banerjee, H.

1980-07-01

Asymptotic behaviour in field theory has been studied and the anomalies are pointed out in two specific cases, (i) the infrared and fixed angle high energy behaviour in the non-trivial case of the 'box' amplitude in a scalar-scalar theory and (ii) high energy behaviour of a sixth order Yang-Mills diagram. A set of rules are presented for writing down the precise leading infrared behaviour of an arbitrary generalised ladder diagram (GLD) in QED. These rules are the final result of a detailed analysis of the relevant amplitudes in the Feynman parameter space. The connection between the infrared and fixed angle high energy limits of generalised ladder diagrams is explained. It is argued that the same set of rules yield the fixed angle high energy limit.

Maunder's Butterfly Diagram in the 21st Century

Science.gov (United States)

Hathaway, David H.

2005-01-01

E. Walter Maunder created his first "Butterfly Diagram" showing the equatorward drift of the sunspot latitudes over the course of each of two solar cycles in 1903. This diagram was constructed from data obtained through the Royal Greenwich Observatory (RGO) starting in 1874. The RGO continued to acquire data up until 1976. Fortunately, the US Air Force (USAF) and the US National Oceanic and Atmospheric Administration (NOAA) have continued to acquire similar data since that time. This combined RGO/USAF/NOAA dataset on sunspot group positions and areas now extends virtually unbroken from the 19th century to the 21st century. The data represented in the Butterfly Diagram contain a wealth of information about solar activity and the solar cycle. Solar activity (as represented by the sunspots) appears at mid-latitudes at the start of each cycle. The bands of activity spread in each hemisphere and then drift toward the equator as the cycle progresses. Although the equator itself tends to be avoided, the spread of activity reaches the equator at about the time of cycle maximum. The cycles overlap at minimum with old cycle spots appearing near the equator while new cycle spots emerge in the mid-latitudes. Large amplitude cycles tend to have activity starting at higher latitudes with the activity spreading to higher latitudes as well. Large amplitude cycles also tend to be preceded by earlier cycles with faster drift rates. These drift rates may be tied to the Sun s meridional circulation - a component in many dynamo theories for the origin of the sunspot cycle. The Butterfly Diagram must be reproduced in any successful dynamo model for the Sun.

Phase diagram and Chiral Magnetic Effect in Dirac Semimetals from Lattice Simulation

Directory of Open Access Journals (Sweden)

Boyda D.L.

2018-01-01

Full Text Available Dirac Semimetals Na3Bi and Cd3As2 are recently discovered materials, which low energy electronic spectrum is described by two flavours of massless 3+1D fermions. In order to study electronic properties of these materials we formulated lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces effective theory of Dirac semimetals. Using the lattice field theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant - Fermi velocity anisotropy. We also measure conductivity of Dirac Semimetals within lattice field theory in external magnetic field. Our results confirm the existence of Chiral Magnetic Effect in Dirac Semimetals.

Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams

International Nuclear Information System (INIS)

Chagarov, E.; Sardashti, K.; Kummel, A. C.; Haight, R.; Mitzi, D. B.

2016-01-01

Density-functional theory simulations of CZTS, CZTSe, and CZTS 0.25 Se 0.75 photovoltaic compounds have been performed to investigate the stability of the CZTS 0.25 Se 0.75 alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS 0.25 Se 0.75 alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS 0.25 Se 0.75 that the chemical potentials for stability differ between typical processing temperature (∼900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS 0.25 Se 0.75 in a thermodynamically stable state to minimize phase decomposition.

Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams

Science.gov (United States)

Chagarov, E.; Sardashti, K.; Haight, R.; Mitzi, D. B.; Kummel, A. C.

2016-08-01

Density-functional theory simulations of CZTS, CZTSe, and CZTS0.25Se0.75 photovoltaic compounds have been performed to investigate the stability of the CZTS0.25Se0.75 alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS0.25Se0.75 alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS0.25Se0.75 that the chemical potentials for stability differ between typical processing temperature (˜900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS0.25Se0.75 in a thermodynamically stable state to minimize phase decomposition.

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume–Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

International Nuclear Information System (INIS)

Ertaş, Mehmet; Keskin, Mustafa; Deviren, Bayram

2012-01-01

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume–Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h 0 /zJ) and (T/zJ, D/zJ), where T absolute temperature, h 0 , the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z). - Highlights: ► The effective-field theory is used to study the kinetic spin-5/2 Ising Blume–Capel model. ► Time variations of average order parameter have been studied to find phases in the system. ► The dynamic magnetization, hysteresis loop area and correlation have been calculated. ► The dynamic phase boundaries of the system depend on D/zJ. ► The dynamic phase diagrams are presented in the (T/zJ, h 0 /zJ) and (D/zJ, T/zJ) planes.

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Energy Technology Data Exchange (ETDEWEB)

Ertas, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Deviren, Bayram [Department of Physics, Nevsehir University, 50300 Nevsehir (Turkey)

2012-04-15

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h{sub 0}/zJ) and (T/zJ, D/zJ), where T absolute temperature, h{sub 0}, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z). - Highlights: Black-Right-Pointing-Pointer The effective-field theory is used to study the kinetic spin-5/2 Ising Blume-Capel model. Black-Right-Pointing-Pointer Time variations of average order parameter have been studied to find phases in the system. Black-Right-Pointing-Pointer The dynamic magnetization, hysteresis loop area and correlation have been calculated. Black-Right-Pointing-Pointer The dynamic phase boundaries of the system depend on D/zJ. Black-Right-Pointing-Pointer The dynamic phase diagrams are presented in the (T/zJ, h{sub 0}/zJ) and (D/zJ, T/zJ) planes.

New relations for gauge-theory amplitudes

International Nuclear Information System (INIS)

Bern, Z.; Carrasco, J. J. M.; Johansson, H.

2008-01-01

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram

Science.gov (United States)

Lian, Biao; Wang, Juven

2018-04-01

Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.

Automation of Feynman diagram evaluations

International Nuclear Information System (INIS)

Tentyukov, M.N.

1998-01-01

A C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented. It consists of two parts: the analyzer of diagrams and the interpreter of a special text manipulating language. This language can be used to create a source code for analytical or numerical evaluations and to keep the control of the process in general

The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

Science.gov (United States)

Litsey, Sean Christopher

We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog

An approach to higher dimensional theories based on lattice gauge theory

International Nuclear Information System (INIS)

Murata, M.; So, H.

2004-01-01

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram

Fock exchange in meson theories of nuclei

International Nuclear Information System (INIS)

Bolsterli, M.

1986-01-01

The Fock exchange term in meson field theories of nuclear systems is shown to arise from a two-loop ground-state self-energy diagram. Evaluation of this diagram gives the relativistic or semirelativistic analog of the Fock exchange energy; it differs from the nucleon-nucleon Fock energy in including retardation effects. In finite meson-field theories of nuclear systems, the variational nature of the meson-field analog of the Hartree-Fock energy functional can be further elucidated. 4 refs

VennDiagramWeb: a web application for the generation of highly customizable Venn and Euler diagrams.

Science.gov (United States)

Lam, Felix; Lalansingh, Christopher M; Babaran, Holly E; Wang, Zhiyuan; Prokopec, Stephenie D; Fox, Natalie S; Boutros, Paul C

2016-10-03

Visualization of data generated by high-throughput, high-dimensionality experiments is rapidly becoming a rate-limiting step in computational biology. There is an ongoing need to quickly develop high-quality visualizations that can be easily customized or incorporated into automated pipelines. This often requires an interface for manual plot modification, rapid cycles of tweaking visualization parameters, and the generation of graphics code. To facilitate this process for the generation of highly-customizable, high-resolution Venn and Euler diagrams, we introduce VennDiagramWeb: a web application for the widely used VennDiagram R package. VennDiagramWeb is hosted at http://venndiagram.res.oicr.on.ca/ . VennDiagramWeb allows real-time modification of Venn and Euler diagrams, with parameter setting through a web interface and immediate visualization of results. It allows customization of essentially all aspects of figures, but also supports integration into computational pipelines via download of R code. Users can upload data and download figures in a range of formats, and there is exhaustive support documentation. VennDiagramWeb allows the easy creation of Venn and Euler diagrams for computational biologists, and indeed many other fields. Its ability to support real-time graphics changes that are linked to downloadable code that can be integrated into automated pipelines will greatly facilitate the improved visualization of complex datasets. For application support please contact Paul.Boutros@oicr.on.ca.

Spacetime representation of topological phononics

Science.gov (United States)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

Systematic implementation of implicit regularization for multi-loop Feynman Diagrams

International Nuclear Information System (INIS)

Cherchiglia, Adriano Lana; Sampaio, Marcos; Nemes, Maria Carolina

2011-01-01

Full text: Implicit Regularization (IR) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. The essence of the method is to write the divergences in terms of loop integrals in one internal momentum which do not need to be explicitly evaluated. Moreover it acts in the physical dimension of the theory and gauge invariance is controlled by regularization dependent surface terms which when set to zero define a constrained version of IR (CIR) and deliver gauge invariant amplitudes automatically. Therefore it is in principle applicable to all physical relevant quantum field theories, supersymmetric gauge theories included. A non trivial question is whether we can generalize this program to arbitrary loop order in consonance with locality, unitarity and Lorentz invariance, especially when overlapping divergences occur. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IR program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multi-loop amplitude in a well defined set of basic divergent integrals in one internal momentum. We present several examples (from 1-loop to n-loops) using scalar φ 6 3 theory in order to help the reader understand and visualize the essence of the IR program. The choice of a scalar theory does not reduce the generality of the method presented since all other physical theories can be treated within the same strategy after space time and internal algebra are performed. Another result of this contribution is to show that if the surface terms are not set to zero they will contaminate the renormalization group coefficients. Thus, we are forced to adopt CIR which is equivalent to demand momentum routing invariance

Genus Ranges of Chord Diagrams.

Science.gov (United States)

Burns, Jonathan; Jonoska, Nataša; Saito, Masahico

2015-04-01

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

Large-order perturbation theory

International Nuclear Information System (INIS)

Wu, T.T.

1982-01-01

The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams

Equivalence between the Arquès-Walsh sequence formula and the number of connected Feynman diagrams for every perturbation order in the fermionic many-body problem

Science.gov (United States)

Castro, E.

2018-02-01

From the perturbative expansion of the exact Green function, an exact counting formula is derived to determine the number of different types of connected Feynman diagrams. This formula coincides with the Arquès-Walsh sequence formula in the rooted map theory, supporting the topological connection between Feynman diagrams and rooted maps. A classificatory summing-terms approach is used, in connection to discrete mathematical theory.

The Mollier diagram in theory and practice. Part 2. Evaporative indirect static dew point cooling and the Mollier diagram; Het Mollierdiagram in theorie en praktijk. Deel 2. Verdampingskoeling verklaard vanuit het Mollierdiagram

Energy Technology Data Exchange (ETDEWEB)

Uges, P.G.H. (ed.) [StatiqCooling, Deventer (Netherlands)

2007-02-15

The use of direct and indirect adiabatic cooling, and recently in particular indirect diabatic cooling (dew point cooling) require knowledge of the Mollier diagram. [Dutch] Het gebruik van direct en indirect werkende adiabatische koeling en recentlijk vooral de indirect werkende systemen zoals diabatische koeling (dauwpuntkoeling, al of niet uitgevoerd als statische koeling) vragen om kennis van het Mollierdiagram.

Disconnected Diagrams in Lattice QCD

Science.gov (United States)

Gambhir, Arjun Singh

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

Disconnected Diagrams in Lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)

2017-08-01

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

({alpha},{eta}) phase diagrams in tilted chiral smectics

Energy Technology Data Exchange (ETDEWEB)

Rjili, M., E-mail: medrjili@yahoo.fr [Laboratoire de Physique de la Matiere Molle et de la Modelisation Electromagnetique, Faculte des Sciences de Tunis, Universite Tunis El Manar, 2092 El Manar Tunis (Tunisia); Marcerou, J.P., E-mail: marcerou@crpp-bordeaux.cnrs.fr [Centre de Recherches Paul Pascal, 115, Av. Albert-Schweitzer, 33600 Pessac (France); Gharbi, A.; Othman, T. [Laboratoire de Physique de la Matiere Molle et de la Modelisation Electromagnetique, Faculte des Sciences de Tunis, Universite Tunis El Manar, 2092 El Manar Tunis (Tunisia)

2013-02-01

The polymorphism of tilted chiral smectics liquid crystals is incredibly rich and encompasses many subphases such as SmC{sub A}{sup Low-Asterisk }; SmC{sub Fi1}{sup Low-Asterisk }; SmC{sub Fi2}{sup Low-Asterisk }; SmC{sup Low-Asterisk }; SmC{sub {alpha}}{sup Low-Asterisk }. The continuum theory established by Marcerou (2010) is used to derive an expression for the free energy density of those subphases. The minimization of this free energy is obtained through a combination of analytical and numerical methods. It leads to a phase diagram built in the ({alpha},{eta}) plane where {alpha} is local angular parameter and {eta} describes the variation of the temperature. From this graphical representation, many experimentally observed phase sequences of ferroelectric liquid crystals can be explained, even them including subphases which were recently observed like the SmC{sub 5}{sup Low-Asterisk} and the SmC{sub 6}{sup Low-Asterisk} ones. However, it should be emphasized that the details of predicted phase diagram are strongly dependent on the compound studied.

Collaborative diagramming during problem based learning in medical education: Do computerized diagrams support basic science knowledge construction?

Science.gov (United States)

De Leng, Bas; Gijlers, Hannie

2015-05-01

To examine how collaborative diagramming affects discussion and knowledge construction when learning complex basic science topics in medical education, including its effectiveness in the reformulation phase of problem-based learning. Opinions and perceptions of students (n = 70) and tutors (n = 4) who used collaborative diagramming in tutorial groups were collected with a questionnaire and focus group discussions. A framework derived from the analysis of discourse in computer-supported collaborative leaning was used to construct the questionnaire. Video observations were used during the focus group discussions. Both students and tutors felt that collaborative diagramming positively affected discussion and knowledge construction. Students particularly appreciated that diagrams helped them to structure knowledge, to develop an overview of topics, and stimulated them to find relationships between topics. Tutors emphasized that diagramming increased interaction and enhanced the focus and detail of the discussion. Favourable conditions were the following: working with a shared whiteboard, using a diagram format that facilitated distribution, and applying half filled-in diagrams for non-content expert tutors and\\or for heterogeneous groups with low achieving students. The empirical findings in this study support the findings of earlier more descriptive studies that diagramming in a collaborative setting is valuable for learning complex knowledge in medicine.

High-pressure phase diagrams of liquid CO2 and N2

Science.gov (United States)

Boates, Brian; Bonev, Stanimir

2011-06-01

The phase diagrams of liquid CO2 and N2 have been investigated using first-principles theory. Both materials exhibit transitions to conducting liquids at high temperatures (T) and relatively modest pressures (P). Furthermore, both liquids undergo polymerization phase transitions at pressures comparable to their solid counterparts. The liquid phase diagrams have been divided into several regimes through a detailed analysis of changes in bonding, as well as structural and electronic properties for pressures and temperatures up to 200 GPa and 10 000 K, respectively. Similarities and differences between the high- P and T behavior of these fluids will be discussed. Calculations of the Hugoniot are in excellent agreement with available experimental data. Work supported by NSERC, LLNL, and the Killam Trusts. Prepared by LLNL under Contract DE-AC52-07NA27344.

Charged Compact Boson Stars in a Theory of Massless Scalar Field

Science.gov (United States)

Kumar, Sanjeev

2018-05-01

In this work we present some new results obtained in a study of the phase diagram of charged compact boson stars in a theory involving a complex scalar field with a conical potential coupled to a U(1) gauge field and gravity. We obtain new bifurcation points in this model. We present a detailed discussion of the various regions of the phase diagram with respect to the bifurcation points. The theory is seen to contain rich physics in a particular domain of the phase diagram.

Penguin diagrams in the charm sector in K{sup +}→π{sup +}νν{sup ¯}

Energy Technology Data Exchange (ETDEWEB)

Mondéjar, J., E-mail: jorge.marin@kit.edu; Rittinger, J.

2013-06-21

We evaluate at next-to-next-to-leading order (NNLO) the QCD corrections to the charm contribution from penguin diagrams to the decay K{sup +}→π{sup +}νν{sup ¯}. A NNLO calculation is already available in the literature (Buras et al., 2006 [1]). We provide an independent check of the results of non-anomalous and anomalous diagrams. We use Renormalization Group improvement and an effective theory framework to resum the large logarithms that appear. In the case of the non-anomalous diagrams, our results for the decoupling coefficients and anomalous dimensions, as well as the final numerical result, are in agreement with those of Buras et al. (2006) [1]. In the anomalous case, analytical and numerical disagreements are observed.

Asymptotic laws for random knot diagrams

Science.gov (United States)

Chapman, Harrison

2017-06-01

We study random knotting by considering knot and link diagrams as decorated, (rooted) topological maps on spheres and pulling them uniformly from among sets of a given number of vertices n, as first established in recent work with Cantarella and Mastin. The knot diagram model is an exciting new model which captures both the random geometry of space curve models of knotting as well as the ease of computing invariants from diagrams. We prove that unknot diagrams are asymptotically exponentially rare, an analogue of Sumners and Whittington’s landmark result for self-avoiding polygons. Our proof uses the same key idea: we first show that knot diagrams obey a pattern theorem, which describes their fractal structure. We examine how quickly this behavior occurs in practice. As a consequence, almost all diagrams are asymmetric, simplifying sampling from this model. We conclude with experimental data on knotting in this model. This model of random knotting is similar to those studied by Diao et al, and Dunfield et al.

Drawing Euler Diagrams with Circles

OpenAIRE

Stapleton, Gem; Zhang, Leishi; Howse, John; Rodgers, Peter

2010-01-01

Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis. As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of manual data analysis and the subsequent task of drawing an appropriate diagram. Various methods have emerged that automatically dra...

Diagrammatics lectures on selected problems in condensed matter theory

CERN Document Server

Sadovskii, Michael V

2006-01-01

The introduction of quantum field theory methods has led to a kind of "revolution" in condensed matter theory. This resulted in the increased importance of Feynman diagrams or diagram technique. It has now become imperative for professionals in condensed matter theory to have a thorough knowledge of this method.There are many good books that cover the general aspects of diagrammatic methods. At the same time, there has been a rising need for books that describe calculations and methodical "know how" of specific problems for beginners in graduate and postgraduate courses. This unique collection

Precipitation diagram of calcium carbonate polymorphs: its construction and significance

International Nuclear Information System (INIS)

Kawano, Jun; Shimobayashi, Norimasa; Miyake, Akira; Kitamura, Masao

2009-01-01

In order to interpret the formation mechanism of calcium carbonate polymorphs, we propose and construct a new 'precipitation diagram', which has two variables: the driving force for nucleation and temperature. The precipitation experiments were carried out by mixing calcium chloride and sodium carbonate aqueous solutions. As a result, a calcite-vaterite co-precipitation zone, a vaterite precipitation zone, a vaterite-aragonite co-precipitation zone and an aragonite precipitation zone can be defined. Theoretical considerations suggest that the steady state nucleation theory can explain well the appearance of these four zones, and the first-order importance of the temperature dependency of surface free energy in the nucleation of aragonite. Furthermore, the addition of an impurity will likely result in the change of these energies, and this precipitation diagram gives a new basis for interpreting the nature of the polymorphs precipitated in both inorganic and biological environments.

On classification of N=2 supersymmetric theories

International Nuclear Information System (INIS)

Cecotti, S.; Vafa, C.

1993-01-01

We find a relation between the spectrum of solitons of massive N=2 quantum field theories in d=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric N=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory. (orig.)

Resource theory for work and heat

Science.gov (United States)

Sparaciari, Carlo; Oppenheim, Jonathan; Fritz, Tobias

2017-11-01

Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilized to describe thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. We apply this resource theory to the case of many noninteracting systems and show that all quantum states are classified by their entropy and average energy, even arbitrarily far away from equilibrium. This implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs, or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for other resource theories.

Quantum field theory

CERN Document Server

Mandl, Franz

2010-01-01

Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic

Supporting learning and promoting conceptual change with box and AVOW diagrams. Part 1: Representational design and instructional approaches

Science.gov (United States)

Cheng, Peter C.-H.; Shipstone, David M.

2003-02-01

A new approach to the teaching of electricity is described that uses box and AVOW diagrams, novel representations of the properties of the electric circuit which portray current, voltage, resistance and power. The diagrams have been developed as aids to learning, understanding and problem solving. They also have the potential to promote conceptual change by challenging a number of commonly held misconceptions. The diagrams have been incorporated into A-level teaching materials on d.c. circuit theory and the rationale for this approach is contrasted with a number of strategies that have previously been reported. Part 2 of this paper (Cheng and Shipstone, International Journal of Science Education, in press) will present the results of preliminary school-based trials.

Perturbation theory from stochastic quantization

International Nuclear Information System (INIS)

Hueffel, H.

1984-01-01

By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)

Academic Training Lecture | Beyond Feynman Diagrams (1/3) | 24 April

CERN Multimedia

2013-01-01

by Prof. Lance Dixon (SLAC National Accelerator Laboratory (US)). Wednesday 24 April 2013, from 11 a.m. to 12 p.m. at CERN (222-R-001 - Filtration Plant) Description: The search for new physics at the LHC, and accurate measurements of Standard Model processes, all benefit from precise theoretical predictions of collider event rates, which in turn rely on higher order computations in QCD, the theory of the strong interactions. Key ingredients for such computations are scattering amplitudes, the quantum-mechanical transition amplitudes between the incoming quarks and gluons and the outgoing produced particles. To go beyond leading order, we need both classical tree amplitudes and quantum loop amplitudes. For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events ...

Two-loop ladder diagram contributions to Bhabha scattering. III

International Nuclear Information System (INIS)

Bjoerkevoll, K.S.; Osland, P.; Faeldt, G.

1992-01-01

The authors evaluate, in the high-energy limit, the sum of the Feynman amplitudes corresponding the six two-loop ladder-like diagrams in Bhabha scattering. This is the limit where s→∞, while t, the electron mass m and the photon mass λ are all being held fixed. In this limit the sum of the six Feynman amplitudes does not depend on the electron mass. When specialized to the region s>>t>>m 2 >>λ 2 , this result complements the one previously obtained. The connection with Φ 3 theory is also investigated. 6 refs

A general analytical equation for phase diagrams of an N-layer ferroelectric thin film with two surface layers

Energy Technology Data Exchange (ETDEWEB)

Lu, Z X; Teng, B H; Rong, Y H; Lu, X H; Yang, X [School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: phytbh@163.com

2010-03-15

Within the framework of effective-field theory with correlations, the phase diagrams of an N-layer ferroelectric thin film with two surface layers are studied by the differential operator technique based on the spin-1/2 transverse Ising model. A general analytical equation for the phase diagram of a ferroelectric thin film with arbitrary layer number as well as exchange interactions and transverse fields is derived, and then the effects of exchange interactions and transverse fields on phase diagrams are discussed for an arbitrary layer number N. Meanwhile, the crossover features, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for various parameters of an N-layer ferroelectric thin film with two surface layers are investigated. As a result, an N-independent common intersection point equation is obtained, and the three-dimensional curved surfaces for the crossover values are constructed. In comparison with the usual mean-field approximation, the differential operator technique with correlations reduces to some extent the ferroelectric features of a ferroelectric thin film.

A mapping between Feynman and string motivated one-loop rules in gauge theories

International Nuclear Information System (INIS)

Bern, Z.

1992-01-01

Recently, computationally efficient rules for one-loop gauge theory amplitudes have been derived from string theory. We demonstrate the relationship of the compact string organization of the amplitude to Feynman diagrams. In particular, we explicitly show how large cancellations inherent in conventional Feynman diagram computations are avoided by the string motivated rules. (orig.)

Conformal Phase Diagram of Complete Asymptotically Free Theories

DEFF Research Database (Denmark)

Pica, Claudio; Ryttov, Thomas A.; Sannino, Francesco

2017-01-01

function. We provide the general conditions that the beta function coefficients must abide for the theory to be completely asymptotically free while simultaneously possessing an infrared stable fixed point. We also uncover special trajectories in coupling space along which some couplings are both...... asymptotically safe and infrared conformal....

Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation

International Nuclear Information System (INIS)

Gonzalez, Ivan; Schmidt, Ivan

2007-01-01

We present an improved form of the integration technique known as NDIM (negative dimensional integration method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a φ 3 +φ 4 theory in D=4-2ε dimensions, considering generic topologies of L loops and E independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n-1), where n is the number of energy scales present in the diagram

Using Affinity Diagrams to Evaluate Interactive Prototypes

DEFF Research Database (Denmark)

Lucero, Andrés

2015-01-01

our particular use of affinity diagramming in prototype evaluations. We reflect on a decade’s experience using affinity diagramming across a number of projects, both in industry and academia. Our affinity diagramming process in interaction design has been tailored and consists of four stages: creating...

The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

CERN Document Server

Castro, C

2004-01-01

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R ) and complexified Clifford Cl_C ( 4 ) algebra related to Twistors. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl ( 1 ,7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M, F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, Brandt's action related the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries) followed by a...

Continual integral in perturbation theory

International Nuclear Information System (INIS)

Slavnov, A.A.

1975-01-01

It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)

Analytical Determining Of The Steinmetz Equivalent Diagram Elements Of Single-Phase Transformer

Directory of Open Access Journals (Sweden)

T. Aly Saandy

2015-08-01

Full Text Available This article presents to an analytical calculation methodology of the Steinmetz Equivalent Diagram Elements applied to the prediction of Eddy current loss in a single-phase transformer. Based on the electrical circuit theory the active and reactive powers consumed by the core are expressed analytically in function of the electromagnetic parameters as resistivity permeability and the geometrical dimensions of the core. The proposed modeling approach is established with the duality parallel series. The equivalent diagram elements empirically determined by Steinmetz are analytically expressed using the expressions of the no loaded transformer consumptions. To verify the relevance of the model validations both by simulations with different powers and measurements were carried out to determine the resistance and reactance of the core. The obtained results are in good agreement with the theoretical approach and the practical results.

Logic verification system for power plant sequence diagrams

International Nuclear Information System (INIS)

Fukuda, Mitsuko; Yamada, Naoyuki; Teshima, Toshiaki; Kan, Ken-ichi; Utsunomiya, Mitsugu.

1994-01-01

A logic verification system for sequence diagrams of power plants has been developed. The system's main function is to verify correctness of the logic realized by sequence diagrams for power plant control systems. The verification is based on a symbolic comparison of the logic of the sequence diagrams with the logic of the corresponding IBDs (interlock Block Diagrams) in combination with reference to design knowledge. The developed system points out the sub-circuit which is responsible for any existing mismatches between the IBD logic and the logic realized by the sequence diagrams. Applications to the verification of actual sequence diagrams of power plants confirmed that the developed system is practical and effective. (author)

An introduction to effective field theory

International Nuclear Information System (INIS)

Donoghue, John F.

1999-01-01

In these lectures I describe the main ideas of effective field theory. These are first illustrated using QED and the linear sigma model as examples. Calculational techniques using both Feynman diagrams and dispersion relations are introduced. Within QCD, chiral perturbation theory is a complete effective field theory, and I give a guide to some calculations in the literature which illustrates key ideas. (author)

Comprehending 3D Diagrams: Sketching to Support Spatial Reasoning.

Science.gov (United States)

Gagnier, Kristin M; Atit, Kinnari; Ormand, Carol J; Shipley, Thomas F

2017-10-01

Science, technology, engineering, and mathematics (STEM) disciplines commonly illustrate 3D relationships in diagrams, yet these are often challenging for students. Failing to understand diagrams can hinder success in STEM because scientific practice requires understanding and creating diagrammatic representations. We explore a new approach to improving student understanding of diagrams that convey 3D relations that is based on students generating their own predictive diagrams. Participants' comprehension of 3D spatial diagrams was measured in a pre- and post-design where students selected the correct 2D slice through 3D geologic block diagrams. Generating sketches that predicated the internal structure of a model led to greater improvement in diagram understanding than visualizing the interior of the model without sketching, or sketching the model without attempting to predict unseen spatial relations. In addition, we found a positive correlation between sketched diagram accuracy and improvement on the diagram comprehension measure. Results suggest that generating a predictive diagram facilitates students' abilities to make inferences about spatial relationships in diagrams. Implications for use of sketching in supporting STEM learning are discussed. Copyright © 2016 Cognitive Science Society, Inc.

Center-symmetric effective theory for high-temperature SU(2) Yang-Mills theory

International Nuclear Information System (INIS)

Forcrand, Ph. de; Kurkela, A.; Vuorinen, A.

2008-01-01

We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using nonperturbative lattice simulations. We find that at lower temperature the theory undergoes a second-order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry

Multiloop divergences in the closed bosonic string theory

International Nuclear Information System (INIS)

Gava, E.; Iengo, R.; Jayaraman, T.; Ramachandran, R.

1985-12-01

We discuss the structure of the divergences in the multiloop vacuum diagrams for the closed bosonic strings in the framework of the Polyakov covariant formalism. We find, by an explicit computation, that all the divergences in the theory may be interpreted as due to tadpole diagrams in which the dilation goes into the vacuum. (author)

Contingency diagrams as teaching tools

OpenAIRE

Mattaini, Mark A.

1995-01-01

Contingency diagrams are particularly effective teaching tools, because they provide a means for students to view the complexities of contingency networks present in natural and laboratory settings while displaying the elementary processes that constitute those networks. This paper sketches recent developments in this visualization technology and illustrates approaches for using contingency diagrams in teaching.

Delimiting diagrams

NARCIS (Netherlands)

Oostrom, V. van

2004-01-01

We introduce the unifying notion of delimiting diagram. Hitherto unrelated results such as: Minimality of the internal needed strategy for orthogonal first-order term rewriting systems, maximality of the limit strategy for orthogonal higher-order pattern rewrite systems (with maximality of the

The hexagon gauge anomaly in type 1 superstring theory

International Nuclear Information System (INIS)

Green, M.B.; Schwarz, J.H.

1985-01-01

Hexagon diagrams with external on-mass-shell Yang-Mills gauge particles are investigated in type I superstring theory. Both the annulus and the Moebuis-strip diagrams are shown to give anomalies, implying that spurious longitudinal modes cannot be consistently decoupled. However, the anomalies cancel when the two diagrams are added together if the gauge group is chosen to be SO(32). In carrying out the analysis, two different regulators are considered, but the same conclusions emerge in both cases. We point out where various terms in the low-energy effective action originate in superstring diagrams. (orig.)

ROLE OF UML SEQUENCE DIAGRAM CONSTRUCTS IN OBJECT LIFECYCLE CONCEPT

Directory of Open Access Journals (Sweden)

Miroslav Grgec

2007-06-01

Full Text Available When modeling systems and using UML concepts, a real system can be viewed in several ways. The RUP (Rational Unified Process defines the "4 + 1 view": 1. Logical view (class diagram (CD, object diagram (OD, sequence diagram (SD, collaboration diagram (COD, state chart diagram (SCD, activity diagram (AD, 2.Process view (use case diagram, CD, OD, SD, COD, SCD, AD, 3. Development view (package diagram, component diagram, 4. Physical view (deployment diagram, and 5. Use case view (use case diagram, OD, SD, COD, SCD, AD which combines the four mentioned above. With sequence diagram constructs we are describing object behavior in scope of one use case and their interaction. Each object in system goes through a so called lifecycle (create, supplement object with data, use object, decommission object. The concept of the object lifecycle is used to understand and formalize the behavior of objects from creation to deletion. With help of sequence diagram concepts our paper will describe the way of interaction modeling between objects through lifeline of each of them, and their importance in software development.

Problem of summing up ladder diagrams in quantum electrodynamics. [Cross sections

Energy Technology Data Exchange (ETDEWEB)

Gadzhiev, S A; Livashvili, A I [Azerbajdzhanskij Gosudarstvennyj Univ., Baku (USSR)

1975-03-01

A class of ladder diagrams in an asymptotic mode is considered, and a series of the perturbation theory for the given class of diagrams reduces to an integral equation obtained without approximations whatsoever. As applications of the method proposed, two electrodynamic processes are considered: the two-photon annihilation of an e/sup +/e/sup -/-pair and scattering of electons in Coulomb field. Matrix elements are provided. To derive the equations, Dirac equations and commutation relations are used. A conclusion is drawn that for the process, the log-log asymptotics and polar approximation lead to the fact that as the energy grows the cross-section of the process drops and the solution obtained indicates that such a drop occurs up to an energy of 10/sup 5/ GeV. For the second process, the region of large pulses transmitted by an electron to the external field does not lead to an increase in amplitude and cross-section.

A novel decision diagrams extension method

International Nuclear Information System (INIS)

Li, Shumin; Si, Shubin; Dui, Hongyan; Cai, Zhiqiang; Sun, Shudong

2014-01-01

Binary decision diagram (BDD) is a graph-based representation of Boolean functions. It is a directed acyclic graph (DAG) based on Shannon's decomposition. Multi-state multi-valued decision diagram (MMDD) is a natural extension of BDD for the symbolic representation and manipulation of the multi-valued logic functions. This paper proposes a decision diagram extension method based on original BDD/MMDD while the scale of a reliability system is extended. Following a discussion of decomposition and physical meaning of BDD and MMDD, the modeling method of BDD/MMDD based on original BDD/MMDD is introduced. Three case studies are implemented to demonstrate the presented methods. Compared with traditional BDD and MMDD generation methods, the decision diagrams extension method is more computationally efficient as shown through the running time

Dynamic phase diagrams of a cylindrical Ising nanowire in the presence of a time dependent magnetic field

International Nuclear Information System (INIS)

Kantar, Ersin; Ertaş, Mehmet; Keskin, Mustafa

2014-01-01

The dynamic phase diagrams of a cylindrical Ising nanowire in the presence of a time dependent magnetic field are obtained by using the effective-field theory with correlations based on the Glauber-type stochastic dynamics. According to the values of interaction parameters, a number of interesting properties have been found in the dynamic phase diagrams, such as many dynamic critical points (tricritical point, double critical end point, critical end point, zero temperature critical point, multicritical point, tetracritical point, and triple point) as well as reentrant phenomena. - Highlights: • The cylindrical Ising nanowire is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a reentrant behavior

Dynamic phase diagrams of a cylindrical Ising nanowire in the presence of a time dependent magnetic field

Energy Technology Data Exchange (ETDEWEB)

Kantar, Ersin; Ertaş, Mehmet, E-mail: mehmetertas@erciyes.edu.tr; Keskin, Mustafa

2014-06-01

The dynamic phase diagrams of a cylindrical Ising nanowire in the presence of a time dependent magnetic field are obtained by using the effective-field theory with correlations based on the Glauber-type stochastic dynamics. According to the values of interaction parameters, a number of interesting properties have been found in the dynamic phase diagrams, such as many dynamic critical points (tricritical point, double critical end point, critical end point, zero temperature critical point, multicritical point, tetracritical point, and triple point) as well as reentrant phenomena. - Highlights: • The cylindrical Ising nanowire is investigated within the Glauber dynamics based on EFT. • The time variations of average order parameters to find phases are studied. • The dynamic phase diagrams are found for the different interaction parameters. • The system displays the critical points as well as a reentrant behavior.

Scheil-Gulliver Constituent Diagrams

Science.gov (United States)

Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.

2017-06-01

During solidification of alloys, conditions often approach those of Scheil-Gulliver cooling in which it is assumed that solid phases, once precipitated, remain unchanged. That is, they no longer react with the liquid or with each other. In the case of equilibrium solidification, equilibrium phase diagrams provide a valuable means of visualizing the effects of composition changes upon the final microstructure. In the present study, we propose for the first time the concept of Scheil-Gulliver constituent diagrams which play the same role as that in the case of Scheil-Gulliver cooling. It is shown how these diagrams can be calculated and plotted by the currently available thermodynamic database computing systems that combine Gibbs energy minimization software with large databases of optimized thermodynamic properties of solutions and compounds. Examples calculated using the FactSage system are presented for the Al-Li and Al-Mg-Zn systems, and for the Au-Bi-Sb-Pb system and its binary and ternary subsystems.

Argumentation Theory. [A Selected Annotated Bibliography].

Science.gov (United States)

Benoit, William L.

Materials dealing with aspects of argumentation theory are cited in this annotated bibliography. The 50 citations are organized by topic as follows: (1) argumentation; (2) the nature of argument; (3) traditional perspectives on argument; (4) argument diagrams; (5) Chaim Perelman's theory of rhetoric; (6) the evaluation of argument; (7) argument…

Operations space diagram for ECRH and ECCD

DEFF Research Database (Denmark)

Bindslev, H.

2004-01-01

at the design phase. At the operations phase it may also prove useful in setting up experimental scenarios by showing operational possibilities, avoiding the need for survey type ray-tracing at the initial planning stages. The diagram may also serve the purpose of communicating operational possibilities to non......A Clemmov-Mullaly-Allis (CMA) type diagram, the ECW-CMA diagram, for representing the operational possibilities of electron cyclotron heating and current drive (ECRH/ECCD) systems for fusion plasmas is presented. In this diagram, with normalized density and normalized magnetic field coordinates......, the parameter range in which it is possible to achieve a given task (e.g. O-mode current drive for stabilizing a neoclassical tearing mode) appears as a region. With also the Greenwald density limit shown, this diagram condenses the information on operational possibilities, facilitating the overview required...

Classification of stresses in pressure components using the GLOSS diagram

International Nuclear Information System (INIS)

Seshadri, R.

1990-01-01

Discontinuity stresses in pressure components are classified as secondary stresses at temperatures below the creep range. The stresses are considered to be deformation-controlled in that shakedown occurs after several load cycles. There are situations, however, where the discontinuity stresses may not be deformation-controlled, and follow-up action might occur. A conservative approach would be to classify the resulting mixed-mode response as a load-controlled situation. The subsequent design could then be unduly wasteful. A simple method for evaluating the mixed-mode response is a technique known as the generalized local stress-strain (GLOSS) analysis. The underlying theory relates the follow-up process to the deformation-controlled uniaxial relaxation. The slope of the mixed-mode response trajectory on the GLOSS diagram determines the relative proportions of deformation and load-controlled actions. In this paper, use is made of the GLOSS diagram to classify stresses or damage due to follow-up in pressure components for temperature below the creep range and elevated temperatures. Some ASME code related perspectives are also discussed in the paper

Penguin-like diagrams from the standard model

International Nuclear Information System (INIS)

Ping, Chia Swee

2015-01-01

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the ‘tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated

Penguin-like diagrams from the standard model

Energy Technology Data Exchange (ETDEWEB)

Ping, Chia Swee [High Impact Research, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2015-04-24

The Standard Model is highly successful in describing the interactions of leptons and quarks. There are, however, rare processes that involve higher order effects in electroweak interactions. One specific class of processes is the penguin-like diagram. Such class of diagrams involves the neutral change of quark flavours accompanied by the emission of a gluon (gluon penguin), a photon (photon penguin), a gluon and a photon (gluon-photon penguin), a Z-boson (Z penguin), or a Higgs-boson (Higgs penguin). Such diagrams do not arise at the tree level in the Standard Model. They are, however, induced by one-loop effects. In this paper, we present an exact calculation of the penguin diagram vertices in the ‘tHooft-Feynman gauge. Renormalization of the vertex is effected by a prescription by Chia and Chong which gives an expression for the counter term identical to that obtained by employing Ward-Takahashi identity. The on-shell vertex functions for the penguin diagram vertices are obtained. The various penguin diagram vertex functions are related to one another via Ward-Takahashi identity. From these, a set of relations is obtained connecting the vertex form factors of various penguin diagrams. Explicit expressions for the gluon-photon penguin vertex form factors are obtained, and their contributions to the flavor changing processes estimated.

Common phase diagram for low-dimensional superconductors

International Nuclear Information System (INIS)

Michalak, Rudi

2003-01-01

A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Feynman diagrams without Feynman parameters

International Nuclear Information System (INIS)

Mendels, E.

1978-01-01

Dimensionally regularized Feynman diagrams are represented by means of products of k-functions. The infinite part of these diagrams is found very easily, also if they are overlapping, and the separation of the several kinds of divergences comes out quite naturally. Ward identities are proven in a transparent way. Series expansions in terms of the external momenta and their inner products are possible

Phase diagrams of the elements

International Nuclear Information System (INIS)

Young, D.A.

1975-01-01

A summary of the pressure-temperature phase diagrams of the elements is presented, with graphs of the experimentally determined solid-solid phase boundaries and melting curves. Comments, including theoretical discussion, are provided for each diagram. The crystal structure of each solid phase is identified and discussed. This work is aimed at encouraging further experimental and theoretical research on phase transitions in the elements

Effects of a strict cutoff on Quantum Field Theory

International Nuclear Information System (INIS)

Sturnfield, J.F.

1987-01-01

Standard Quantum Field Theory has a number of integrals which are infinite. Although these are eliminated for some cases by renormalization, this aspect of the theory is not fully satisfactory. A number of theories with fundamental lengths have been introduced as alternatives and it would be useful to be able to distinguish between them. In particular, the effects that a strict cutoff would have on Quantum Field Theory is studied. It is noted that care must be taken in the method used to apply a strict cutoff. This lead to considering a theory where the cutoffs are defined by restricting each internal line. This theory is only piece-wise analytic. The resulting scattering matrix is frame dependent, yet the theory still satisfies the special relativity view that all frames are subjectively identical. The renormalization of this theory is finite. The change in mass from the electron self-energy will be a spinor operator. The main distinctions of this theory from standard theory will occur at super high energies. New poles and resonances which arise from new endpoint singularities will be found. The locations of these singularities will be frame dependent. Some of these singularities will correspond to creations or interactions of the normal particles with tachyons. It will be shown that for the one loop diagram, the form of the cutoff singularities are closely related to the standard singularities. When there is more than one loop, there can appear some new type of behavior. In particular, a cube root type of behavior in the two loop self-energy diagram will be found. Also the asymptotic behavior of the ladder diagram is studied

Perturbation Expansion in Dynamical Nuclear Field Theory and Its Relation with Boson Expansion Theory : Nuclear Physics

OpenAIRE

Teruo, KISHIMOTO; Tetsuo, KAMMURI; Institute of Physics, University of Tsukuba; Department of Physics, Osaka University

1990-01-01

With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use thses constants renormalized by the effect of bubble diagrams, in t...

The application of diagrams in architectural design

Directory of Open Access Journals (Sweden)

Dulić Olivera

2014-01-01

Full Text Available Diagrams in architecture represent the visualization of the thinking process, or selective abstraction of concepts or ideas translated into the form of drawings. In addition, they provide insight into the way of thinking about and in architecture, thus creating a balance between the visual and the conceptual. The subject of research presented in this paper are diagrams as a specific kind of architectural representation, and possibilities and importance of their application in the design process. Diagrams are almost old as architecture itself, and they are an element of some of the most important studies of architecture during all periods of history - which results in a large number of different definitions of diagrams, but also very different conceptualizations of their features, functions and applications. The diagrams become part of contemporary architectural discourse during the eighties and nineties of the twentieth century, especially through the work of architects like Bernard Tschumi, Peter Eisenman, Rem Koolhaas, SANAA and others. The use of diagrams in the design process allows unification of some of the essential aspects of the profession: architectural representation and design process, as well as the question of the concept of architectural and urban design at a time of rapid changes at all levels of contemporary society. The aim of the research is the analysis of the diagram as a specific medium for processing large amounts of information that the architect should consider and incorporate into the architectural work. On that basis, it is assumed that an architectural diagram allows the creator the identification and analysis of specific elements or ideas of physical form, thereby constantly maintaining concept of the integrity of the architectural work.

First-principles interatomic potentials for transition-metal aluminides. III. Extension to ternary phase diagrams

Science.gov (United States)

Widom, Mike; Al-Lehyani, Ibrahim; Moriarty, John A.

2000-08-01

Modeling structural and mechanical properties of intermetallic compounds and alloys requires detailed knowledge of their interatomic interactions. The first two papers of this series [Phys. Rev. B 56, 7905 (1997); 58, 8967 (1998)] derived first-principles interatomic potentials for transition-metal (TM) aluminides using generalized pseudopotential theory (GPT). Those papers focused on binary alloys of aluminum with first-row transition metals and assessed the ability of GPT potentials to reproduce and elucidate the alloy phase diagrams of Al-Co and Al-Ni. This paper addresses the phase diagrams of the binary alloy Al-Cu and the ternary systems Al-Co-Cu and Al-Co-Ni, using GPT pair potentials calculated in the limit of vanishing transition-metal concentration. Despite this highly simplifying approximation, we find rough agreement with the known low-temperature phase diagrams, up to 50% total TM concentration provided the Co fraction is below 25%. Full composition-dependent potentials and many-body interactions would be required to correct deficiencies at higher Co concentration. Outside this troublesome region, the experimentally determined stable and metastable phases all lie on or near the convex hull of a scatter plot of energy versus composition. We verify, qualitatively, reported solubility ranges extending binary alloys into the ternary diagram in both Al-Co-Cu and Al-Co-Ni. Finally, we reproduce previously conjectured transition-metal positions in the decagonal quasicrystal phase.

Density-functional theory computer simulations of CZTS{sub 0.25}Se{sub 0.75} alloy phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Chagarov, E.; Sardashti, K.; Kummel, A. C. [Departments of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093 (United States); Haight, R. [IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598 (United States); Mitzi, D. B. [Departments of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708 (United States)

2016-08-14

Density-functional theory simulations of CZTS, CZTSe, and CZTS{sub 0.25}Se{sub 0.75} photovoltaic compounds have been performed to investigate the stability of the CZTS{sub 0.25}Se{sub 0.75} alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS{sub 0.25}Se{sub 0.75} alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS{sub 0.25}Se{sub 0.75} that the chemical potentials for stability differ between typical processing temperature (∼900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS{sub 0.25}Se{sub 0.75} in a thermodynamically stable state to minimize phase decomposition.

Multi-currency Influence Diagrams

DEFF Research Database (Denmark)

Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn V.

2007-01-01

When using the influence diagrams framework for solving a decision problem with several different quantitative utilities, the traditional approach has been to convert the utilities into one common currency. This conversion is carried out using a tacit transformation, under the assumption...... that the converted problem is equivalent to the original one. In this paper we present an extension of the influence diagram framework. The extension allows for these decision problems to be modelled in their original form. We present an algorithm that, given a linear conversion function between the currencies...

Twistor Cosmology and Quantum Space-Time

International Nuclear Information System (INIS)

Brody, D.C.; Hughston, L.P.

2005-01-01

The purpose of this paper is to present a model of a 'quantum space-time' in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space-time imply that the pseudo-Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space-time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space-time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen-dimensional analogue of the Friedmann-Robertson-Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space-time is an even perfect square, there exists a canonical way of breaking the global quantum space-time symmetry so that a generic point of quantum space-time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space-time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space-time description is an emergent feature arising as a consequence of a

Students’ learning activities while studying biological process diagrams

NARCIS (Netherlands)

Kragten, M.; Admiraal, W.; Rijlaarsdam, G.

2015-01-01

Process diagrams describe how a system functions (e.g. photosynthesis) and are an important type of representation in Biology education. In the present study, we examined students’ learning activities while studying process diagrams, related to their resulting comprehension of these diagrams. Each

Superconformal quantum field theories in string. Gauge theory dualities

Energy Technology Data Exchange (ETDEWEB)

Wiegandt, Konstantin

2012-08-14

In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Superconformal quantum field theories in string. Gauge theory dualities

International Nuclear Information System (INIS)

Wiegandt, Konstantin

2012-01-01

In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Operations space diagram for ECRH and ECCD

International Nuclear Information System (INIS)

Bindslev, Henrik

2004-01-01

A Clemmov-Mullaly-Allis (CMA) type diagram, the ECW-CMA diagram, for representing the operational possibilities of electron cyclotron heating and current drive (ECRH/ECCD) systems for fusion plasmas is presented. In this diagram, with normalized density and normalized magnetic field coordinates, the parameter range in which it is possible to achieve a given task (e.g. O-mode current drive for stabilizing a neoclassical tearing mode) appears as a region. With also the Greenwald density limit shown, this diagram condenses the information on operational possibilities, facilitating the overview required at the design phase. At the operations phase it may also prove useful in setting up experimental scenarios by showing operational possibilities, avoiding the need for survey type ray-tracing at the initial planning stages. The diagram may also serve the purpose of communicating operational possibilities to non-experts. JET and ITER like plasmas are used, but the method is generic. (author)

Safety-barrier diagrams as a safety management tool

DEFF Research Database (Denmark)

Duijm, Nijs Jan

2009-01-01

Safety-barrier diagrams and “bow-tie” diagrams have become popular methods in risk analysis and safety management. This paper describes the syntax and principles for constructing consistent and valid safety-barrier diagrams. The latter's relation to other methods such as fault trees and Bayesian...

Effects of the randomly distributed magnetic field on the phase diagrams of the Ising Nanowire II: Continuous distributions

International Nuclear Information System (INIS)

Akıncı, Ümit

2012-01-01

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system. - Highlights: ► We give the phase diagrams of the Ising nanowire under the continuous randomly distributed magnetic field. ► Ground state magnetization values obtained. ► Different partially ordered phases observed.

Gauge field geometry from complex and harmonic analyticities

International Nuclear Information System (INIS)

Gal'perin, A.S.; Ivanov, E.A.; Ogievetsky, V.I.; Sokatchev, E.

1987-01-01

The analyticity preservation principle is employed to demonstrate and impressive affinity between field theories with intrinsic analytic structure and superfield gauge theories. The defining constraints of the former theories are interpreted as the integrability conditions for the existence of appropriate analytic subspaces and are solved by passing to the basis with manifest analyticity. We prefer to work within the analytic basis. This allows, e.g., to replace the nonlinear splitting problem of twistor approach by solving a linear equation

Near threshold expansion of Feynman diagrams

International Nuclear Information System (INIS)

Mendels, E.

2005-01-01

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an arbitrary number of internal lines and an arbitrary number of loops, in n dimensions and all masses may be different. The expansions are considered both below and above threshold. Rules, giving real and imaginary part, are derived. Unitarity of a sunset diagram with I internal lines is checked in a direct way by showing that its imaginary part is equal to the phase space integral of I particles

Perturbative quantum gravity as a double copy of gauge theory.

Science.gov (United States)

Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

2010-08-06

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

On the question of calculation methods of phase diagrams

International Nuclear Information System (INIS)

Vasil'ev, M.V.

1983-01-01

The technique of determining interaction parameters of components of binary alloys is suggested. U-Mo and Cu-Al systems are used as example with the aid of experimental state diagrams. It is shown that the search for new regularities is necessary with the aim of analytical description of state diagrams and forecast of the shape of phase equilibria curves in real systems. Optimum combinations of experimental investigations with the aim of reliable determination of supporting points and forecasting possibilities of typical equations can considerably decrease the volume of experimental work when preparing state diagrams, in cases of repeated state diagrams of more reliable state diagrams with the application of more advanced methods of investigation. The translation of state diagrams from geometric to analytical language with the use of typical equations opens up new possibilities for establishing a compact information bank for state diagrams

A geometric proof of confluence by decreasing diagrams

NARCIS (Netherlands)

Klop, J.W.; Oostrom, V. van; Vrijer, R. de

The criterion for confluence using decreasing diagrams is a generalization of several well-known confluence criteria in abstract rewriting, such as the strong confluence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of in finite reduction diagrams, arising

Compact flow diagrams for state sequences

NARCIS (Netherlands)

Buchin, K.A.; Buchin, M.E.; Gudmundsson, J.; Horton, M.J.; Sijben, S.

2016-01-01

We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified,

Local homotopy theory

CERN Document Server

Jardine, John F

2015-01-01

This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, n...

Voronoi diagram and microstructure of weldment

Energy Technology Data Exchange (ETDEWEB)

Cho, Jung Ho [Chungbuk National University, Cheongju (Korea, Republic of)

2015-01-15

Voronoi diagram, one of the well-known space decomposition algorithms has been applied to express the microstructure of a weldment for the first time due to the superficial analogy between a Voronoi cell and a metal's grain. The area of the Voronoi cells can be controlled by location and the number of the seed points. This can be correlated to the grain size in the microstructure and the number of nuclei formed. The feasibility of representing coarse and fine grain structures were tested through Voronoi diagrams and it is applied to expression of cross-sectional bead shape of a typical laser welding. As result, it successfully described coarsened grain size of heat affected zone and columnar crystals in fusion zone. Although Voronoi diagram showed potential as a microstructure prediction tool through this feasible trial but direct correlation control variable of Voronoi diagram to solidification process parameter is still remained as further works.

Interpolating string field theories

International Nuclear Information System (INIS)

Zwiebach, B.

1992-01-01

This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles

The role of perceptual cues in matrix diagrams

NARCIS (Netherlands)

van der Meij, Jan; van Amelsvoort, Marije; Anjewierden, A.

An experiment was conducted to assess whether the design of a matrix diagram influences how people study the diagram and whether this has an effect on recall of the presented information. We compared four versions of a matrix diagram on antisocial personality disorder. It consisted of four header

The role of perceptual cues in matrix diagrams

NARCIS (Netherlands)

van der Meij, Jan; Amelsvoort, Marije; Anjewierden, Anjo Allert

2015-01-01

An experiment was conducted to assess whether the design of a matrix diagram influences how people study the diagram and whether this has an effect on recall of the presented information. We compared four versions of a matrix diagram on antisocial personality disorder. It consisted of four header

Compact flow diagrams for state sequences

NARCIS (Netherlands)

Buchin, Kevin; Buchin, Maike; Gudmundsson, Joachim; Horton, Michael; Sijben, Stef

2017-01-01

We introduce the concept of using a flow diagram to compactly represent the segmentation of a large number of state sequences according to a set of criteria. We argue that this flow diagram representation gives an intuitive summary that allows the user to detect patterns within the segmentations. In

Diagrams of natural deductions

Energy Technology Data Exchange (ETDEWEB)

Popov, S V

1982-01-01

The concept of natural deductions was investigated by the author in his analysis of the complexity of deductions in propositional computations (1975). Here some natural deduction systems are considered, and an analytical procedure proposed which results in a deduction diagram for each system. Each diagram takes the form of an orientated, charge graph, features of which can be used to establish the equivalence of classes of deductions. For each of the natural deduction systems considered, a system of equivalent transformation schemes is derived, which is complete with respect to the given definition of equivalence. 2 references.

Perturbation Theory of Massive Yang-Mills Fields

Science.gov (United States)

Veltman, M.

1968-08-01

Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

Gravitational field mass

International Nuclear Information System (INIS)

Penrose, R.

1986-01-01

The author's definition for the mass-momentum/angular momentum surrounded by a spacelike 2-surface with S/sup 2/ topology is presented. This definition is motivated by some ideas from twistor theory in relation to linearized gravitational theory. The status of this definition is examined in relation to many examples which have been worked out. The reason for introducing a slight modification of the original definition is also presented

Control wiring diagrams

International Nuclear Information System (INIS)

McCauley, T.M.; Eskinazi, M.; Henson, L.L.

1989-01-01

This paper discusses the changes in electrical document requirements that occur when construction is complete and a generating station starts commercial operation. The needs of operations and maintenance (O and M) personnel are analyzed and contrasted with those of construction to illustrate areas in which the construction documents (drawings, diagrams, and databases) are difficult to use for work at an operating station. The paper discusses the O and M electrical documents that the Arizona Nuclear Power Project (ANPP) believes are most beneficial for the three operating units at Palo Verde; these are control wiring diagrams and an associated document cross-reference list. The benefits offered by these new, station O and M-oriented documents are weighted against the cost of their creation and their impact on drawing maintenance

New detectors for powders diagrams

International Nuclear Information System (INIS)

Convert, P.

1975-01-01

During the last few years, all the classical neutron diffractometers for powders have used one or maybe a few counters. So, it takes a long time to obtain a diagram which causes many disadvantages: 1) very long experiments: one or two days (or flux on the sample about 10 6 n/cm 2 /a); 2) necessity of big samples: many cm 3 ; 3) necessity of having the whole diagram before changing anything in the experiment: magnetic field, temperature, quality of the sample; 4) necessity of having collimators of a few times ten minutes to obtain correct statistics in the diagram. Because of these disadvantages, several attempts have been made to speed up the experimental procedure such as using more counters, the detection of neutrons on a resistive wire, etc. In Grenoble, new position-sensitive detectors have been constructed using a digital technique

Causal Diagrams for Empirical Research

OpenAIRE

Pearl, Judea

1994-01-01

The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifiying causal effects from non-experimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in ter...

Graphical matching rules for cardinality based service feature diagrams

Directory of Open Access Journals (Sweden)

Faiza Kanwal

2017-03-01

Full Text Available To provide efficient services to end-users, variability and commonality among the features of the product line is a challenge for industrialist and researchers. Feature modeling provides great services to deal with variability and commonality among the features of product line. Cardinality based service feature diagrams changed the basic framework of service feature diagrams by putting constraints to them, which make service specifications more flexible, but apart from their variation in selection third party services may have to be customizable. Although to control variability, cardinality based service feature diagrams provide high level visual notations. For specifying variability, the use of cardinality based service feature diagrams raises the problem of matching a required feature diagram against the set of provided diagrams.

Critical exponents predicted by grouping of Feynman diagrams in φ4 model

International Nuclear Information System (INIS)

Kaupuzs, J.

2001-01-01

Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments. (orig.)

c-T phase diagram and Landau free energies of (AgAu)55 nanoalloy via neural-network molecular dynamic simulations.

Science.gov (United States)

Chiriki, Siva; Jindal, Shweta; Bulusu, Satya S

2017-10-21

For understanding the structure, dynamics, and thermal stability of (AgAu) 55 nanoalloys, knowledge of the composition-temperature (c-T) phase diagram is essential due to the explicit dependence of properties on composition and temperature. Experimentally, generating the phase diagrams is very challenging, and therefore theoretical insight is necessary. We use an artificial neural network potential for (AgAu) 55 nanoalloys. Predicted global minimum structures for pure gold and gold rich compositions are lower in energy compared to previous reports by density functional theory. The present work based on c-T phase diagram, surface area, surface charge, probability of isomers, and Landau free energies supports the enhancement of catalytic property of Ag-Au nanoalloys by incorporation of Ag up to 24% by composition in Au nanoparticles as found experimentally. The phase diagram shows that there is a coexistence temperature range of 70 K for Ag 28 Au 27 compared to all other compositions. We propose the power spectrum coefficients derived from spherical harmonics as an order parameter to calculate Landau free energies.

On the Impact of Layout Quality to Understanding UML Diagrams: Diagram Type and Expertise

DEFF Research Database (Denmark)

Störrle, Harald

2012-01-01

Practical experience suggests that the use and understanding of UML diagrams is greatly affected by the quality of their layout. In previous work, we have presented evidence supporting this intuition. This contrasts with earlier experiments that yielded weak or inconclusive evidence only. In the ......Practical experience suggests that the use and understanding of UML diagrams is greatly affected by the quality of their layout. In previous work, we have presented evidence supporting this intuition. This contrasts with earlier experiments that yielded weak or inconclusive evidence only...

The sine-Gordon model and the small κ+ region of light- cone perturbation theory

International Nuclear Information System (INIS)

Griffin, P.A.

1992-01-01

The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the k + = 0 region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non- perturbative β 2 = 8π critical point by a light-cone version of Coleman's variational method. Vacuum bubbles, which are k + = 0 diagram in light-cone field theory and are individually finite and non-vanishing for all β, conspire to generate ultraviolet divergences of the light-cone energy density. The k + = 0 region of momentum also contributed to connected Green's functions: the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at k + = 0 are properly included. This analysis shows in a simple way how the k + = 0 region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory

Introduction to set theory and topology

CERN Document Server

Kuratowski, Kazimierz; Stark, M

1972-01-01

Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its applica

S-duality and noncommutative gauge theory

International Nuclear Information System (INIS)

Gopakumar, R.; Maldacena, J.; Minwalla, S.; Strominger, A.

2000-01-01

It is conjectured that strongly coupled, spatially noncommutative CN=4 Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the non-planar one-loop open string diagram. The open string theory can be viewed as living in a geometry in which space and time coordinates do not commute. (author)

First-principles interatomic potentials for transition-metal aluminides. III. Extension to ternary phase diagrams

International Nuclear Information System (INIS)

Widom, Mike; Al-Lehyani, Ibrahim; Moriarty, John A.

2000-01-01

Modeling structural and mechanical properties of intermetallic compounds and alloys requires detailed knowledge of their interatomic interactions. The first two papers of this series [Phys. Rev. B 56, 7905 (1997); 58, 8967 (1998)] derived first-principles interatomic potentials for transition-metal (TM) aluminides using generalized pseudopotential theory (GPT). Those papers focused on binary alloys of aluminum with first-row transition metals and assessed the ability of GPT potentials to reproduce and elucidate the alloy phase diagrams of Al-Co and Al-Ni. This paper addresses the phase diagrams of the binary alloy Al-Cu and the ternary systems Al-Co-Cu and Al-Co-Ni, using GPT pair potentials calculated in the limit of vanishing transition-metal concentration. Despite this highly simplifying approximation, we find rough agreement with the known low-temperature phase diagrams, up to 50% total TM concentration provided the Co fraction is below 25%. Full composition-dependent potentials and many-body interactions would be required to correct deficiencies at higher Co concentration. Outside this troublesome region, the experimentally determined stable and metastable phases all lie on or near the convex hull of a scatter plot of energy versus composition. We verify, qualitatively, reported solubility ranges extending binary alloys into the ternary diagram in both Al-Co-Cu and Al-Co-Ni. Finally, we reproduce previously conjectured transition-metal positions in the decagonal quasicrystal phase. (c) 2000 The American Physical Society

Beyond Feynman Diagrams (1/3)

CERN Multimedia

CERN. Geneva

2013-01-01

For decades the central theoretical tool for computing scattering amplitudes has been the Feynman diagram. However, Feynman diagrams are just too slow, even on fast computers, to be able to go beyond the leading order in QCD, for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past few years, alternative methods that go beyond ...

Wind Diagrams in Medieval Iceland

DEFF Research Database (Denmark)

Kedwards, Dale

2014-01-01

This article presents a study of the sole wind diagram that survives from medieval Iceland, preserved in the encyclopaedic miscellany in Copenhagen's Arnamagnæan Institute with the shelf mark AM 732b 4to (c. 1300-25). It examines the wind diagram and its accompanying text, an excerpt on the winds...... from Isidore of Seville's Etymologies. It also examines the perimeter of winds on two medieval Icelandic world maps, and the visual traditions from which they draw....

Bayesian Networks and Influence Diagrams

DEFF Research Database (Denmark)

Kjærulff, Uffe Bro; Madsen, Anders Læsø

 Probabilistic networks, also known as Bayesian networks and influence diagrams, have become one of the most promising technologies in the area of applied artificial intelligence, offering intuitive, efficient, and reliable methods for diagnosis, prediction, decision making, classification......, troubleshooting, and data mining under uncertainty. Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. Intended...

Proof test diagrams for Zerodur glass-ceramic

Science.gov (United States)

Tucker, D. S.

1991-01-01

Proof test diagrams for Zerodur glass-ceramics are calculated from available fracture mechanics data. It is shown that the environment has a large effect on minimum time-to-failure as predicted by proof test diagrams.

Conformal gauge-Yukawa theories away from four dimensions

Energy Technology Data Exchange (ETDEWEB)

Codello, Alessandro; Langæble, Kasper [CP-Origins, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark); Danish Institute for Advanced Study, Danish IAS, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark)

2016-07-22

We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d=4+ϵ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD{sub d} and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.

Conformal Gauge-Yukawa Theories away From Four Dimensions

DEFF Research Database (Denmark)

Codello, Alessandro; Langaeble, Kasper; Litim, Daniel

2016-01-01

We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD$...

Phase Diagrams of the Aqueous Two-Phase Systems of Poly(ethylene glycol/Sodium Polyacrylate/Salts

Directory of Open Access Journals (Sweden)

Adalberto Pessoa Junior

2011-03-01

Full Text Available Aqueous two-phase systems consisting of polyethylene glycol (PEG, sodium polyacrylate (NaPAA, and a salt have been studied. The effects of the polymer size, salt type (NaCl, Na2SO4, sodium adipate and sodium azelate and salt concentrations on the position of the binodal curve were investigated. The investigated PEG molecules had a molar mass of 2,000 to 8,000 g/mol, while that of NaPAA was 8,000 g/mol. Experimental phase diagrams, and tie lines and calculated phase diagrams, based on Flory-Huggins theory of polymer solutions are presented. Due to strong enthalpic and entropic balancing forces, the hydrophobicity of the added salt has a strong influence on the position of the binodal, which could be reproduced by model calculations.

Atlas of hot isostatic beryllium powder pressing diagrams

International Nuclear Information System (INIS)

Stoev, P.I.; Papirov, I.I.; Tikhinskij, G.F.; Vasil'ev, A.A.

1995-01-01

Diagrams of hot isotopic pressing (HIP) of beryllium powder with different grain size in a wide range of pressing parameters are built by mathematical modeling methods. The HIP diagrams presented are divided into 3 groups: parametric dependencies D=f(P,T); technological HIP diagrams; compacting mechanisms. The created data bank permits to optimise beryllium powder HIP with changing parameters. 4 refs., 23 figs

Calculation of the hyperfine interaction using an effective-operator form of many-body theory

International Nuclear Information System (INIS)

Garpman, S.; Lindgren, I.; Lindgren, J.; Morrison, J.

1975-01-01

The effective-operator form of many-body theory is reviewed and applied to the calculation of the hyperfine structure. Numerical results are given for the 2p, 3p, and 4p excited states of Li and the 3p state of Na. This is the first complete calculation of the hyperfine structure using an effective-operator form of perturbation theory. As in the Brueckner-Goldstone form of many-body theory, the various terms in the perturbation expansion are represented by Feynman diagrams which correspond to basic physical processes. The angular part of the perturbation diagrams are evaluated by taking advantage of the formal analogy between the Feynman diagrams and the angular-momentum diagrams, introduced by Jucys et al. The radial part of the diagrams is calculated by solving one- and two-particle equations for the particular linear combination of excited states that contribute to the Feynman diagrams. In this way all second- and third-order effects are accurately evaluated without explicitly constructing the excited orbitals. For the 2p state of Li our results are in agreement with the calculations of Nesbet and of Hameed and Foley. However, our quadrupole calculation disagrees with the work of Das and co-workers. The many-body results for Li and Na are compared with semiempirical methods for evaluating the quadrupole moment from the hyperfine interaction, and a new quadrupole moment of 23 Na is given

Visualizing Metrics on Areas of Interest in Software Architecture Diagrams

NARCIS (Netherlands)

Byelas, Heorhiy; Telea, Alexandru; Eades, P; Ertl, T; Shen, HW

2009-01-01

We present a new method for the combined visualization of software architecture diagrams, Such as UML class diagrams or component diagrams, and software metrics defined on groups of diagram elements. Our method extends an existing rendering technique for the so-called areas of interest in system

Updating the Nomographical Diagrams for Dimensioning the Beams

Directory of Open Access Journals (Sweden)

Pop Maria T.

2015-12-01

Full Text Available In order to reduce the time period needed for structures design it is strongly recommended to use nomographical diagrams. The base for formation and updating the nomographical diagrams, stands on the charts presented by different technical publications. The updated charts use the same algorithm and calculation elements as the former diagrams in accordance to the latest prescriptions and European standards. The result consists in a chart, having the same properties, similar with the nomogragraphical diagrams already in us. As a general conclusion, even in our days, the nomographical diagrams are very easy to use. Taking into consideration the value of the moment it’s easy to find out the necessary reinforcement area and vice-verse, having the reinforcement area you can find out the capable moment. It still remains a useful opportunity for pre-sizing and designs the reinforced concrete sections.

Phase diagram of classical electronic bilayers

International Nuclear Information System (INIS)

Ranganathan, S; Johnson, R E

2006-01-01

Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength Γ and interlayer separation d to delineate its phase diagram in the Γ-d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for Γ greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones

Phase diagram of classical electronic bilayers

Energy Technology Data Exchange (ETDEWEB)

Ranganathan, S [Department of Physics, Royal Military College of Canada, Kingston, Ontario K7K 7B4 (Canada); Johnson, R E [Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Ontario K7K 7B4 (Canada)

2006-04-28

Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength {gamma} and interlayer separation d to delineate its phase diagram in the {gamma}-d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for {gamma} greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones.

Effect of elastic compliances and higher order Landau coefficients on the phase diagram of single domain epitaxial Pb(Zr,TiO3 (PZT thin films

Directory of Open Access Journals (Sweden)

M. Mtebwa

2014-12-01

Full Text Available We report the qualitative study of the influence of both elastic compliances and higher order terms of Landau free energy potential on the phase diagram of Pb(Zr0.5Ti0.5O3 thin films by using a single domain Landau theory. Although the impact of elastic compliances and higher order terms of the Landau free energy potential on the phase diagram of ferroelectric thin films are known, the sensitivity of the phase diagram of PZT thin film on these parameters have not been reported. It is demonstrated that, while values of elastic compliances affect the positions of the phase boundaries including phase transition temperature of the cubic phase; higher order terms can potentially introduce an a1a2-phase previously predicted in PbTiO3 phase diagram.

Modeling cancer registration processes with an enhanced activity diagram.

Science.gov (United States)

Lyalin, D; Williams, W

2005-01-01

Adequate instruments are needed to reflect the complexity of routine cancer registry operations properly in a business model. The activity diagram is a key instrument of the Unified Modeling Language (UML) for the modeling of business processes. The authors aim to improve descriptions of processes in cancer registration, as well as in other public health domains, through the enhancements of an activity diagram notation within the standard semantics of UML. The authors introduced the practical approach to enhance a conventional UML activity diagram, complementing it with the following business process concepts: timeline, duration for individual activities, responsibilities for individual activities within swimlanes, and descriptive text. The authors used an enhanced activity diagram for modeling surveillance processes in the cancer registration domain. Specific example illustrates the use of an enhanced activity diagram to visualize a process of linking cancer registry records with external mortality files. Enhanced activity diagram allows for the addition of more business concepts to a single diagram and can improve descriptions of processes in cancer registration, as well as in other domains. Additional features of an enhanced activity diagram allow to advance the visualization of cancer registration processes. That, in turn, promotes the clarification of issues related to the process timeline, responsibilities for particular operations, and collaborations among process participants. Our first experiences in a cancer registry best practices development workshop setting support the usefulness of such an approach.

Bifurcation and phase diagram of turbulence constituted from three different scale-length modes

Energy Technology Data Exchange (ETDEWEB)

Itoh, S.-I.; Kitazawa, A.; Yagi, M. [Kyushu Univ., Research Inst. for Applied Mechanics, Kasuga, Fukuoka (Japan); Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan)

2002-04-01

Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses. (author)

Fishbone Diagrams: Organize Reading Content with a "Bare Bones" Strategy

Science.gov (United States)

Clary, Renee; Wandersee, James

2010-01-01

Fishbone diagrams, also known as Ishikawa diagrams or cause-and-effect diagrams, are one of the many problem-solving tools created by Dr. Kaoru Ishikawa, a University of Tokyo professor. Part of the brilliance of Ishikawa's idea resides in the simplicity and practicality of the diagram's basic model--a fish's skeleton. This article describes how…

Muonium and the Breit-Rabi diagram

International Nuclear Information System (INIS)

Cox, S.F.J.

1984-01-01

This chapter introduces the study of muonium, as opposed to that of unbound muons. The properties and behaviour of muonium are compared and contrasted with those of hydrogen and of positronium. The special significance of muonium in atomic and molecular physics is explained, and its utility as a lightweight or radioactive isotope of hydrogen in solid state physics and chemistry illustrated. The identification of atomic muonium by means of its ground state magnetic properties is described with reference to the Breit-Rabi diagram. This diagram is invaluable for interpreting or predicting MuSR observations, both in transverse and longitudinal magnetic fields, so its construction and properties are explained in some detail. The precession signals observed in transverse-field MuSR correspond to transitions allowed between the energy levels in this diagram; particular attention is paid to the spectra characteristic of the high and low field regimes. The different states of muonium observed in dielectric, semiconducting and metallic materials are introduced. The influence of the host medium on the spectral parameters, hyperfine interaction and linewidth, is considered both for atomic muonium and for muonium which is chemically bound in paramagnetic molecules, for which the Breit-Rabi diagram also applies. (orig.)

Impulse-Momentum Diagrams

Science.gov (United States)

Rosengrant, David

2011-01-01

Multiple representations are a valuable tool to help students learn and understand physics concepts. Furthermore, representations help students learn how to think and act like real scientists. These representations include: pictures, free-body diagrams, energy bar charts, electrical circuits, and, more recently, computer simulations and…

From emblems to diagrams: Kepler's new pictorial language of scientific representation.

Science.gov (United States)

Chen-Morris, Raz

2009-01-01

Kepler's treatise on optics of 1604 furnished, along with technical solutions to problems in medieval perspective, a mathematically-based visual language for the observation of nature. This language, based on Kepler's theory of retinal pictures, ascribed a new role to geometrical diagrams. This paper examines Kepler's pictorial language against the backdrop of alchemical emblems that flourished in and around the court of Rudolf II in Prague. It highlights the cultural context in which Kepler's optics was immersed, and the way in which Kepler attempted to demarcate his new science from other modes of the investigation of nature.

Phase diagrams and heterogeneous equilibria a practical introduction

CERN Document Server

Predel, Bruno; Pool, Monte

2004-01-01

This graduate-level textbook provides an introduction to the practical application of phase diagrams. It is intended for students and researchers in chemistry, metallurgy, mineralogy, and materials science as well as in engineering and physics. Heterogeneous equilibria are described by a minimum of theory illustrated by practical examples and realistic case discussions from the different fields of application. The treatment of the physical and energetic background of phase equilibria leads to the discussion of the thermodynamics of mixtures and the correlation between energetics and composition. Thus, tools for the prediction of energetic, structural, and physical quantities are provided. The authors treat the nucleation of phase transitions, the production and stability of technologically important metastable phases, and metallic glasses. Furthermore, the text also concisely presents the thermodynamics and composition of polymer systems.

How design guides learning from matrix diagrams

NARCIS (Netherlands)

van der Meij, Jan; Amelsvoort, Marije; Anjewierden, Anjo

2017-01-01

Compared to text, diagrams are superior in their ability to structure and summarize information and to show relations between concepts and ideas. Perceptual cues, like arrows, are expected to improve the retention of diagrams by guiding the learner towards important elements or showing a preferred

Diagram of state of stiff amphiphilic macromolecules

NARCIS (Netherlands)

Markov, Vladimir A.; Vasilevskaya, Valentina V.; Khalatur, Pavel G.; ten Brinke, Gerrit; Khokhlov, Alexei R.

2007-01-01

We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of

Atomic energy levels and Grotrian diagrams

CERN Document Server

Bashkin, Stanley

1975-01-01

Atomic Energy Levels and Grotrian Diagrams, Volume I: Hydrogen I - Phosphorus XV presents diagrams of various elements that show their energy level and electronic transitions. The book covers the first 15 elements according to their atomic number. The text will be of great use to researchers and practitioners of fields such as astrophysics that requires pictorial representation of the energy levels and electronic transitions of elements.

Renormalization of self-consistent approximation schemes at finite temperature. II. Applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, Hendrik van; Knoll, Joern

2002-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, devised in the first paper of this series, are applied to first example cases of φ 4 theory. In addition to the tadpole (Hartree) approximation, as a novel part the numerical solutions are presented, which include the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or the two-particle irreducible effective action concept

Renormalization of self-consistent approximation schemes at finite temperature II: applications to the sunset diagram

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-01-01

The theoretical concepts for the renormalization of self-consistent Dyson resummations, deviced in the first paper of this series, are applied to first example cases for the φ 4 -theory. Besides the tadpole (Hartree) approximation as a novel part the numerical solutions are presented which includes the sunset self-energy diagram into the self-consistent scheme based on the Φ-derivable approximation or 2PI effective action concept. (orig.)

FIRST-PRINCIPLES PHASE DIAGRAM OF THE Ce-Th SYSTEM

International Nuclear Information System (INIS)

Landa, A; Soderlind, P

2005-01-01

Actinide physics has seen a remarkable focus the last decade or so due to the combination of improved experimental diamond-anvil-cell techniques and the development of fast computers and more advanced theory. All f-electron systems are expected to have multiphase phase diagrams due to the sensitivity of the f-electron band to external influences such as pressure and temperature. For instance, compression of an f-electron metal generally causes the occupation of f-states to change due to the shift of these bands relative to others. This can in some cases, as in the Ce-Th system, cause the crystal to adopt a lower symmetry structure at elevated pressures. Here we study the phase stabilities of Ce, Th, and the Ce-Th system as a function of compression. Theoretically, both Ce and Th metals are rather well described within the DFT, although a proper treatment of the Ce-Th alloys has not yet been presented. In the present paper we revisit this problem by applying the modern theory of random alloys based on the coherent potential approximation (CPA)

Xenon spectator and diagram L3-M4,5M4,5 Auger intensities near the L3 threshold

International Nuclear Information System (INIS)

Armen, G.B.; Levin, J.C.; Southworth, S.H.; LeBrun, T.; Arp, U.; MacDonald, M.A.

1997-01-01

Calculations based on the theory of radiationless resonant Raman scattering are employed in the interpretation of new XeL 3 -M 4,5 M 4,5 Auger spectra recorded using synchrotron radiation tuned to energies across the L 3 edge. Fits of theoretical line shapes to the spectra are employed in separating intensities due to nd spectator (resonant) and diagram Auger processes. Near-threshold Auger intensity, previously attributed to diagram decay, is found to be due to the large-n spectator lines that result from postcollision-interaction endash induced open-quotes recaptureclose quotes of threshold photoelectrons to nd orbitals. copyright 1997 The American Physical Society

Updating the Nomographical Diagrams for Dimensioning the Beams

OpenAIRE

Pop Maria T.

2015-01-01

In order to reduce the time period needed for structures design it is strongly recommended to use nomographical diagrams. The base for formation and updating the nomographical diagrams, stands on the charts presented by different technical publications. The updated charts use the same algorithm and calculation elements as the former diagrams in accordance to the latest prescriptions and European standards. The result consists in a chart, having the same properties, similar with the nomogragra...

Influence diagram in evaluating the subjective judgment

International Nuclear Information System (INIS)

Hong, Y.

1997-01-01

The author developed the idea of the subjective influence diagrams to evaluate subjective judgment. The subjective judgment of a stake holder is a primary decision making proposition. It involves a basic decision process an the individual attitude of the stake holder for his decision purpose. The subjective judgment dominates the some final decisions. A complex decision process may include the subjective judgment. An influence diagram framework is a simplest tool for analyzing subjective judgment process. In the framework, the characters of influence diagrams generate the describing the analyzing, and the evaluating of the subjective judgment. The relationship between the information and the decision, such as independent character between them, is the main issue. Then utility function is the calculating tool to evaluation, the stake holder can make optimal decision. Through the analysis about the decision process and relationship, the building process of the influence diagram identically describes the subjective judgment. Some examples are given to explain the property of subjective judgment and the analysis process

Wavelet-Based Quantum Field Theory

Directory of Open Access Journals (Sweden)

Mikhail V. Altaisky

2007-11-01

Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

Lattice and Phase Diagram in QCD

International Nuclear Information System (INIS)

Lombardo, Maria Paola

2008-01-01

Model calculations have produced a number of very interesting expectations for the QCD Phase Diagram, and the task of a lattice calculations is to put these studies on a quantitative grounds. I will give an overview of the current status of the lattice analysis of the QCD phase diagram, from the quantitative results of mature calculations at zero and small baryochemical potential, to the exploratory studies of the colder, denser phase.

Ferroelectric Phase Diagram of PVDF:PMMA

OpenAIRE

Li, Mengyuan; Stingelin, Natalie; Michels, Jasper J.; Spijkman, Mark-Jan; Asadi, Kamal; Feldman, Kirill; Blom, Paul W. M.; de Leeuw, Dago M.

2012-01-01

We have investigated the ferroelectric phase diagram of poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA). The binary nonequilibrium temperature composition diagram was determined and melting of alpha- and beta-phase PVDF was identified. Ferroelectric beta-PVDF:PMMA blend films were made by melting, ice quenching, and subsequent annealing above the glass transition temperature of PMMA, close to the melting temperature of PVDF. Addition of PMMA suppresses the crystallizatio...

Local supertwistors and N=2 conformal supergravity

International Nuclear Information System (INIS)

Merkulov, S.A.

1989-01-01

N = 2 sypersymmetric extension of the local twistor theory is formulated. A supertwistor superconnection determined by the superconformal structure of the base superspace is introduced on the bundle of N = 2 local supertwistors. It is proved that the Yang - Mills equations for this superconnection coincide exactly with the Bach equations describing the dynamics of N 2 conformal supergravity

Decoupling theorem in supersymmetric theories

Energy Technology Data Exchange (ETDEWEB)

Leon, J; Perez-Mercader, J; Sanchez, M F

1988-07-21

We introduce a superfield extension of Weisberger's method for decoupling calculations in multiscale field theories and generalize our previous method which does not require the computation of any Feynman diagram. We illustrate this for the two-scale Wess-Zumino model, showing explicitly how the decoupling takes place.

A Critical Appraisal of the "Day" Diagram

Science.gov (United States)

Roberts, Andrew P.; Tauxe, Lisa; Heslop, David; Zhao, Xiang; Jiang, Zhaoxia

2018-04-01

The "Day" diagram (Day et al., 1977, https://doi.org/10.1016/0031-9201(77)90108-X) is used widely to make inferences about the domain state of magnetic mineral assemblages. Based on theoretical and empirical arguments, the Day diagram is demarcated into stable "single domain" (SD), "pseudo single domain" ("PSD"), and "multidomain" (MD) zones. It is straightforward to make the necessary measurements for a sample and to plot results within the "domain state" framework based on the boundaries defined by Day et al. (1977, https://doi.org/10.1016/0031-9201(77)90108-X). We discuss 10 issues that limit Day diagram interpretation, including (1) magnetic mineralogy, (2) the associated magnetocrystalline anisotropy type, (3) mineral stoichiometry, (4) stress state, (5) surface oxidation, (6) magnetostatic interactions, (7) particle shape, (8) thermal relaxation, (9) magnetic particle mixtures, and (10) definitional/measurement issues. In most studies, these variables are unknowns and cannot be controlled for, so that hysteresis parameters for single bulk samples are nonunique and any data point in a Day diagram could result from infinite combinations of relevant variables. From this critical appraisal, we argue that the Day diagram is fundamentally ambiguous for domain state diagnosis. Widespread use of the Day diagram has also contributed significantly to prevalent but questionable views, including underrecognition of the importance of stable SD particles in the geological record and reinforcement of the unhelpful PSD concept and of its geological importance. Adoption of approaches that enable correct domain state diagnosis should be an urgent priority for component-specific understanding of magnetic mineral assemblages and for quantitative rock magnetic interpretation.

Pitfalls and feedback when constructing topological pressure-temperature phase diagrams

Science.gov (United States)

Ceolin, R.; Toscani, S.; Rietveld, Ivo B.; Barrio, M.; Tamarit, J. Ll.

2017-04-01

The stability hierarchy between different phases of a chemical compound can be accurately reproduced in a topological phase diagram. This type of phase diagrams may appear to be the result of simple extrapolations, however, experimental complications quickly increase in the case of crystalline trimorphism (and higher order polymorphism). To ensure the accurate positioning of stable phase domains, a topological phase diagram needs to be consistent. This paper gives an example of how thermodynamic feedback can be used in the topological construction of phase diagrams to ensure overall consistency in a phase diagram based on the case of piracetam crystalline trimorphism.

Planar theory made plainer

International Nuclear Information System (INIS)

Smith, R.A.

1986-01-01

This paper discusses two important steps which have been taken to extend the parquet method to fermion systems and for systems with spin- and isospin-dependent forces. The parquet diagrams are shown and they are constructed by taking any two boxes and joining them together by connecting two legs from one box to the other box. Some results are presented of a study of the formal inclusion of spin and tensor forces for problems involving bosons. A parquet perspective table is presented which starts with the exact theory and shows what has been done and what remains to be done to deal with interesting systems. Additional structure may be added to this diagram at many points

Phase diagram of spiking neural networks.

Science.gov (United States)

Seyed-Allaei, Hamed

2015-01-01

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2%, 20% of neurons are inhibitory and 80% are excitatory. These common values are based on experiments, observations, and trials and errors, but here, I take a different perspective, inspired by evolution, I systematically simulate many networks, each with a different set of parameters, and then I try to figure out what makes the common values desirable. I stimulate networks with pulses and then measure their: dynamic range, dominant frequency of population activities, total duration of activities, maximum rate of population and the occurrence time of maximum rate. The results are organized in phase diagram. This phase diagram gives an insight into the space of parameters - excitatory to inhibitory ratio, sparseness of connections and synaptic weights. This phase diagram can be used to decide the parameters of a model. The phase diagrams show that networks which are configured according to the common values, have a good dynamic range in response to an impulse and their dynamic range is robust in respect to synaptic weights, and for some synaptic weights they oscillates in α or β frequencies, independent of external stimuli.

On hidden symmetries of a super gauge theory and twistor string theory

International Nuclear Information System (INIS)

Wolf, Martin

2005-01-01

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N=4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn - by a supersymmetric extension of Ward's conjecture - reduce to the super hierarchies of integrable models in D<4 dimensions. (author)

Repair of Partly Misspecified Causal Diagrams.

Science.gov (United States)

Oates, Chris J; Kasza, Jessica; Simpson, Julie A; Forbes, Andrew B

2017-07-01

Errors in causal diagrams elicited from experts can lead to the omission of important confounding variables from adjustment sets and render causal inferences invalid. In this report, a novel method is presented that repairs a misspecified causal diagram through the addition of edges. These edges are determined using a data-driven approach designed to provide improved statistical efficiency relative to de novo structure learning methods. Our main assumption is that the expert is "directionally informed," meaning that "false" edges provided by the expert would not create cycles if added to the "true" causal diagram. The overall procedure is cast as a preprocessing technique that is agnostic to subsequent causal inferences. Results based on simulated data and data derived from an observational cohort illustrate the potential for data-assisted elicitation in epidemiologic applications. See video abstract at, http://links.lww.com/EDE/B208.

Simple method for evaluating Goldstone diagrams in an angular momentum coupled representation

International Nuclear Information System (INIS)

Kuo, T.T.S.; Shurpin, J.; Tam, K.C.; Osnes, E.; Ellis, P.J.

1981-01-01

A simple and convenient method is derived for evaluating linked Goldstone diagrams in an angular momentum coupled representation. Our method is general, and can be used to evaluate any effective interaction and/or effective operator diagrams for both closed-shell nuclei (vacuum to vacuum linked diagrams) and open-shell nuclei (valence linked diagrams). The techniques of decomposing diagrams into ladder diagrams, cutting open internal lines and cutting off one-body insertions are introduced. These enable us to determine angular momentum factors associated with diagrams in the coupled representation directly, without the need for carrying out complicated angular momentum algebra. A summary of diagram rules is given

The zero-bin and mode factorization in quantum field theory

International Nuclear Information System (INIS)

Manohar, Aneesh V.; Stewart, Iain W.

2007-01-01

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In nonrelativistic field theories, the subtractions remove unphysical pinch singularities in box-type diagrams, and give a derivation of the known pullup mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formulas occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long-standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays

Orientation dependence of phase diagrams and physical properties in epitaxial Ba0.6Sr0.4TiO3 films

Science.gov (United States)

Qiu, J. H.; Zhao, T. X.; Chen, Z. H.; Yuan, N. Y.; Ding, J. N.

2018-04-01

Orientation dependence of phase diagrams and physical properties of Ba0.6Sr0.4TiO3 films are investigated by using a phenomenological Landau-Devonshire theory. New ferroelectric phases, such as the tetragonal a1 phase and the orthorhombic a2 c phase in (110) oriented film and the monoclinic MA phase in (111) oriented film, appear in the "misfit strain-temperature" phase diagrams as compared with (001) oriented film. Moreover, the phase diagrams of (110) and (111) oriented films are more complex than that of (001) oriented film due to the nonlinear coupling terms appeared in the thermodynamic potential. The dielectric and piezoelectric properties largely depend on the misfit strain and orientation. (111) oriented film has the better piezoelectric property than (110) oriented film. Furthermore, the compressive misfit strain is prone to induce the larger piezoelectric property than tensile misfit strain.

How Design Guides Learning from Matrix Diagrams

Science.gov (United States)

van der Meij, Jan; van Amelsvoort, Marije; Anjewierden, Anjo

2017-01-01

Compared to text, diagrams are superior in their ability to structure and summarize information and to show relations between concepts and ideas. Perceptual cues, like arrows, are expected to improve the retention of diagrams by guiding the learner towards important elements or showing a preferred reading sequence. In our experiment, we analyzed…

Kinetic Ising model in a time-dependent oscillating external magnetic field: effective-field theory

International Nuclear Information System (INIS)

Deviren, Bayram; Canko, Osman; Keskin, Mustafa

2010-01-01

Recently, Shi et al. [2008 Phys. Lett. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tomé and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tomé and de Oliveira; hence the dynamic phase diagrams calculated by Shi et al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (ω) and static external field amplitude (h 0 ) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of ω and h 0 . (general)

Phase Diagram in a Random Mixture of Two Antiferromagnets with Competing Spin Anisotropies. I

Science.gov (United States)

Someya, Yoshiko

1981-12-01

The phase diagram of a random mixture of two antiferromagnets with competing spin anisotropies (A1-xBx) has been analyzed by extending the theory of Matsubara and Inawashiro, and Oguchi and Ishikawa. In the model assumed, the anisotropy energies are expressed by the anisotropic exchange interactions. According to this formulation, it has been shown that the concentration dependence of TN becomes a function of \\includegraphics{dummy.eps}, where P, Q=A, B; SP is a magnitude of P-spin, and JPQη is a η component of exchange integral between P- and Q-spin). Further, the phase boundary between an AF phase and an OAF (oblique antiferromagnetic) phase at T{=}0 K has been shown to be determined by α({\\equiv}SB/SA), if \\includegraphics{dummy.eps} are given. The obtained phase diagrams for Fe1-xCoxCl2, K2Mn1-xFexF4 and Fe1-xCoxCl2\\cdot2H2O are compared with the experimental ones.

Interrelations between random walks on diagrams (graphs) with and without cycles.

Science.gov (United States)

Hill, T L

1988-05-01

Three topics are discussed. A discrete-state, continuous-time random walk with one or more absorption states can be studied by a presumably new method: some mean properties, including the mean time to absorption, can be found from a modified diagram (graph) in which each absorption state is replaced by a one-way cycle back to the starting state. The second problem is a random walk on a diagram (graph) with cycles. The walk terminates on completion of the first cycle. This walk can be replaced by an equivalent walk on a modified diagram with absorption. This absorption diagram can in turn be replaced by another modified diagram with one-way cycles back to the starting state, just as in the first problem. The third problem, important in biophysics, relates to a long-time continuous walk on a diagram with cycles. This diagram can be transformed (in two steps) to a modified, more-detailed, diagram with one-way cycles only. Thus, the one-way cycle fluxes of the original diagram can be found from the state probabilities of the modified diagram. These probabilities can themselves be obtained by simple matrix inversion (the probabilities are determined by linear algebraic steady-state equations). Thus, a simple method is now available to find one-way cycle fluxes exactly (previously Monte Carlo simulation was required to find these fluxes, with attendant fluctuations, for diagrams of any complexity). An incidental benefit of the above procedure is that it provides a simple proof of the one-way cycle flux relation Jn +/- = IIn +/- sigma n/sigma, where n is any cycle of the original diagram.

Peircean diagrams of time

DEFF Research Database (Denmark)

Øhrstrøm, Peter

2011-01-01

Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can...... be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation can be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1......) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models....

Conformal window of gauge theories with four-fermion interactions and ideal walking technicolor

DEFF Research Database (Denmark)

Sannino, Francesco; Sakuma, Hidenori

2010-01-01

We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four...... discover that when the extended technicolor sector, responsible for giving masses to the standard model fermions, is sufficiently strongly coupled the technicolor theory, in isolation, must have an infrared fixed point for the full model to be phenomenologically viable. Using the new phase diagram we show...

Extended sequence diagram for human system interaction

International Nuclear Information System (INIS)

Hwang, Jong Rok; Choi, Sun Woo; Ko, Hee Ran; Kim, Jong Hyun

2012-01-01

Unified Modeling Language (UML) is a modeling language in the field of object oriented software engineering. The sequence diagram is a kind of interaction diagram that shows how processes operate with one another and in what order. It is a construct of a message sequence chart. It depicts the objects and classes involved in the scenario and the sequence of messages exchanged between the objects needed to carry out the functionality of the scenario. This paper proposes the Extended Sequence Diagram (ESD), which is capable of depicting human system interaction for nuclear power plants, as well as cognitive process of operators analysis. In the conventional sequence diagram, there is a limit to only identify the activities of human and systems interactions. The ESD is extended to describe operators' cognitive process in more detail. The ESD is expected to be used as a task analysis method for describing human system interaction. The ESD can also present key steps causing abnormal operations or failures and diverse human errors based on cognitive condition

Lattice simulations of QCD-like theories at finite baryon density

Energy Technology Data Exchange (ETDEWEB)

Scior, Philipp Friedrich

2016-07-13

The exploration of the phase diagram of quantum chromodynamics (QCD) is of great importance to describe e.g. the properties of neutron stars or heavy-ion collisions. Due to the sign problem of lattice QCD at finite chemical potential we need effective theories to study QCD at finite density. Here, we use a three-dimensional Polyakov-loop theory to study the phase diagrams of QCD-like theories. In particular, we investigate the heavy quark limit of the QCD-like theories where the effective theory can be derived from the full theory by a combined strong coupling and hopping expansion. This expansion can be systematically improved order by order. Since there is no sign problem for the QCD-like theories we consider, we can compare our results to data from lattice calculations of the full theories to make qualitative and quantitative statements of the effective theory's validity. We start by deriving the effective theory up to next-to-next-to leading-order, in particular for two-color and G{sub 2}-QCD where replace the three colors in QCD with only two colors or respectively replace the gauge group SU(3) of QCD with G{sub 2}. We will then apply the effective theory at finite temperature mainly to test the theory and the implementation but also to make some predictions for the deconfinement phase transition in G{sub 2} Yang-Mills theory. Finally, we turn our attention to the cold and dense regime of the phase diagram where we observe a sharp increase of the baryon density with the quark chemical potential μ, when μ reaches half the diquark mass. At vanishing temperature this is expected to happen in a quantum phase transition with Bose-Einstein-condensation of diquarks. In contrast to the liquid-gas transition in QCD, the phase transition to the Bose-Einstein condensate is continuous. We find evidence that the effective theories for heavy quarks are able to describe the qualitative difference between first and second order phase transitions. For even higher μ we

Lattice simulations of QCD-like theories at finite baryon density

International Nuclear Information System (INIS)

Scior, Philipp Friedrich

2016-01-01

The exploration of the phase diagram of quantum chromodynamics (QCD) is of great importance to describe e.g. the properties of neutron stars or heavy-ion collisions. Due to the sign problem of lattice QCD at finite chemical potential we need effective theories to study QCD at finite density. Here, we use a three-dimensional Polyakov-loop theory to study the phase diagrams of QCD-like theories. In particular, we investigate the heavy quark limit of the QCD-like theories where the effective theory can be derived from the full theory by a combined strong coupling and hopping expansion. This expansion can be systematically improved order by order. Since there is no sign problem for the QCD-like theories we consider, we can compare our results to data from lattice calculations of the full theories to make qualitative and quantitative statements of the effective theory's validity. We start by deriving the effective theory up to next-to-next-to leading-order, in particular for two-color and G_2-QCD where replace the three colors in QCD with only two colors or respectively replace the gauge group SU(3) of QCD with G_2. We will then apply the effective theory at finite temperature mainly to test the theory and the implementation but also to make some predictions for the deconfinement phase transition in G_2 Yang-Mills theory. Finally, we turn our attention to the cold and dense regime of the phase diagram where we observe a sharp increase of the baryon density with the quark chemical potential μ, when μ reaches half the diquark mass. At vanishing temperature this is expected to happen in a quantum phase transition with Bose-Einstein-condensation of diquarks. In contrast to the liquid-gas transition in QCD, the phase transition to the Bose-Einstein condensate is continuous. We find evidence that the effective theories for heavy quarks are able to describe the qualitative difference between first and second order phase transitions. For even higher μ we find the rise of the

An Introduction to Binary Decision Diagrams

DEFF Research Database (Denmark)

Andersen, Henrik Reif

1996-01-01

This note is a short introduction to Binary Decision Diagrams (BDDs). It provides some background knowledge and describes the core algorithms. It is used in the course "C4340 Advanced Algorithms" at the Technical University of Denmark, autumn 1996.......This note is a short introduction to Binary Decision Diagrams (BDDs). It provides some background knowledge and describes the core algorithms. It is used in the course "C4340 Advanced Algorithms" at the Technical University of Denmark, autumn 1996....

The Butterfly diagram leopard skin pattern

Science.gov (United States)

Ternullo, Maurizio

2011-08-01

A time-latitude diagram where spotgroups are given proportional relevance to their area is presented. The diagram reveals that the spotted area distribution is higly dishomogeneous, most of it being concentrated in few, small portions (``knots'') of the Butterfly Diagram; because of this structure, the BD may be properly described as a cluster of knots. The description, assuming that spots scatter around the ``spot mean latitude'' steadily drifting equatorward, is challenged. Indeed, spots cluster around at as many latitudes as knots; a knot may appear at either lower or higher latitudes than previous ones, in a seemingly random way; accordingly, the spot mean latitude abruptly drifts equatorward or even poleward at any knot activation, in spite of any smoothing procedure. Preliminary analyses suggest that the activity splits, in any hemisphere, into two or more distinct ``activity waves'', drifting equatorward at a rate higher than the spot zone as a whole.

Theorems for asymptotic safety of gauge theories

Energy Technology Data Exchange (ETDEWEB)

Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)

2017-06-15

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)

Construction of UML class diagram with Model-Driven Development

Directory of Open Access Journals (Sweden)

Tomasz Górski

2016-03-01

Full Text Available Model transformations play a key role in software development projects based on Model--Driven Development (MDD principles. Transformations allow for automation of repetitive and well-defined steps, thus shortening design time and reducing a number of errors. In the object-oriented approach, the key elements are use cases. They are described, modelled and later designed until executable application code is obtained. The aim of the paper is to present transformation of a model-to-model type, Communication-2-Class, which automates construction of Unified Modelling Language (UML class diagram in the context of the analysis/design model. An UML class diagram is created based on UML communication diagram within use case realization. As a result, a class diagram shows all of the classes involved in the use case realization and the relationships among them. The plug-in which implements Communication-2-Class transformation was implemented in the IBM Rational Software Architect. The article presents the tests results of developed plug-in, which realizes Communication-2-Class transformation, showing capabilities of shortening use case realization’s design time.[b]Keywords[/b]: Model-Driven Development, transformations, Unified Modelling Language, analysis/design model, UML class diagram, UML communication diagram

Efficient computation of clipped Voronoi diagram for mesh generation

KAUST Repository

Yan, Dongming

2013-04-01

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved.

Efficient computation of clipped Voronoi diagram for mesh generation

KAUST Repository

Yan, Dongming; Wang, Wen Ping; Lé vy, Bruno L.; Liu, Yang

2013-01-01

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved.

Community detection by graph Voronoi diagrams

Science.gov (United States)

Deritei, Dávid; Lázár, Zsolt I.; Papp, István; Járai-Szabó, Ferenc; Sumi, Róbert; Varga, Levente; Ravasz Regan, Erzsébet; Ercsey-Ravasz, Mária

2014-06-01

Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra- or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid- and density-based clustering methods.

A Community Based Systems Diagram of Obesity Causes.

Directory of Open Access Journals (Sweden)

Steven Allender

Full Text Available Application of system thinking to the development, implementation and evaluation of childhood obesity prevention efforts represents the cutting edge of community-based prevention. We report on an approach to developing a system oriented community perspective on the causes of obesity.Group model building sessions were conducted in a rural Australian community to address increasing childhood obesity. Stakeholders (n = 12 built a community model that progressed from connection circles to causal loop diagrams using scripts from the system dynamics literature. Participants began this work in identifying change over time in causes and effects of childhood obesity within their community. The initial causal loop diagram was then reviewed and elaborated by 50 community leaders over a full day session.The process created a causal loop diagram representing community perceptions of determinants and causes of obesity. The causal loop diagram can be broken down into four separate domains; social influences; fast food and junk food; participation in sport; and general physical activity.This causal loop diagram can provide the basis for community led planning of a prevention response that engages with multiple levels of existing settings and systems.

An approach for continuous cooling transformation (CCT) diagrams of aluminium alloys

International Nuclear Information System (INIS)

Herding, T.; Kessler, O.; Hoffmann, F.; Mayr, P.

2002-01-01

Two different kinds of time temperature transformation (TTT) diagrams are known. The first one are isothermal transformation (IT) diagrams and the second one continuous cooling transformation (CCT) diagrams. These diagrams are important for the correct heat treatment of aluminium alloys, because they provide information about the required quenching rate, which is necessary to obtain a supersaturated solid solution during age hardening. Furthermore, it is possible to determine the lowest quenching rate, which permits both a high strength and a small distortion of the component after age hardening. In the literature IT diagrams for different aluminium alloys are available. To determine these diagrams, a solution annealing followed by quenching to defined temperatures is necessary. At these temperatures the alloy is kept isothermally until a transformation has started. These diagrams are not directly portable on continuous cooling, because of the different cooling paths. (orig.)

Effects of Three Diagram Instruction Methods on Transfer of Diagram Comprehension Skills: The Critical Role of Inference While Learning

Science.gov (United States)

Cromley, Jennifer G.; Bergey, Bradley W.; Fitzhugh, Shannon; Newcombe, Nora; Wills, Theodore W.; Shipley, Thomas F.; Tanaka, Jacqueline C.

2013-01-01

Can students be taught to better comprehend the diagrams in their textbooks? Can such teaching transfer to uninstructed diagrams in the same domain or even in a new domain? What methods work best for these goals? Building on previous research showing positive results compared to control groups in both laboratory studies and short-term…

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Science.gov (United States)

Micallef, Luana; Rodgers, Peter

2014-01-01

Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

Directory of Open Access Journals (Sweden)

Luana Micallef

Full Text Available Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

XLOOPS - a package calculating one- and two-loop diagrams

International Nuclear Information System (INIS)

Bruecher, L.

1997-01-01

A program package for calculating massive one- and two-loop diagrams is introduced. It consists of five parts: - a graphical user interface, - routines for generating diagrams from particle input, - procedures for calculating one-loop integrals both analytically and numerically, - routines for massive two-loop integrals, - programs for numerical integration of two-loop diagrams. Here the graphical user interface and the text interface to Maple are presented. (orig.)

Oak Ridge K-25 Site Technology Logic Diagram. Volume 2, Technology Logic Diagrams

Energy Technology Data Exchange (ETDEWEB)

Fellows, R.L. [ed.

1993-02-26

The Oak Ridge K-25 Technology Logic Diagram (TLD), a decision support tool for the K-25 Site, was developed to provide a planning document that relates envirorunental restoration and waste management problems at the Oak Ridge K-25 Site to potential technologies that can remediate these problems. The TLD technique identifies the research necessary to develop these technologies to a state that allows for technology transfer and application to waste management, remedial action, and decontamination and decommissioning activities. The TLD consists of four separate volumes-Vol. 1, Vol. 2, Vol. 3A, and Vol. 3B. Volume 1 provides introductory and overview information about the TLD. This volume, Volume 2, contains logic diagrams with an index. Volume 3 has been divided into two separate volumes to facilitate handling and use.

Grotrian diagrams of highly ionized iron Fe(VIII)-Fe(XXVI)

International Nuclear Information System (INIS)

Mori, Kazuo; Otsuka, Masamoto; Kato, Takako.

1977-08-01

Energy levels and Grotrian diagrams of Fe(VIII) to Fe(XXVI) are presented. This report summarized the data published recently up to 1976, and the wavelength tables compiled were converted to the Grotrian diagrams. The diagrams showing transition from one energy level to another are called Grotrian diagrams. Typical examples of the diagrams are found in the book by Bashkin et al. In the present diagrams, all lines are drawn in parallel, and connected to the extended lines from lower levels. As the results, locally dense packing of lines and figures is avoided. The ordinate of the diagrams indicates level energy, and the J values are shown on the left side of the levels. The wavelength values in angstrom unit are written in parallel with the vertical transition lines. This vertical lines show the resonance transition having absorption oscillator strength f larger than 0.1. The present diagrams are the combination of the tables of wavelength and energy level. Accordingly, the desired wavelength and level energy are easily found. The figures of wavelength are lined up in various groups, so that the characteristics of the transition can be discriminated at a glance. Wavelength and level energy have been mostly derived from experimental spectra in laboratory or solar plasma, except a few by Fawcett's prediction. (Kato, T.)

Interdependent binary choices under social influence: Phase diagram for homogeneous unbiased populations

Science.gov (United States)

Fernández del Río, Ana; Korutcheva, Elka; de la Rubia, Javier

2012-07-01

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered. The nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice. The local or individual interdependence model represents a single group where agents make two binary choices which depend on each other. For both models, phase diagrams, and their implications in socioeconomic contexts, are described and compared in the absence of private deterministic utilities (zero opinion fields).

Magnetic phase diagram of the Ca1-xMnxO systems

International Nuclear Information System (INIS)

Masrour, R.; Hamedoun, M.

2008-01-01

The magnetic properties of the Ca 1-x Mn x O systems in the range 0≤x≤1 have been studied by mean field theory and high-temperature series expansions (HTSEs). By using the first theory, we have evaluated the nearest neighbour and the next-neighbour super-exchange interaction J 1 (x) and J 2 (x) respectively, in the range 0.45≤x≤1. The corresponding classical exchange energy for magnetic structure is obtained for the Ca 1-x Mn x O systems. The HTSEs combined with the Pade approximants (PA) method is applied to the Ca 1-x Mn x O systems; we have obtained the magnetic phase diagrams (T N or T SG versus dilution x) in the range 0≤x≤1. The obtained theoretical results are in agreement with experimental ones obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) are deduced in the range 0≤x≤1

Phase diagram of dense two-color QCD within lattice simulations

Directory of Open Access Journals (Sweden)

Braguta V.V.

2017-01-01

Full Text Available We present the results of a low-temperature scan of the phase diagram of dense two-color QCD with Nf = 2 quarks. The study is conducted using lattice simulation with rooted staggered quarks. At small chemical potential we observe the hadronic phase, where the theory is in a confining state, chiral symmetry is broken, the baryon density is zero and there is no diquark condensate. At the critical point μ = mπ/2 we observe the expected second order transition to Bose-Einstein condensation of scalar diquarks. In this phase the system is still in confinement in conjunction with nonzero baryon density, but the chiral symmetry is restored in the chiral limit. We have also found that in the first two phases the system is well described by chiral perturbation theory. For larger values of the chemical potential the system turns into another phase, where the relevant degrees of freedom are fermions residing inside the Fermi sphere, and the diquark condensation takes place on the Fermi surface. In this phase the system is still in confinement, chiral symmetry is restored and the system is very similar to the quarkyonic state predicted by SU(Nc theory at large Nc.

Triangular Diagrams Teach Steady and Dynamic Behaviour of Catalytic Reactions.

Science.gov (United States)

Klusacek, K.; And Others

1989-01-01

Illustrates how triangular diagrams can aid in presenting some of the rather complex transient interactions that occur among gas and surface species during heterogeneous catalytic reactions. The basic equations and numerical examples are described. Classroom use of the triangular diagram is discussed. Several diagrams and graphs are provided. (YP)

Analysis of Sequence Diagram Layout in Advanced UML Modelling Tools

Directory of Open Access Journals (Sweden)

Ņikiforova Oksana

2016-05-01

Full Text Available System modelling using Unified Modelling Language (UML is the task that should be solved for software development. The more complex software becomes the higher requirements are stated to demonstrate the system to be developed, especially in its dynamic aspect, which in UML is offered by a sequence diagram. To solve this task, the main attention is devoted to the graphical presentation of the system, where diagram layout plays the central role in information perception. The UML sequence diagram due to its specific structure is selected for a deeper analysis on the elements’ layout. The authors research represents the abilities of modern UML modelling tools to offer automatic layout of the UML sequence diagram and analyse them according to criteria required for the diagram perception.

New twistorial integral formulas for massless free fields of arbitrary spin

International Nuclear Information System (INIS)

Cardoso, J.G.

1991-01-01

A manifestly scaling-invariant version of the Kirchoff-D'Adhemar-Penrose field integrals is presented. The invariant integral expressions for the spinning massless free fields are directly transcribed into the framework of twistor theory. It is then shown that the resulting twistorial field integrals can be thought of as being equivalent to the universal Penrose contour integral formulas for these fields

Introduction to field theory

CERN Multimedia

CERN. Geneva; CERN. Geneva

2001-01-01

Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.

Theory of Rare-Earth Alloys

DEFF Research Database (Denmark)

Lindgård, Per-Anker

1977-01-01

A mean-field random alloy theory combined with a simple calculation of the exchange interaction J(c,Q) is shown to quantitatively account for the phase diagrams for alloys of rare-earth metals with Y, Lu, Sc, and other rare-earth metals. A concentration-dependent J(c,Q) explains the empirical 2...

String amplitudes: from field theories to number theory

CERN Multimedia

CERN. Geneva

2017-01-01

In a variety of recent developments, scattering amplitudes hint at new symmetries of and unexpected connections between physical theories which are otherwise invisible in their conventional description via Feynman diagrams or Lagrangians. Yet, many of these hidden structures are conveniently accessible to string theory where gauge interactions and gravity arise as the low-energy excitations of open and closed strings. In this talk, I will give an intuitive picture of gravity as a double copy of gauge interactions and extend the web of relations to scalar field theories including chiral Lagrangians for Goldstone bosons. The string corrections to gauge and gravity amplitudes beyond their point-particle limit exhibit elegant mathematical structures and offer a convenient laboratory to explore modern number-theoretic concepts in a simple context. As a common theme with Feynman integrals, string amplitudes introduce a variety of periods and special functions including multiple zeta values and polylogarithms, orga...

Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

International Nuclear Information System (INIS)

Adamatzky, Andrew; De Lacy Costello, Ben; Holley, Julian; Gorecki, Jerzy; Bull, Larry

2011-01-01

Highlights: → We model irregular arrangements of vesicles filled with chemical systems. → We examine influence of precipitation threshold on the system's computational potential. → We demonstrate computation of Voronoi diagram and skeleton. - Abstract: Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata - finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape.

Developing Tool Support for Problem Diagrams with CPN and VDM++

DEFF Research Database (Denmark)

Tjell, Simon; Lassen, Kristian Bisgaard

2008-01-01

In this paper, we describe ongoing work on the development of tool support for formal description of domains found in Problem Diagrams. The purpose of the tool is to handle the generation of a CPN model based on a collection of Problem Diagrams. The Problem Diagrams are used for representing the ...

A Generalized Wave Diagram for Moving Sources

Science.gov (United States)

Alt, Robert; Wiley, Sam

2004-12-01

Many introductory physics texts1-5 accompany the discussion of the Doppler effect and the formation of shock waves with diagrams illustrating the effect of a source moving through an elastic medium. Typically these diagrams consist of a series of equally spaced dots, representing the location of the source at different times. These are surrounded by a series of successively smaller circles representing wave fronts (see Fig. 1). While such a diagram provides a clear illustration of the shock wave produced by a source moving at a speed greater than the wave speed, and also the resultant pattern when the source speed is less than the wave speed (the Doppler effect), the texts do not often show the details of the construction. As a result, the key connection between the relative distance traveled by the source and the distance traveled by the wave is not explicitly made. In this paper we describe an approach emphasizing this connection that we have found to be a useful classroom supplement to the usual text presentation. As shown in Fig. 2 and Fig. 3, the Doppler effect and the shock wave can be illustrated by diagrams generated by the construction that follows.

Testing of multidimensional tectonomagmatic discrimination diagrams on fresh and altered rocks

Directory of Open Access Journals (Sweden)

Rivera-Gómez M. Abdelaly

2016-04-01

Full Text Available We evaluated 55 multidimensional diagrams proposed during 2004-2013 for the tectonic discrimination of ultrabasic, basic, intermediate, and acid magmas. The Miocene to Recent rock samples for testing the diagrams had not been used for constructing them. Eighteen test studies (2 from ocean island; 2 from ocean island/continental rift; 6 from continental rift; 4 from continental arc; 2 from island arc; 1 from mid-ocean ridge, and 1 from collision of relatively fresh rocks fully confirmed the satisfactory functioning of these diagrams for all tectonic fields for which they were proposed. Eight additional case studies on hydrothermally altered or moderately to highly weathered rocks were also presented to achieve further understanding of the functioning of these diagrams. For these rocks as well, the diagrams indicated the expected tectonic setting. We also show that for testing or using these diagrams the freely-available geochemistry databases should be used with caution but certainly after ascertaining the correct magma types to select the appropriate diagram sets. The results encourage us to recommend these diagrams for deciphering the tectonic setting of older terranes or areas with complex or transitional tectonic settings.

Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation

Directory of Open Access Journals (Sweden)

Lorenz Demey

2017-09-01

Full Text Available Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study (connections between various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B 4 , viz. the rhombic dodecahedron, the tetrakis hexahedron, the tetraicosahedron and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation (or lack thereof between logical (Hamming and geometrical (Euclidean distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design.

Mollier-h,x diagram for moist flue gas

Energy Technology Data Exchange (ETDEWEB)

Mueller, H; Hultsch, T; Suder, M

1984-07-01

Diagrams and formulae are presented for calculation of enthalpy and moisture content of flue gas from brown coal, heating oil, black coal and brown coal briquet combustion. The enthalpy (in kJ/kg) and moisture (g/kg) diagrams were established by computer graphics for pressure 0.1 MPa. A further diagram is provided for enthalpy and flue gas moisture, varying the combustion air supply according to coal dust and to grate firing. These thermodynamic calculations are regarded as significant for assessing methods of flue gas cooling below the moisture dew point and for waste heat recovery. 3 references.

Research principles and the construction of mnemonic diagrams

Science.gov (United States)

Venda, V. F.; Mitkin, A. A.

1973-01-01

Mnemonic diagrams are defined as a variety of information display devices, the essential element of which is conventional graphical presentation of technological or functional-operational links in a controlled system or object. Graphically displaying the operational structure of an object, the interd dependence between different parameters, and the interdependence between indicators and control organs, the mneomonic diagram reduces the load on the operator's memory and facilitates perception and reprocessing of information and decision making, while at the same time playing the role of visual support to the information activity of the operator. The types of mnemonic diagrams are listed.

Infrared thermography method for fast estimation of phase diagrams

Energy Technology Data Exchange (ETDEWEB)

Palomo Del Barrio, Elena [Université de Bordeaux, Institut de Mécanique et d’Ingénierie, Esplanade des Arts et Métiers, 33405 Talence (France); Cadoret, Régis [Centre National de la Recherche Scientifique, Institut de Mécanique et d’Ingénierie, Esplanade des Arts et Métiers, 33405 Talence (France); Daranlot, Julien [Solvay, Laboratoire du Futur, 178 Av du Dr Schweitzer, 33608 Pessac (France); Achchaq, Fouzia, E-mail: fouzia.achchaq@u-bordeaux.fr [Université de Bordeaux, Institut de Mécanique et d’Ingénierie, Esplanade des Arts et Métiers, 33405 Talence (France)

2016-02-10

Highlights: • Infrared thermography is proposed to determine phase diagrams in record time. • Phase boundaries are detected by means of emissivity changes during heating. • Transition lines are identified by using Singular Value Decomposition techniques. • Different binary systems have been used for validation purposes. - Abstract: Phase change materials (PCM) are widely used today in thermal energy storage applications. Pure PCMs are rarely used because of non adapted melting points. Instead of them, mixtures are preferred. The search of suitable mixtures, preferably eutectics, is often a tedious and time consuming task which requires the determination of phase diagrams. In order to accelerate this screening step, a new method for estimating phase diagrams in record time (1–3 h) has been established and validated. A sample composed by small droplets of mixtures with different compositions (as many as necessary to have a good coverage of the phase diagram) deposited on a flat substrate is first prepared and cooled down to ambient temperature so that all droplets crystallize. The plate is then heated at constant heating rate up to a sufficiently high temperature for melting all the small crystals. The heating process is imaged by using an infrared camera. An appropriate method based on singular values decomposition technique has been developed to analyze the recorded images and to determine the transition lines of the phase diagram. The method has been applied to determine several simple eutectic phase diagrams and the reached results have been validated by comparison with the phase diagrams obtained by Differential Scanning Calorimeter measurements and by thermodynamic modelling.

Theory of itinarant ferromagnetism in superconducting semimetals. Theorie du ferromagnetisme itinerant dans des semimetaux supraconducteurs

Energy Technology Data Exchange (ETDEWEB)

Do Tran, C; Nguyen Van, C [Groupe de Physique Theorique, Inst. National Polytechnique de Hanoi (Viet Nam); Nguyen Manh, D [Groupe de Physique Theorique, Inst. National Polytechnique de Hanoi (Viet Nam) Centre National de la Recherche Scientifique, Lab. d' Etudes des Proprietes Electroniques des Solides, 38 - Grenoble (France)

1991-11-01

A theory of itinerant ferromagnetism in superconducting semimetals is proposed. A nonzero mean magnetisation appears in the superconducting state due to the interaction (interference) of spin density wave (SDW), charge density wave (CDW) and Cooper pair wave. Phase diagram and physical properties of the states considered are investigated analytically and numerically. (orig.).

Analytical methods applied to the study of lattice gauge and spin theories

International Nuclear Information System (INIS)

Moreo, Adriana.

1985-01-01

A study of interactions between quarks and gluons is presented. Certain difficulties of the quantum chromodynamics to explain the behaviour of quarks has given origin to the technique of lattice gauge theories. First the phase diagrams of the discrete space-time theories are studied. The analysis of the phase diagrams is made by numerical and analytical methods. The following items were investigated and studied: a) A variational technique was proposed to obtain very accurated values for the ground and first excited state energy of the analyzed theory; b) A mean-field-like approximation for lattice spin models in the link formulation which is a generalization of the mean-plaquette technique was developed; c) A new method to study lattice gauge theories at finite temperature was proposed. For the first time, a non-abelian model was studied with analytical methods; d) An abelian lattice gauge theory with fermionic matter at the strong coupling limit was analyzed. Interesting results applicable to non-abelian gauge theories were obtained. (M.E.L.) [es

Improvements in Logic Diagram of Computerized Procedure System of APR1400

Energy Technology Data Exchange (ETDEWEB)

Kang, Sungkweon; Seong, Nokyu [KHNP CRI, Daejeon (Korea, Republic of)

2016-10-15

The Computerized Procedure System (CPS) has been improved since it is installed in Shin-Kori 3 and 4 Nuclear Power Plants. It is one of operating support systems of digital Main Control Room (MCR) and provides many functions to operators in executing the procedure. CPS can effectively remove the human errors by supporting the procedure flow and logic diagram. This paper describes the logic diagram of CPS of reference power plant and shows the improved logic diagram of CPS of Shin-Kori unit 5 and 6. This paper describes the current logic diagram of CPS and suggests improved design for logic diagram. The improved logic diagram shall be validated through human factors engineering verification and validation. The improved design will help operators execute the computerized procedure fast and remove the human error.

Perturbative quantum field theory in the framework of the fermionic projector

International Nuclear Information System (INIS)

Finster, Felix

2014-01-01

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur

Perturbative Quantum Field Theory in the Framework of the Fermionic Projector

OpenAIRE

Finster, Felix

2013-01-01

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

Perturbative quantum field theory in the framework of the fermionic projector

Energy Technology Data Exchange (ETDEWEB)

Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)

2014-04-15

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

Perturbative quantum field theory in the framework of the fermionic projector

Science.gov (United States)

Finster, Felix

2014-04-01

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

State diagram of Pr-Bi system

International Nuclear Information System (INIS)

Abulkhaev, V.L.; Ganiev, I.N.

1994-01-01

By means of thermal differential analysis, X-ray and microstructural analysis the state diagram of Pr-Bi system was studied. Following intermetallic compounds were defined in the system: Pr 2 Bi, Pr 5 Bi 3 , Pr 4 Bi 3 , Pr Bi, PrBi 2 , Pr 2 Bi, Pr 5 Bi 3 , Pr 4 Bi 3 and PrBi 2 . The data analysis on Ln-Bi diagram allowed to determine the regularity of change of properties of intermetallic compounds in the line of rare earth elements of cerium subgroup.

Fusion Diagrams in the - and - Systems

Science.gov (United States)

Asadov, M. M.; Akhmedova, N. A.

2014-10-01

A calculation model of the Gibbs energy of ternary oxide compounds from the binary components was used. Thermodynamic properties of -- ternary systems in the condensed state were calculated. Thermodynamic data of binary and ternary compounds were used to determine the stable sections. The probability of reactions between the corresponding components in the -- system was estimated. Fusibility diagrams of systems - and - were studied by physical-chemical analysis. The isothermal section of the phase diagram of -- at 298 K is built, as well as the projection of the liquid surface of --.

Wilsonian effective action of superstring theory

Energy Technology Data Exchange (ETDEWEB)

Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India); Homi Bhabha National Institute,Training School Complex, Anushakti Nagar, Mumbai 400085 (India)

2017-01-25

By integrating out the heavy fields in type II or heterotic string field theory one can construct the effective action for the light fields. This effective theory inherits all the algebraic structures of the parent theory and the effective action automatically satisfies the Batalin-Vilkovisky quantum master equation. This theory is manifestly ultraviolet finite, has only light fields as its explicit degrees of freedom, and the Feynman diagrams of this theory reproduce the exact scattering amplitudes of light states in string theory to any arbitrary order in perturbation theory. Furthermore in this theory the degrees of freedom of light fields above certain energy scale are also implicitly integrated out. This energy scale is determined by a particular parameter labelling a family of equivalent actions, and can be made arbitrarily low, leading to the interpretation of the effective action as the Wilsonian effective action.

An Application of Mosaic Diagrams to the Visualization of Set Relationships

OpenAIRE

Luz, Saturnino; Masoodian, Masood

2017-01-01

We present an application of mosaic diagrams to the visualisation of set relations. Venn and Euler diagrams are the best known visual representations of sets and their relationships (intersections, containment or subsets, exclusion or disjointness). In recent years, alternative forms of visualisation have been proposed. Among them, linear diagrams have been shown to compare favourably to Venn and Euler diagrams, in supporting non-interactive assessment of set relationships. Recent studies tha...

On renormalisation of lambda phi4 field theory in curved space-time

International Nuclear Information System (INIS)

Bunch, T.S.; Panangaden, P.

1980-01-01

An explicit renormalisation of all second-order physical processes occurring in lambdaphi 4 field theory in conformally flat space-time, including vacuum-to-vacuum processes, is performed. Although divergences dependent on the definition of the vacuum state appear in some Feynman diagrams, physical amplitudes obtained by summing all diagrams which contribute to a single physical process are independent of these divergences. Consequently, the theory remains renormalisable in curved space-time, at least to second order in lambda. Renormalisations of the mass m, the coupling constant lambda and the constant xi which couples the field to the Ricci scalar are required to make two- and four-particle creation amplitudes finite. (author)

Perturbation theories for the dipolar fluids

International Nuclear Information System (INIS)

Lee, L.L.; Chung, T.H.

1983-01-01

We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ 2 /(epsilonsigma 3 )] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out

A new double-scaling limit of N = 4 super-Yang-Mills theory and pp-wave strings

DEFF Research Database (Denmark)

Kristjansen, C.; Plefka, J.; Semenoff, G. W.

2002-01-01

. In this paper we shall show that, contrary to widespread expectation, non-planar diagrams survive this limiting procedure in the gauge theory. Using matrix model techniques as well as combinatorial reasoning it is demonstrated that a subset of diagrams of arbitrary genus survives and that a non-trivial double......The metric of a spacetime with a parallel plane (pp)-wave can be obtained in a certain limit of the space AdS5 × S5. According to the AdS/CFT correspondence, the holographic dual of superstring theory on that background should be the analogous limit of N = 4 supersymmetric Yang-Mills theory...

Plotting and Analyzing Data Trends in Ternary Diagrams Made Easy

Science.gov (United States)

John, Cédric M.

2004-04-01

Ternary plots are used in many fields of science to characterize a system based on three components. Triangular plotting is thus useful to a broad audience in the Earth sciences and beyond. Unfortunately, it is typically the most expensive commercial software packages that offer the option to plot data in ternary diagrams, and they lack features that are paramount to the geosciences, such as the ability to plot data directly into a standardized diagram and the possibility to analyze temporal and stratigraphic trends within this diagram. To address these issues, δPlot was developed with a strong emphasis on ease of use, community orientation, and availability free of charges. This ``freeware'' supports a fully graphical user interface where data can be imported as text files, or by copying and pasting. A plot is automatically generated, and any standard diagram can be selected for plotting in the background using a simple pull-down menu. Standard diagrams are stored in an external database of PDF files that currently holds some 30 diagrams that deal with different fields of the Earth sciences. Using any drawing software supporting PDF, one can easily produce new standard diagrams to be used with δPlot by simply adding them to the library folder. An independent column of values, commonly stratigraphic depths or ages, can be used to sort the data sets.

Adding Value to Force Diagrams: Representing Relative Force Magnitudes

Science.gov (United States)

Wendel, Paul

2011-05-01

Nearly all physics instructors recognize the instructional value of force diagrams, and this journal has published several collections of exercises to improve student skill in this area.1-4 Yet some instructors worry that too few students perceive the conceptual and problem-solving utility of force diagrams,4-6 and over recent years a rich variety of approaches has been proposed to add value to force diagrams. Suggestions include strategies for identifying candidate forces,6,7 emphasizing the distinction between "contact" and "noncontact" forces,5,8 and the use of computer-based tutorials.9,10 Instructors have suggested a variety of conventions for constructing force diagrams, including approaches to arrow placement and orientation2,11-13 and proposed notations for locating forces or marking action-reaction force pairs.8,11,14,15

Phase diagram of an extended Agassi model

Science.gov (United States)

García-Ramos, J. E.; Dukelsky, J.; Pérez-Fernández, P.; Arias, J. M.

2018-05-01

Background: The Agassi model [D. Agassi, Nucl. Phys. A 116, 49 (1968), 10.1016/0375-9474(68)90482-X] is an extension of the Lipkin-Meshkov-Glick (LMG) model [H. J. Lipkin, N. Meshkov, and A. J. Glick, Nucl. Phys. 62, 188 (1965), 10.1016/0029-5582(65)90862-X] that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960s by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss [J. Phys. G: Nucl. Phys. 12, 805 (1986), 10.1088/0305-4616/12/9/006] generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.

Single-particle potential from resummed ladder diagrams

International Nuclear Information System (INIS)

Kaiser, N.

2013-01-01

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential U(p, k f ) + i W(p, k f ) p > k f . The on-shell single-particle potential is constructed by means of a complex-valued in-medium loop that includes corrections from a test particle of momentum vector p added to the filled Fermi sea. The single-particle potential U(k f , k f ) at the Fermi surface as obtained from the resummation of the combined particle and hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem. The perturbative contributions at various orders a n in the scattering length are deduced and checked against the known analytical results at order a 1 and a 2 . The limit a → ∞ is studied as a special case and a strong momentum dependence of the real (and imaginary) single-particle potential is found. This feature indicates an instability against a phase transition to a state with an empty shell inside the Fermi sphere such that the density gets reduced by about 5%. The imaginary single-particle potential vanishes linearly at the Fermi surface. For comparison, the same analysis is performed for the resummed particle-particle ladder diagrams alone. In this truncation an instability for hole excitations near the Fermi surface is found at strong coupling. For the set of particle-hole ring diagrams the single-particle potential is calculated as well. Furthermore, the resummation of in-medium ladder diagrams to all orders is studied for a two-dimensional Fermi gas with a short-range two-body contact interaction. (orig.)

Refined phase diagram of boron nitride

International Nuclear Information System (INIS)

Solozhenko, V.; Turkevich, V.Z.

1999-01-01

The equilibrium phase diagram of boron nitride thermodynamically calculated by Solozhenko in 1988 has been now refined on the basis of new experimental data on BN melting and extrapolation of heat capacities of BN polymorphs into high-temperature region using the adapted pseudo-Debye model. As compared with the above diagram, the hBN left-reversible cBN equilibrium line is displaced by 60 K toward higher temperatures. The hBN-cBN-L triple point has been calculated to be at 3480 ± 10 K and 5.9 ± 0.1 GPa, while the hBN-L-V triple point is at T = 3400 ± 20 K and p = 400 ± 20 Pa, which indicates that the region of thermodynamic stability of vapor in the BN phase diagram is extremely small. It has been found that the slope of the cBN melting curve is positive whereas the slope of hBN melting curve varies from positive between ambient pressure and 3.4 GPa to negative at higher pressures

Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer

International Nuclear Information System (INIS)

Tarasov, O.V.

1978-01-01

An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer

The Mollier diagram in theory and practice. Part 3. Examples on Calculation of Dew Point Cooling; Het Mollierdiagram in theorie en praktijk. Deel 3. Rekenvoorbeelden Dauwpuntkoeling

Energy Technology Data Exchange (ETDEWEB)

Kouwenhoven, H.J.L. [Frigidarium, Driebergen-Rijsenburg (Netherlands); Huizinga, H.T. [Heat Transfer Holland HTH, Zuidwolde (Netherlands); Bootsveld, N.R. [YNO, Delft (Netherlands); Janssen, M. [Re-gent, Helmond (Netherlands); Uges, P.G.H. [StatiqCooling, Deventer (Netherlands)

2007-04-15

The use of direct and indirect adiabatic cooling, and recently in particular indirect diabatic cooling (dew point cooling) require knowledge of the Mollier diagram. [Dutch] Het gebruik van direct en indirect werkende adiabatische koeling en recentlijk vooral de indirect werkende systemen zoals diabatische koeling (dauwpuntkoeling, al of niet uitgevoerd als statische koeling) vragen om kennis van het Mollierdiagram.

A criterion for flatness in minimal area metrics that define string diagrams

International Nuclear Information System (INIS)

Ranganathan, K.; Massachusetts Inst. of Tech., Cambridge, MA

1992-01-01

It has been proposed that the string diagrams of closed string field theory be defined by a minimal area problem that requires that all nontrivial homotopy curves have length greater than or equal to 2π. Consistency requires that the minimal area metric be flat in a neighbourhood of the punctures. The theorem proven in this paper, yields a criterion which if satisfied, will ensure this requirement. The theorem states roughly that the metric is flat in an open set, U if there is a unique closed curve of length 2π through every point in U and all of these closed curves are in the same free homotopy class. (orig.)

Screening of Coulomb interaction and many-body perturbation theory in atoms

International Nuclear Information System (INIS)

Dzyuba, V.A.; Flambaum, V.V.; Sil'vestrov, P.G.; Sushkov, O.P.

1988-01-01

Taking into account the electron Coulomb interaction screening considerably improves the convergence of perturbation theory in residual interaction. The developed technique allows to take into account screening diagrams in all orders of perturbation theory. Calculation of the correlation corrections to the thallium energy levels is carried out as an example

Theory of amorphous ices.

Science.gov (United States)

Limmer, David T; Chandler, David

2014-07-01

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. Whereas the amorphous solids are long-lived and slowly aging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower-density glass before accessing a nonequilibrium liquid from which ice coarsens.

Homotopy Diagrams of Algebras

Czech Academy of Sciences Publication Activity Database

Markl, Martin

2002-01-01

Roč. 69, - (2002), s. 161-180 ISSN 0009-725X. [Winter School "Geometry and Physics" /21./. Srní, 13.01.2001-20.01.2001] R&D Projects: GA ČR GA201/99/0675 Keywords : colored operad%cofibrant model%homotopy diagram Subject RIV: BA - General Mathematics

Random Young diagrams in a Rectangular Box

DEFF Research Database (Denmark)

Beltoft, Dan; Boutillier, Cédric; Enriquez, Nathanaël

We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape.......We exhibit the limit shape of random Young diagrams having a distribution proportional to the exponential of their area, and confined in a rectangular box. The Ornstein-Uhlenbeck bridge arises from the fluctuations around the limit shape....

Formal Analysis Of Use Case Diagrams

Directory of Open Access Journals (Sweden)

Radosław Klimek

2010-01-01

Full Text Available Use case diagrams play an important role in modeling with UML. Careful modeling is crucialin obtaining a correct and efficient system architecture. The paper refers to the formalanalysis of the use case diagrams. A formal model of use cases is proposed and its constructionfor typical relationships between use cases is described. Two methods of formal analysis andverification are presented. The first one based on a states’ exploration represents a modelchecking approach. The second one refers to the symbolic reasoning using formal methodsof temporal logic. Simple but representative example of the use case scenario verification isdiscussed.

Phase Stability Diagrams for High Temperature Corrosion Processes

Directory of Open Access Journals (Sweden)

J. J. Ramos-Hernandez

2013-01-01

Full Text Available Corrosion phenomena of metals by fused salts depend on chemical composition of the melt and environmental conditions of the system. Detail knowledge of chemistry and thermodynamic of aggressive species formed during the corrosion process is essential for a better understanding of materials degradation exposed to high temperature. When there is a lack of kinetic data for the corrosion processes, an alternative to understand the thermodynamic behavior of chemical species is to utilize phase stability diagrams. Nowadays, there are several specialized software programs to calculate phase stability diagrams. These programs are based on thermodynamics of chemical reactions. Using a thermodynamic data base allows the calculation of different types of phase diagrams. However, sometimes it is difficult to have access to such data bases. In this work, an alternative way to calculate phase stability diagrams is presented. The work is exemplified in the Na-V-S-O and Al-Na-V-S-O systems. This system was chosen because vanadium salts is one of the more aggressive system for all engineering alloys, especially in those processes where fossil fuels are used.

Resonant count diagram and solar g mode oscillations

International Nuclear Information System (INIS)

Guenther, D.B.; Demarque, P.

1984-01-01

Evidence is provided to support the hypothesis that, because of the particular frequency separations of the solar g modes, resonant three-wave interactions stimulate only a selected few g modes. A resonant count diagram was obtained by plotting the total number of possible resonant three-wave interactions or a given beat frequency against the inverse of the beat frequency (the beat period), within a given frequency tolerance. The 1 = 1, 2, 3, 4 g modes calculated by Christensen-Dalsgaard, Gough and Morgan (1979) for a standard model of the Sun were used. The diagram has a significant peak at 160 minutes as well as other peaks at longer periods. The g modes that Delache and Scherrer (1983) tentatively identified from the Crimea-Stanford data were also plotted. These modes were found to correspond with the other peaks in the diagram. This coincidence between the observed g modes and the peaks in the resonant count diagram suggest that the observed g modes do owe their observability to resonant three-wave interactions

Einsteins dream

International Nuclear Information System (INIS)

Parker, B.

1986-01-01

This book discusses the following topics: the search for meaning; Einstein's dream; curved space; Einstein and warped space-time and extreme wraping; early unified field theories; star death; beyond the white dwarf; the early universe; the hadron, Lepton, and Radiation eras; the redshift controversy; other universes; the final fate of the universe; the missing mass; bounce; fate of the open universe; the world of particles and fields; Dirac's equation; Yukawa; gauge theory; quantum chromodynamics; supergravity and superstrings; twistors and heaven; and the new Einstein

Revised Pourbaix diagrams for Copper at 5-150 C

International Nuclear Information System (INIS)

Beverskog, B.; Puigdomenech, I.

1995-10-01

Pourbaix diagrams have been revised. Predominance diagrams for dissolved copper species have also been calculated. Five different total concentrations for dissolved copper have been used in the calculations (from 10 -3 to 10 -9 ). The complete hydrolysis series of copper(I) and (II) have not been included in earlier published Pourbaix diagrams, and these species are covered for the first time in this work. At acidic pH, increasing temperature decreases the immunity area, and therefore, it increases the corrosion of the copper. At alkaline pH-values corrosion also increases with the temperature due to the decrease of both passivity and immunity areas. The calculated diagrams are used as a base for the discussion of the corrosion behaviour of the copper canisters in the Swedish radioactive waste management program. 62 refs, 37 figs, 3 tabs

Solid gas reaction phase diagram under high gas pressure

International Nuclear Information System (INIS)

Ishizaki, K.

1992-01-01

This paper reports that to evaluate which are the stable phases under high gas pressure conditions, a solid-gas reaction phase diagram under high gas pressure (HIP phase diagram) has been proposed by the author. The variables of the diagram are temperature, reactant gas partial pressure and total gas pressure. Up to the present time the diagrams have been constructed using isobaric conditions. In this work, the stable phases for a real HIP process were evaluated assuming an isochoric condition. To understand the effect of the total gas pressure on stability is of primary importance. Two possibilities were considered and evaluated, those are: the total gas pressure acts as an independent variable, or it only affects the fugacity values. The results of this work indicate that the total gas pressure acts as an independent variable, and in turn also affects the fugacity values

Equational binary decision diagrams

NARCIS (Netherlands)

J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)

2000-01-01

textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and

On the Impact of Diagram Layout: How Are Models Actually Read?

DEFF Research Database (Denmark)

Störrle, Harald; Baltsen, Nick; Christoffersen, Henrik

2014-01-01

This poster presents the latest results from a very large eye tracking study (n=29) that explores how modelers read UML diagrams. We find that various factors like layout quality, modeler experience, and diagram type lead to significant differences in diagram reading strategies. We derive elements...

A Critical Appraisal of the `Day' Diagram

Science.gov (United States)

Roberts, A. P.; Tauxe, L.; Heslop, D.

2017-12-01

The `Day' diagram [Day et al., 1977; doi:10.1016/0031-9201(77)90108-X] is used widely to infer the mean domain state of magnetic mineral assemblages. The Day plot coordinates are the ratios of the saturation remanent magnetization to saturation magnetization (Mrs/Ms) and the coercivity of remanence to coercivity (Bcr/Bc), as determined from a major hysteresis loop and a backfield demagnetization curve. Based on theoretical and empirical arguments, Day plots are typically demarcated into stable single domain (SD), `pseudosingle domain' (`PSD'), and multidomain (MD) zones. It is a simple task to determine Mrs/Ms and Bcr/Bc for a sample and to assign a mean domain state based on the boundaries defined by Day et al. [1977]. Many other parameters contribute to variability in a Day diagram, including surface oxidation, mineral stoichiometry, stress state, magnetostatic interactions, and mixtures of magnetic particles with different sizes and shapes. Bulk magnetic measurements usually lack detailed independent evidence to constrain each free parameter, which makes the Day diagram fundamentally ambiguous. This raises questions about its usefulness for diagnosing magnetic particle size variations. The Day diagram is also used to make inferences about binary mixing of magnetic particles, where, for example, mixtures of SD and MD particles give rise to a bulk `PSD' response even though the concentration of `PSD' grains could be zero. In our assessment of thousands of hysteresis measurements of geological samples, binary mixing occurs in a tiny number of cases. Ternary, quaternary, and higher order mixing are usually observed. Also, uniaxial SD and MD end-members are nearly always inappropriate for considering mixing because uniaxial SD particles are virtually non-existent in igneous rocks. Thus, use of mixing lines in Day diagrams routinely provides unsatisfactory representations of particle size variations. We critically appraise the Day diagram and argue that its many