From twistor string theory to recursion relations
Spradlin, Marcus; Volovich, Anastasia
2009-10-01
Witten’s twistor string theory gives rise to an enigmatic formula known as the “connected prescription” for tree-level Yang-Mills scattering amplitudes. We derive a link representation for the connected prescription by Fourier transforming it to mixed coordinates in terms of both twistor and dual twistor variables. We show that it can be related to other representations of amplitudes by applying the global residue theorem to deform the contour of integration. For six and seven particles we demonstrate explicitly that certain contour deformations rewrite the connected prescription as the Britto-Cachazo-Feng-Witten representation, thereby establishing a concrete link between Witten’s twistor string theory and the dual formulation for the S matrix of the N=4 SYM recently proposed by Arkani-Hamed Other choices of integration contour also give rise to “intermediate prescriptions.” We expect a similar though more intricate structure for more general amplitudes.
Spacetime foam in twistor string theory
Hartnoll, S A; Hartnoll, Sean A.; Policastro, Giuseppe
2004-01-01
We show how a Kahler spacetime foam in four dimensional conformal (super)gravity may be mapped to twistor spaces carrying the D1 brane charge of the B model topological string theory. The spacetime foam is obtained by blowing up an arbitrary number of points in $\\C^2$ and can be interpreted as a sum over gravitational instantons. Some twistor spaces for blowups of $\\C^2$ are known explicitly. In these cases we write down a meromorphic volume form and suggest a relation to a holomorphic superform on a corresponding super Calabi-Yau manifold.
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
On perturbative field theory and twistor string theory
Bedford, James
2007-01-01
It is well-known that perturbative calculations in field theory can lead to far simpler answers than the Feynman diagram approach might suggest. In some cases scattering amplitudes can be constructed for processes with any desired number of external legs yielding compact expressions which are inaccessible from the point of view of conventional perturbation theory. In this thesis we discuss some attempts to address the nature of this underlying simplicity and then use the results to calculate some previously unknown amplitudes of interest. Witten's twistor string theory is introduced and the CSW rules at tree-level and one-loop are described. We use these techniques to calculate the one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of their validity and then proceed to evaluate the general MHV amplitudes in pure Yang-Mills with a scalar running in the loop. This latter amplitude is a new result in QCD. In addition to this, we review some recent on-shell recursion relations for tree-leve...
Studies In Field Theories: Mhv Vertices, Twistor Space, Recursion Relations And Chiral Rings
Svrcek, P
2005-01-01
In this thesis we study different aspects of four dimensional field theories. In the first chapter we give introduction and overview of the thesis. In the second chapter we review the connection between perturbative Yang-Mills and twistor string theory. Inspired by this, we propose a new way of constructing Yang-Mills scattering amplitudes from Feynman graphs in which the vertices are off-shell continuations of the tree level MHV amplitudes. The MHV diagrams lead to simple formulas for tree-level amplitudes. We then give a heuristic derivation of the diagrams from twistor string theory. In the third chapter, we explore the twistor structure of scattering amplitudes in theories for which a twistor string theory analogous to the one for N = 4 gauge theory has not yet been proposed. We study the differential equations of one-loop amplitudes of gluons in gauge theories with reduced supersymmetry and of tree level and one-loop amplitudes of gravitons in general relativity and supergravity. We find that the scat...
Conformal Higher Spin Theory and Twistor Space Actions
Haehnel, Philipp
2016-01-01
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincare invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we introduce anti-self-dual interaction terms to define a twistor action for the full conformal higher spin theory.
Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
Bena, I; Kosower, D A
2004-01-01
Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.
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.
Confluence of general Schlesinger systems and Twistor theory
Kimura, Hironobu; Tseveennamjil, Damiran
2016-01-01
We give a description of confluence for the general Schlesinger systems (GSS) from the view point of twistor theory. GSS is a system of nonlinear di¤erential equations on the Grassmannian manifold $G_{2,N}(\\mathbf{C}$ which is obtained, for any partition $\\lambda$ of $N$, as the integrability condition of a connection $\
AdS twistors for higher spin theory
Cederwall, M
2004-01-01
We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7 from twistors describing massless (super-)particles on AdS spaces. A massless twistor transform is derived in a geometric way from classical kinematics. Relaxing the spin-shell constraints on twistor space gives an infinite tower of massless states of a ``higher spin particle'', generalising previous work of Bandos et al. This can generically be done in a number of ways, each defining the states of a distinct higher spin theory, and the method provides a systematic way of finding these. We reproduce known results in D=4, minimal supersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of Vasiliev's Sp-models as special cases. In the latter models a dimensional enhancement takes place, meaning that the theory lives on a space of higher dimension than the original AdS space, and becomes a theory of doubletons. This talk was presented at the XIXth Max Born Symposium ``Fundamental Interactions and Twistor-Like Methods''...
N=2 Conformal Supergravity from Twistor-String Theory
Ahn, C
2004-01-01
A chiral superfield strength in N=2 conformal supergravity at linearized level is obtained by acting two superspace derivatives on N=4 chiral superfield strength which can be described in terms of N=4 twistor superfields. By decomposing SU(4)_R representation of N=4 twistor superfields into the SU(2)_R representation with an invariant U(1)_R charge, the surviving N=2 twistor superfields contain the physical states of N=2 conformal supergravity. These N=2 twistor superfields are functions of homogeneous coordinates of weighted complex projective space WCP^{3|4} where the two weighted fermionic coordinates have weight -1 and 3.
Composite Operators in the Twistor Formulation of $\\mathcal{N}=4$ SYM Theory
Koster, Laura; Staudacher, Matthias; Wilhelm, Matthias
2016-01-01
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many interaction vertices and we argue that the same applies to composite operators. To test our definition of the local composite operators in twistor space, we compute several corresponding form factors, thereby also initiating the study of form factors using the position twistor-space framework. Throughout this letter, we use the composite operator built from two identical complex scalars as a pedagogical example; we treat the general case in a follow-up paper.
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.
Bena, I; Kosower, D A; Roiban, R; Bena, Iosif; Bern, Zvi; Kosower, David A.; Roiban, Radu
2004-01-01
We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the `holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.
Gauged twistor spinors and symmetry operators
Ertem, Ümit
2016-01-01
We consider gauged twistor spinors which are supersymmetry generators of supersymmetric and superconformal field theories in curved backgrounds. We show that the spinor bilinears of gauged twistor spinors satify the gauged conformal Killing-Yano equation. We prove that the symmetry operators of the gauged twistor spinor equation can be constructed from ordinary conformal Killing-Yano forms in constant curvature backgrounds. This provides a way to obtain gauged twistor spinors from ordinary twistor spinors.
BPS Preons in Supergravity and Higher Spin Theories. An Overview From the Hill of Twistor Approach
Bandos, I. A.
2005-04-01
We review briefly the notion of BPS preons, first introduced in 11-dimensional context as hypothetical constituents of M-theory, in its generalization to arbitrary dimensions and emphasizing the relation with twistor approach. In particular, the use of a "twistor-like" definition of BPS preon (almost) allows us to remove supersymmetry arguments from the discussion of the relation of the preons with higher spin theories and also of the treatment of BPS preons as constituents. We turn to the supersymmetry in the second part of this contribution, where we complete the algebraic discussion with supersymmetric arguments based on the M-algebra (generalized Poincaré superalgebra), discuss the possible generalization of BPS preons related to the osp(1|n) (generalized AdS) superalgebra, review a twistor-like κ-symmetric superparticle in tensorial superspace, which provides a point-like dynamical model for BPS preon, and the rôle of BPS preons in the analysis of supergravity solutions. Finally we describe resent results on the concise superfield description of the higher spin field equations and on superfield supergravity in tensorial superspaces.
BPS preons in supergravity and higher spin theories. An overview from the hill of twistor appraoch
Bandos, I A
2005-01-01
We review briefly the notion of BPS preons, first introduced in 11-dimensional context as hypothetical constituents of M-theory, in its generalization to arbitrary dimensions and emphasizing the relation with twistor approach. In particular, the use of a 'twistor-like' definition of BPS preon (almost) allows us to remove supersymmetry arguments from the discussion of the relation of the preons with higher spin theories and also of the treatment of BPS preons as constituents. We turn to the supersymmetry in the second part of this contribution, where we complete the algebraic discussion with supersymmetric arguments based on the M-algebra (generalized Poincare superalgebra), discuss the possible generalization of BPS preons related to the osp(1|n) (generalized AdS) superalgebra, review a twistor-like kappa-symmetric superparticle in tensorial superspace, which provides a point-like dynamical model for BPS preon, and the role of BPS preons in the analysis of supergravity solutions. Finally we describe resent re...
A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
Bedford, J; Spence, B; Travaglini, G; Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
General split helicity gluon tree amplitudes in open twistor string theory
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].
Scattering amplitudes and BCFW recursion in twistor space
Mason, Lionel; Skinner, David
2010-01-01
Twistor ideas have led to a number of recent advances in our understanding of scattering amplitudes. Much of this work has been indirect, determining the twistor space support of scattering amplitudes by examining the amplitudes in momentum space. In this paper, we construct the actual twistor scattering amplitudes themselves. We show that the recursion relations of Britto, Cachazo, Feng and Witten have a natural twistor formulation that, together with the three-point seed amplitudes, allows us to recursively construct general tree amplitudes in twistor space. We obtain explicit formulae for n-particle MHV and NMHV super-amplitudes, their CPT conjugates (whose representations are distinct in our chiral framework), and the eight particle N2MHV super-amplitude. We also give simple closed form formulae for the mathcal{N} = 8 supergravity recursion and the MHV and overline {text{MHV}} amplitudes. This gives a formulation of scattering amplitudes in maximally supersymmetric theories in which superconformal symmetry and its breaking is manifest. For N k MHV, the amplitudes are given by 2 n - 4 integrals in the form of Hilbert transforms of a product of n - k - 2 purely geometric, superconformally invariant twistor delta functions, dressed by certain sign operators. These sign operators subtly violate conformal invariance, even for tree-level amplitudes in mathcal{N} = 4 super Yang-Mills, and we trace their origin to a topological property of split signature space-time. We develop the twistor transform to relate our work to the ambidextrous twistor diagram approach of Hodges and of Arkani-Hamed, Cachazo, Cheung and Kaplan.
On Form Factors and Correlation Functions in Twistor Space
Koster, Laura; Staudacher, Matthias; Wilhelm, Matthias
2016-01-01
In this paper, we continue our study of form factors and correlation functions of gauge-invariant local composite operators in the twistor-space formulation of N=4 super Yang-Mills theory. Using the vertices for these operators obtained in our recent papers arXiv:1603.04471 and arXiv:1604.00012, we show how to calculate the twistor-space diagrams for general N^kMHV form factors via the inverse soft limit, in analogy to the amplitude case. For general operators without $\\dot\\alpha$ indices, we then reexpress the NMHV form factors from the position-twistor calculation in terms of momentum twistors, deriving and expanding on a relation between the two twistor formalisms previously observed in the case of amplitudes. Furthermore, we discuss the calculation of generalized form factors and correlation functions as well as the extension to loop level, in particular providing an argument promised in arXiv:1410.6310.
Demystifying the twistor construction of composite operators in N=4 super-Yang-Mills theory
Chicherin, Dmitry
2016-01-01
We explain some details of the construction of composite operators in N=4 SYM that we have elaborated earlier in the context of Lorentz harmonic chiral (LHC) superspace. We give a step-by-step elementary derivation and show that the result coincides with the recent hypothesis put forward in arXiv:1603.04471 within the twistor approach. We provide the appropriate LHC-to-twistors dictionary.
Twistors and antipodes in de Sitter space
Neiman, Yasha
2014-03-01
We develop the basics of twistor theory in de Sitter space, up to the Penrose transform for free massless fields. We treat de Sitter space as fundamental, as one does for Minkowski space in conventional introductions to twistor theory. This involves viewing twistors as spinors of the de Sitter group SO(4,1). When attached to a spacetime point, such a twistor can be reinterpreted as a local SO(3,1) Dirac spinor. Our approach highlights the antipodal map in de Sitter space, which gives rise to doublings in the standard relations between twistors and spacetime. In particular, one can generate a field with both handedness signs from a single twistor function. Such fields naturally live on antipodally identified de Sitter space dS4/Z2, which has been put forward as the ideal laboratory for quantum gravity with a positive cosmological constant.
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.
Adamo, Tim; Williams, Jack
2016-01-01
We consider the application of twistor theory to five-dimensional anti-de Sitter space. The twistor space of AdS$_5$ 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.
Scattering amplitudes and Wilson loops in twistor space
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Mason, Lionel [Mathematical Institute, 24-29 St. Giles' , Oxford OX1 3LB (United Kingdom); Bullimore, Mathew [Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Skinner, David, E-mail: adamo@maths.ox.ac.uk [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2 L 2Y5 (Canada)
2011-11-11
This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for N=4 super-Yang-Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang-Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svrcek and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'. (review)
Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
Herfray, Yannick
2016-01-01
This paper establishes the relation between traditional results from (euclidean) twistor theory and chiral formulations of General Relativity, especially the pure connection formulation. Starting from a $SU(2)$-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 we also review all known chiral Lagrangians for GR.
A Note on Dual MHV Diagrams in N=4 SYM
Brandhuber, Andreas; Travaglini, Gabriele; Yang, Gang
2010-01-01
Recently a reformulation of the MHV diagram method in N=4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric Wilson loop in momentum twistor space. In this note we present related explicit Feynman rules in dual momentum space, which should have the interpretation of Wilson loop diagrams in dual momentum space. We show that these novel rules are completely equivalent to ordinary spacetime MHV rules and can be naturally viewed as their graph dual representation.
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 repo...
Roiban, Radu; Volovich, Anastasia
2004-09-24
It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.
Causality and Borromean linking in twistor space
Energy Technology Data Exchange (ETDEWEB)
Low, Robert J, E-mail: mtx014@coventry.ac.uk [Department of Mathematics, Statistics and Engineering Science, Coventry University, Coventry CV1 5FB (United Kingdom)
2011-10-01
We consider the notion of the Borromean triple from classical linking theory, and develop an analogue of it in the case of linking of skies in twistor space. I would like to dedicate this paper to Roger Penrose, on the occasion of his 80th birthday.
Twistor Transform in d Dimensions and a Unifying Role for Twistors
Bars, Itzhak; Bars, Itzhak; Picon, Moises
2006-01-01
Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it was shown that the same d=4 twistor provides also a unified description of an assortment of other particle dynamical systems, including special examples of massless or massive particles, relativistic or non-relativistic, interacting or non-interacting, in flat space or curved spaces. In this paper, using 2T-physics as the primary theory, we derive the general twistor transform in d-dimensions that applies to all cases, and show that these more general twistor transforms provide d dimensional holographic images of an underlying phase space in flat spacetime in d+2 dimensions. Certain parameters, such as mass, parameters of spacetime metric, and some coupling constants appear as moduli in the holographic image while projecting from d+2 dimensions to (d-1)+1 dimensions or to twistors. We also extend the concept of t...
Studies In Non-anticommutative Gauge Theories, Geometric Dualities, And Twistor Strings
Robles Llana, D
2005-01-01
In this Dissertation we consider three different topics. The first one is the study of instantons in U(2) super Yang-Mills theories defined on non-anticommutative superspace. We extend the ordinary instanton calculus to this class of theories by solving the appropriate equations of motion iteratively in the deformation parameter C. In the case without matter, we solve the equations exactly. We find that the SU(2) part of the instanton is the same as in ordinary SU (2) N = 1 super Yang-Mills, but acquires in addition a non-trivial U(1) part which depends on the fermionic collective coordinates and the deformation parameter C. In the case with matter we solve the equations of motion to leading order in the coupling constant. We find that also the profile of the matter fields is deformed through linear and quadratic corrections in C. The instanton effective action for pure gluodynamics is unaffected by C, but gets a contribution of order C2 in addition to the usual 't Hooft term when the matter is included....
BOOK REVIEW: Solitons, Instantons, and Twistors Solitons, Instantons, and Twistors
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
Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
Attard, J.; François, J.
2017-04-01
Tractor and Twistor bundles provide natural conformally covariant calculi on 4D-Riemannian manifolds. They have different origins but are closely related, and usually constructed bottom–up through prolongation of defining differential equations. We propose alternative top–down gauge theoretic constructions, starting from the conformal Cartan bundle P and its vectorial E and spinorial {E associated bundles. Our key ingredient is the dressing field method of gauge symmetry reduction, which allows tractors and twistors and their associated connections to exhibit as gauge fields of a non-standard kind as far as Weyl rescaling transformation is concerned. By non-standard we mean that they implement the gauge principle of physics, but are of a different geometric nature than the well-known differential geometric objects usually underlying gauge theories. We provide the corresponding BRST treatment. In a companion paper we dealt with tractors, in the present one we address the case of twistors.
Neitzke, A.; Pioline, B.; Vandoren, S.
2007-01-01
Motivated by black hole physics in N = 2,D = 4 supergravity, we study the geometry of quaternionic-K¨ahler manifolds Mobtained by the c-map construction from projective special Kähler manifolds Ms. Improving on earlier treatments, we compute the Käahler potentials on the twistor space Z and Swann sp
A note on dual MHV diagrams in mathcal{N} = 4 SYM
Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele; Yang, Gang
2010-12-01
Recently a reformulation of the MHV diagram method in mathcal{N} = 4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric Wilson loop in momentum twistor space. In this note we present related explicit Feynman rules in dual momentum space, which should have the interpretation of Wilson loop diagrams in dual momentum space. We show that these novel rules are completely equivalent to ordinary spacetime MHV rules and can be naturally viewed as their graph dual representation.
The classification of diagrams in perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Phillips, D.R.; Afnan, I.R. [School of Physical Sciences, The Flinders University of South Australia, GPO Box 2100, Adelaide 5001 (Australia)
1995-06-01
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.
The Classification of Diagrams in Perturbation Theory
Phillips, D. R.; Afnan, I. R.
1995-06-01
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. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan, and Blankleider (TRAB). Secondly, 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. It 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.
Improving perturbation theory with cactus diagrams
Constantinou, M; Skouroupathis, A; Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos
2006-01-01
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermio...
Instantons, Twistors, and Emergent Gravity
Heckman, Jonathan J
2011-01-01
Motivated by potential applications to holography on space-times of positive curvature, and by the successful twistor description of scattering amplitudes, we propose a new dual matrix formulation of N = 4 gauge theory on S(4) coupled to 4D gravity. The matrix model is defined by taking the low energy limit of a holomorphic Chern-Simons theory on CP(3|4), in the presence of a large instanton flux. The theory comes with a choice of S(4) radius L and a parameter N controlling the overall size of the matrices. The flat space variant of the 4D effective theory arises by taking the large N scaling limit of the matrix model, with l_pl^2 ~ L^2 / N held fixed. Its massless spectrum contains both spin one and spin two excitations, which we identify with gluons and gravitons. As shown in the companion paper, the matrix model correlation functions of both these excitations correctly reproduce the corresponding MHV scattering amplitudes. We present evidence that the scaling limit defines a gravitational theory with a fin...
Neitzke, A; Vandoren, S; Neitzke, Andrew; Pioline, Boris; Vandoren, Stefan
2007-01-01
Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \\Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function ...
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
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.
Galaktionov, V. A.
2009-01-01
Various formal blow-up scenarious for the Navier--Stokes equaitons in 3D are discussed. A particular interest is payed to "twistor mechanisms" based on angular logarithmic blow-up travelling waves, and to a formation of "blow-up tornado" about the singular stationary Slezkin--Landau solutions (1934--44) of a submerged jet. A survey on various related aspects of singularity analysis for nonlinear parabolic PDEs is enclosed.
Drawing Euler Diagrams with Circles: The Theory of Piercings.
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.
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.
Quasi-Hopf twistors for elliptic quantum groups
Jimbo, M; Odake, S; Shiraishi, J
1997-01-01
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al., Felder). Fronsdal made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebra U_q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universal R matrix of U_q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Fronsdal's findings. This construction entails that, for generic values of the deformation parameters, representation theory for U_q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebra A_{q,p}(^sl_2).
All Tree-Level MHV Form Factors in $\\mathcal{N}=4$ SYM from Twistor Space
Koster, Laura; Staudacher, Matthias; Wilhelm, Matthias
2016-01-01
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 arXiv: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.
On-shell Diagrams, Gra{\\ss}mannians and Integrability for Form Factors
Frassek, Rouven; Nandan, Dhritiman; Wilhelm, Matthias
2015-01-01
We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-energy multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as an additional building block. Moreover, we obtain analytic representations in terms of Gra{\\ss}mannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that form factors are eigenstates of the integrable transfer matrix. As a consequence, we can construct them via the method of R operators, which also allows to introduce deformations that preserve the integrable structure.
Approximate twistors and positive mass
Bäckdahl, Thomas; Valiente Kroon, Juan A.
2011-04-01
In this paper, the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. This is not done in a coordinate sense, but through quantification of the deviation from a specific symmetry. In a recent paper (Bäckdahl and Valiente Kroon 2010 Phys. Rev. Lett. 104 231102), this problem was studied with the Kerr solution as a reference solution. This analysis was based on valence 2 Killing spinors. In order to better understand this construction, we analyse the analogous construction for valence 1 spinors solving the twistor equation. This yields an invariant that measures how much the initial data deviates from Minkowski data. Furthermore, we prove that this invariant vanishes if and only if the mass vanishes. Hence, we get a proof of the positivity of mass.
Approximate twistors and positive mass
Energy Technology Data Exchange (ETDEWEB)
Baeckdahl, Thomas; Valiente Kroon, Juan A, E-mail: t.backdahl@qmul.ac.uk, E-mail: j.a.valiente-kroon@qmul.ac.uk [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom)
2011-04-07
In this paper, the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. This is not done in a coordinate sense, but through quantification of the deviation from a specific symmetry. In a recent paper (Baeckdahl and Valiente Kroon 2010 Phys. Rev. Lett. 104 231102), this problem was studied with the Kerr solution as a reference solution. This analysis was based on valence 2 Killing spinors. In order to better understand this construction, we analyse the analogous construction for valence 1 spinors solving the twistor equation. This yields an invariant that measures how much the initial data deviates from Minkowski data. Furthermore, we prove that this invariant vanishes if and only if the mass vanishes. Hence, we get a proof of the positivity of mass.
Twistor variables for Anti-de Sitter (super)particles
Arvanitakis, Alex S; Townsend, Paul K
2016-01-01
Starting from the classical action for a spin-zero particle in a (D + 1)-dimensional anti-Sitter spacetime, we recover the Breitenlohner-Freedman bound by quantization. We then find a twistor form of the action for D = 3, 4, 6 for which the SO(2, D) isometry group is a linearly realized symmetry. The supertwistor generalization yields superparticle actions that are manifestly invariant under the isometry supergroup of the near-horizon geometries of the M2, D3 and M5 brane solutions of string/M-theory; in each case quantization yields a supermultiplet with 128 + 128 states.
The twistor geometry of three-qubit entanglement
Lévai, Peter
2004-01-01
A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.
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.
Scattering Equations, Twistor-string Formulas and Double-soft Limits in Four Dimensions
He, Song; Wu, Jun-Bao
2016-01-01
We study scattering equations and formulas for tree amplitudes of various theories in four dimensions, in terms of spinor helicity variables and on-shell superspace for supersymmetric theories. As originally obtained in Witten's twistor string theory and other twistor-string models, the equations can take either polynomial or rational forms, and we clarify the simple relation between them. We present new, four-dimensional formulas for all tree amplitudes in the non-linear sigma model, a special Galileon theory and the maximally supersymmetric completion of the Dirac-Born-Infeld theory. Furthermore, we apply the formulas to study various double-soft theorems in these theories, including the emissions of a pair of soft photons, fermions and scalars for super-amplitudes in super-DBI theory.
Noncommutative Space-time from Quantized Twistors
Lukierski, Jerzy
2013-01-01
We consider the relativistic phase space coordinates (x_{\\mu},p_{\\mu}) as composite, described by functions of the primary pair of twistor coordinates. It appears that if twistor coordinates are canonicaly quantized the composite space-time coordinates are becoming noncommutative. We obtain deformed Heisenberg algebra which in order to be closed should be enlarged by the Pauli-Lubanski four-vector components. We further comment on star-product quantization of derived algebraic structures which permit to introduce spin-extended deformed Heisenberg algebra.
Conformal higher spin scattering amplitudes from twistor space
Adamo, Tim; McLoughlin, Tristan
2016-01-01
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 anti-MHV 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.
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.
D3-instantons, Mock Theta Series and Twistors
Alexandrov, Sergei; Pioline, Boris
2013-01-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.
D3-instantons, mock theta series and twistors
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2013-04-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2, {Z} ). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2, {Z} ) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.
Block diagrams and the cancellation of divergences in energy-level perturbation theory
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
Twisted geometries, twistors and conformal transformations
Långvik, Miklos
2016-01-01
The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a time-like direction singled out. The isomorphism depends on the Immirzi parameter, and reduces to the identity when the parameter goes to infinity. Using this twistorial representation we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a 1-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one - that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view, and compare it with a discretisation of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuu...
Poisson equation for the Mercedes diagram in string theory at genus one
Basu, Anirban
2015-01-01
The Mercedes diagram has four trivalent vertices which are connected by six links such that they form the edges of a tetrahedron. This three loop Feynman diagram contributes to the D^{12} R^4 amplitude at genus one in type II string theory, where the vertices are the points of insertion of the graviton vertex operators, and the links are the scalar propagators on the toroidal worldsheet. We obtain a modular invariant Poisson equation satisfied by the Mercedes diagram, where the source terms involve one and two loop Feynman diagrams. We calculate its contribution to the D^{12} R^4 amplitude.
Poisson equation for the three loop ladder diagram in string theory at genus one
Basu, Anirban
2016-01-01
The three loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D^{12} R^4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one, two and three loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.
Poisson equation for the three-loop ladder diagram in string theory at genus one
Basu, Anirban
2016-11-01
The three-loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D12ℛ4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one-, two- and three-loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five-point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples.
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.)
Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory
Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito
2015-01-01
We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.
Drawing theories apart the dispersion of Feynman diagrams in postwar physics
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...
Particle diagrams and embedded many-body random matrix theory.
Small, R A; Müller, S
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤ m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m,3 k = m,...,nk = m.
Particle diagrams and embedded many-body random matrix theory
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
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...
Random 3-D young diagrams and representation theory
Gorin, V.
2011-01-01
The topic of the thesis is related to statistical mechanics and probability theory from one side, and to the representation theory of ``big'' groups on the other side. A typical example of a ``big'' group is the union of unitary groups naturally embedded one into another; it is called the infinite--
Multi-soft theorems in Gauge Theory from MHV Diagrams
Georgiou, George
2015-01-01
In this work we employ the MHV technique to show that scattering amplitudes with any number of consecutive soft particles behave universally in the multi-soft limit in which all particles go soft simultaneously. After identifying the diagrams which give the leading contribution we give the general rules for writing down compact expressions for the multi-soft factor of m gluons, k of which have negative helicity. We explicitly consider the cases where k equals 1 and 2. In N =4 SYM, the multi-soft factors of 2 scalars or 2 fermions forming a singlet, and m-2 positive helicity gluons are derived. The special case of the double-soft limit gives an amplitude whose leading divergence is 1/\\delta^2 and not 1/\\delta as in the case of 2 scalars or 2 fermions that do not form a singlet under SU(4). The construction based on the analytic supervertices allows us to obtain simple expressions for the triple-soft limit of 1 scalar and 2 positive helicity fermions, as well as for the quadrapole-soft limit of 4 positive helic...
Conformal Phase Diagram of Complete Asymptotically Free Theories
Pica, Claudio; Sannino, Francesco
2016-01-01
We investigate the ultraviolet and infrared fixed point structure of gauge-Yukawa theories featuring a single gauge coupling, Yukawa coupling and scalar self coupling. Our investigations are performed using the two loop gauge beta function, one loop Yukawa beta function and one loop scalar beta 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.
Two-loop Feynman Diagrams in Yang-Mills Theory from Bosonic String Amplitudes
Körs, B; Kors, Boris; Schmidt, Michael G.
2000-01-01
We present intermediate results of an ongoing investigation which attempts a generalization of the well known one-loop Bern Kosower rules of Yang-Mills theory to higher loop orders. We set up a general procedure to extract the field theoretical limit of bosonic open string diagrams, based on the sewing construction of higher loop world sheets. It is tested with one- and two-loop scalar field theory, as well as one-loop and two-loop vacuum Yang-Mills diagrams, reproducing earlier results. It is then applied to two-loop two-point Yang-Mills diagrams in order to extract universal renormalization coefficients that can be compared to field theory. While developing numerous technical tools to compute the relevant contributions, we hit upon important conceptual questions: Do string diagrams reproduce Yang-Mills Feynman diagrams in a certain preferred gauge? Do they employ a certain preferred renormalization scheme? Are four gluon vertices related to three gluon vertices? Unfortunately, our investigations remained in...
The calculation of Feynman diagrams in the superstring perturbation theory
Danilov, G S
1995-01-01
The method of the calculation of the multi-loop superstring amplitudes is proposed. The amplitudes are calculated from the equations that are none other than Ward identities. They are derived from the requirement that the discussed amplitudes are independent from a choice of gauge of both the vierbein and the gravitino field. The amplitudes are calculated in the terms of the superfields vacuum correlators on the complex (1|1) supermanifolds. The superconformal Schottky groups appropriate for this aim are built for all the spinor structures. The calculation of the multi- loop boson emission amplitudes in the closed, oriented Ramond-Neveu-Schwarz superstring theory is discussed in details. The main problem arises for those spinor structures that correspond to the Ramond fermion loops. Indeed, in this case the superfield vacuum correlators can not be derived by a simple extension of the boson string results. The method of the calculation of the above correlators is proposed. The discussed amplitudes due to all t...
Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer
Park, J.-M.; Deem, M. W.
2007-02-01
We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.
On-shell diagrams, Graßmannians and integrability for form factors
Energy Technology Data Exchange (ETDEWEB)
Frassek, Rouven [Department of Mathematical Sciences, Durham University,South Road, Durham DH1 3LE (United Kingdom); Meidinger, David; Nandan, Dhritiman; Wilhelm, Matthias [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Gebäude, Zum Großen Windkanal 6, 12489 Berlin (Germany)
2016-01-29
We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-tensor multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as further building block in addition to the three-point amplitudes. Moreover, we obtain analytic representations in terms of Graßmannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that the form factors are eigenstates of the integrable spin-chain transfer matrix built from the monodromy matrix that yields the Yangian generators. Constructing them via the method of R operators allows to introduce deformations that preserve the integrable structure. We finally show that the integrable properties extend to minimal tree-level form factors of generic composite operators as well as certain leading singularities of their n-point loop-level form factors.
Single twistor description of massless, massive, AdS, and other interacting particles
Bars, Itzhak; 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 non-relativistic, interacting or non-interacting, in flat space or curved spaces. Our unified construction involves always the \\it{same} twistor Z^A with only four complex degrees of freedom and subject to the \\it{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 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.
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.
Quaternionic (super) twistors extensions and general superspaces
Cirilo-Lombardo, Diego Julio; Pervushin, Victor N.
2017-09-01
In a attempt to treat a supergravity as a tensor representation, the four-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with N = p + k. These quaternionic superspaces have 4 + k(N - k) even-quaternionic coordinates and 4N odd-quaternionic coordinates, where each coordinate is a quaternion composed by four ℂ-fields (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case, the number of fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp(N) = Sp(N, ℍℂ) ∩ U(N, ℍℂ) is elucidated from this theoretical context.
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....
Phase diagrams of diblock copolymers in electric fields: a self-consistent field theory study.
Wu, Ji; Wang, Xianghong; Ji, Yongyun; He, Linli; Li, Shiben
2016-04-21
We investigated the phase diagrams of diblock copolymers in external electrostatic fields by using real-space self-consistent field theory. The lamella, cylinder, sphere, and ellipsoid structures were observed and analyzed by their segment distributions, which were arranged to two types of phase diagrams to examine the phase behavior in weak and strong electric fields. One type was constructed on the basis of Flory-Huggins interaction parameter and volume fraction. We identified an ellipsoid structure with a body-centered cuboid arrangement as a stable phase and discussed the shift of phase boundaries in the electric fields. The other type of phase diagrams was established on the basis of the dielectric constants of two blocks in the electric fields. We then determined the regions of ellipsoid phase in the phase diagrams to examine the influence of dielectric constants on the phase transition between ellipsoidal and hexagonally packed cylinder phases. A general agreement was obtained by comparing our results with those described in previous experimental and theoretical studies.
Complex Variable Methods for 3D Applied Mathematics: 3D Twistors and the biharmonic equation
Shaw, William T
2010-01-01
In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points with complex numbers via the assignment w = x+i y. In this framework 2D potential flow can be treated through the use of holomorphic functions and biharmonic flow through a simple, but superficially non-holomorphic extension. This paper explains how to elevate the use of complex methods to three dimensions, using Penrose's theory of twistors as adapted to intrinsically 3D and non-relativistic problems by Hitchin. We first summarize the equations of 3D steady viscous fluid flow in their basic geometric form. We then explain the theory of twistors for 3D, resulting in complex holomorphic representations of solutions to harmonic and biharmonic problems. It is shown how this intrinsically holomorphic 3D approach reduces naturally to the well-known 2D situations when there is translational or rotational symmetry, and an example is given...
Spinors and Twistors in Loop Gravity and Spin Foams
Dupuis, Maite; Tambornino, Johannes
2012-01-01
Spinorial tools have recently come back to fashion in loop gravity and spin foams. They provide an elegant tool relating the standard holonomy-flux algebra to the twisted geometry picture of the classical phase space on a fixed graph, and to twistors. In these lectures we provide a brief and technical introduction to the formalism and some of its applications.
Weyl-Euler-Lagrange equations on twistor space for tangent structure
Kasap, Zeki
2016-06-01
Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler-Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler-Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.
Solving differential equations for 3-loop diagrams relation to hyperbolic geometry and knot theory
Broadhurst, D J
1998-01-01
In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be accounted as a derivation; rather it certifies that an Ansatz found by PSLQ satisfies a more easily derived pair of partial differential equations. The result is similar to Schläfli's formula for the volume of a bi-rectangular hyperbolic tetrahedron, revealing a novel connection between 3-loop diagrams and 1-loop boxes. We show that each reduces to a common basis: volumes of ideal tetrahedra, corresponding to 1-loop massless triangle diagrams. Ideal tetrahedra are also obtained when evaluating the volume complementary to a hyperbolic knot. In the case that the knot is positive, and hence implicated in field theory, ease of ideal reduction correlates with likely appearance in counterterms. Volumes of knots relevant to the number content of multi-loop diagrams are evaluated;...
Kleinert; Pelster; Kastening; Bachmann
2000-08-01
The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation that can be turned into a recursion relation. This is solved order by order in the coupling constant to find all connected vacuum diagrams with their proper multiplicities. The procedure is applied to a multicomponent scalar field theory with a straight phi(4) self-interaction and then to a theory of two scalar fields straight phi and A with an interaction straight phi2A. All Feynman diagrams with external lines are obtained from functional derivatives of the connected vacuum diagrams with respect to the free correlation function. Finally, the recursive graphical construction is automatized by computer algebra with the help of a unique matrix notation for the Feynman diagrams.
Phase diagram and reentrance for the 3D Edwards–Anderson model using information theory
Energy Technology Data Exchange (ETDEWEB)
Cortez, V. [Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal las Torres 2640, Peñalolén, Santiago (Chile); Saravia, G.; Vogel, E.E. [Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54-D, Temuco (Chile)
2014-12-15
Data compressor techniques are used to study the phase diagram of the generalized Edwards–Anderson model in three dimensions covering the full range of mixture between ferromagnetic (concentration 1−x) and antiferromagnetic interactions (concentration x). The recently proposed data compressor wlzip is used to recognize criticality by the maximum information content in the files storing the simulation processes. The method allows not only the characterization of the ferromagnetic to paramagnetic (FP) transition (x<0.22, or x>0.78) but also it equally well yields the spin-glass to paramagnetic (SP) transition (0.22
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.
Differential and Twistor Geometry of the Quantum Hopf Fibration
Brain, Simon
2011-01-01
We study a quantum version of the SU(2) Hopf fibration $S^7 \\to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.
On-shell diagrams and the geometry of planar N < 4 SYM theories
Benincasa, Paolo
2016-01-01
We continue the discussion of the decorated on-shell diagrammatics for planar N < 4 Supersymmetric Yang-Mills theories started in arXiv:1510.03642. In particular, we focus on its relation with the structure of varieties on the Grassmannian. The decoration of the on-shell diagrams, which physically keeps tracks of the helicity of the coherent states propagating along their edges, defines new on-shell functions on the Grassmannian and can introduce novel higher-order singularities, which graphically are reflected into the presence of helicity loops in the diagrams. These new structures turn out to have similar features as in the non-planar case: the related higher-codimension varieties are identified by either the vanishing of one (or more) Plucker coordinates involving at least two non-adjacent columns, or new relations among Plucker coordinates. A distinctive feature is that the functions living on these higher-codimenson varieties can be thought of distributionally as having support on derivative delta-fu...
Phase diagram of 4D field theories with chiral anomaly from holography
Ammon, Martin; Macedo, Rodrigo P
2016-01-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Cheng, Peter C-H
2011-07-01
The representational epistemic approach to the design of visual displays and notation systems advocates encoding the fundamental conceptual structure of a knowledge domain directly in the structure of a representational system. It is claimed that representations so designed will benefit from greater semantic transparency, which enhances comprehension and ease of learning, and plastic generativity, which makes the meaningful manipulation of the representation easier and less error prone. Epistemic principles for encoding fundamental conceptual structures directly in representational schemes are described. The diagrammatic recodification of probability theory is undertaken to demonstrate how the fundamental conceptual structure of a knowledge domain can be analyzed, how the identified conceptual structure may be encoded in a representational system, and the cognitive benefits that follow. An experiment shows the new probability space diagrams are superior to the conventional approach for learning this conceptually challenging topic.
Phase diagram for the Eigen quasispecies theory with a truncated fitness landscape
Saakian, David B.; Biebricher, Christof K.; Hu, Chin-Kun
2009-04-01
Using methods of statistical physics, we present rigorous theoretical calculations of Eigen’s quasispecies theory with the truncated fitness landscape which dramatically limits the available sequence space of information carriers. As the mutation rate is increased from small values to large values, one can observe three phases: the first (I) selective (also known as ferromagnetic) phase, the second (II) intermediate phase with some residual order, and the third (III) completely randomized (also known as paramagnetic) phase. We calculate the phase diagram for these phases and the concentration of information carriers in the master sequence (also known as peak configuration) x0 and other classes of information carriers. As the phase point moves across the boundary between phase I and phase II, x0 changes continuously; as the phase point moves across the boundary between phase II and phase III, x0 has a large change. Our results are applicable for the general case of a fitness landscape.
Enhanced Gauged Symmetry in Type II and F-Theory Compactifications Dynkin Diagrams from Polyhedra
Perevalov, E V; Perevalov, Eugene; Skarke, Harald
1997-01-01
We explain the observation by Candelas and Font that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron $\\Delta^*$ that provides the toric description of the Calabi--Yau manifold used for compacification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also explain how even the occurrence of monodromy and non-simply laced groups in the latter case is visible in the toric picture. These methods also work in the fourfold case.
The phase diagram and transport properties of MgO from theory and experiment
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.
Sannino, Francesco
2008-01-01
We summarize basic features associated to dynamical breaking of the electroweak symmetry. The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when trying to construct viable extensions of the standard model (SM). Therefore we will report on the status of the phase diagram for SU(N) gauge theories with fermionic matter transforming according to arbitrary representations of the underlying gauge group. We will discuss how the phase diagram can be used to construct unparticle models. We will then review Minimal Walking Technicolor (MWT) and other extensions, such as partially gauged and split technicolor. MWT is a sufficiently general, symmetry wise, model to be considered as a benchmark for any model aiming at breaking the electroweak symmetry dynamically. The unification of the standard model gauge couplings will be revisited within technicolor extensions of the SM. A number of appendices are added to rev...
Condensation phase diagram of cavity polaritons in GaN-based microcavities: Experiment and theory
Levrat, Jacques; Butté, Raphaël; Feltin, Eric; Carlin, Jean-François; Grandjean, Nicolas; Solnyshkov, Dmitry; Malpuech, Guillaume
2010-03-01
The evolution of the polariton condensation threshold (Pthr) under incoherent optical pumping is investigated both theoretically and experimentally over a wide range of temperatures (4-340 K) and exciton-cavity photon detunings (-120-0meV) in a multiple quantum-well GaN-based microcavity. The condensation phase diagram of these bosonic quasiparticles is first theoretically described within the framework of Bose-Einstein condensation of polaritons in the thermodynamic limit. Then a qualitative picture of cavity polariton relaxation kinetics including the impact of detuning and temperature is given before introducing a modeling of cavity polariton relaxation kinetics with semiclassical Boltzmann equations. The results of the theoretical modeling are finally compared with systematic measurements of Pthr . At low temperature and negative detunings, the polariton gas is far from thermal equilibrium and the condensation threshold is governed by the efficiency of the relaxation kinetics of the particles. Conversely, at high temperature and for less negative detunings, the relaxation kinetics is efficient enough to allow the achievement of a thermal polariton distribution function with a critical density for condensation given by the thermodynamic theory of Bose-Einstein condensation. For temperatures ranging between ˜140 and 340 K, an optimum detuning is found experimentally, where the condensation threshold power is minimized. At high temperatures, polariton detrapping effects from the bottom of the trap formed in k∥ space by the lower polariton branch are found to play a supplementary role among the processes governing Pthr .
About Twistor Spinors with Zero in Lorentzian Geometry
Directory of Open Access Journals (Sweden)
Felipe Leitner
2009-07-01
Full Text Available We describe the local conformal geometry of a Lorentzian spin manifold (M,g admitting a twistor spinor φ with zero. Moreover, we describe the shape of the zero set of φ. If φ has isolated zeros then the metric g is locally conformally equivalent to a static monopole. In the other case the zero set consists of null geodesic(s and g is locally conformally equivalent to a Brinkmann metric. Our arguments utilise tractor calculus in an essential way. The Dirac current of φ, which is a conformal Killing vector field, plays an important role for our discussion as well.
Integrable systems twistors, loop groups, and Riemann surfaces
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
Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards’ field theory
Morse, David C.
2006-10-01
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
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new easy method has been presented to calculate the variable intervals corresponding to the stable univariant curves and to discriminate the stabilities of invariant points. This method and the one reported previously constitute a simple and universal theory for the computer-plotting of the equilibrium phase diagrams of a multisystem sign function matrix (SFM) discrimination method. Its main steps are: determining the stable univariant scheme according to the derivative (or difference) of ΔrGm; grouping the univariant curves by comparisons of the mutual relations among them; determining the existing intervals of the variables for the stable curves by comparisons of coordinate values of the curves about the invariant point; determining the stabilities of invariant points by comparisons of relations between the common curves and the invariant points. This method is suitable for any kind of phase diagram of closed or open systems in a phase diagram "space" with either 2 or more than 2 dimensions.
One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
Brandhuber, A; Travaglini, G; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We propose a new, twistor string theory inspired formalism to calculate loop amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices, using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and combined into effective diagrams that incorporate large numbers of conventional Feynman diagrams. As an example, we apply this formalism to the particular class of MHV one-loop scattering amplitudes with an arbitrary number of external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads to a representation of the amplitudes as dispersion integrals, which we evaluate exactly. Our results for the MHV amplitudes are in precise agreement with the expressions for this class of amplitudes obtained previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
Gauged twistor formulation of a massive spinning particle in four dimensions
Deguchi, Shinichi
2015-01-01
We present a gauged twistor model of a free massive spinning particle in four-dimensional Minkowski space. This model is governed by an action, referred to here as the gauged generalized Shirafuji (GGS) action, that consists of twistor variables, auxiliary variables, and $U(1)$ and $SU(2)$ gauge fields on the one-dimensional parameter space of a particle's world-line. The GGS action remains invariant under reparametrization and the local $U(1)$ and $SU(2)$ transformations of the relevant variables, although the $SU(2)$ symmetry is nonlinearly realized. We consider the canonical Hamiltonian formalism based on the GGS action in the unitary gauge by following Dirac's recipe for constrained Hamiltonian systems. It is shown that just sufficient constraints for the twistor variables are consistently derived by virtue of the gauge symmetries of the GGS action. In the subsequent quantization procedure, these constraints turn into simultaneous differential equations for a twistor function. We perform the Penrose trans...
Fermions, Gauge Theories, and the Sinc Function Representation for Feynman Diagrams
Petrov, D; Guralnik, G S; Hahn, S; Wang, W M; Petrov, Dmitri; Easther, Richard; Guralnik, Gerald; Hahn, Stephen; Wang, Wei-Mun
2001-01-01
We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin-1/2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function representation for scalar field Feynman integrals are shared by fields with non-zero spin. We then investigate the application of the Sinc function representation to simple QED diagrams, including first order corrections to the propagators and the vertex.
A twistor sphere of generalized Kahler potentials on hyperkahler manifolds
Dyckmanns, Malte
2011-01-01
We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be used to determine the generalized Kahler potential for hyperkahler manifolds whose description in projective superspace is fully understood. We use this relation to determine an S^2-family of generalized Kahler potentials for Euclidean space and for the Eguchi-Hanson geometry. Cotangent bundles of Hermitian symmetric spaces constitute a class of hyperkahler manifolds where our method can be applied immediately since the necessary results from projective superspace are already available. As a non-trivial higher-dimensional example, we determine the generalized potential for T*CP^n, which generalizes the Eguchi-Hanson result.
The connected prescription for form factors in twistor space
Brandhuber, Andreas; Panerai, Rodolfo; Spence, Bill; Travaglini, Gabriele
2016-01-01
We propose a connected prescription formula in twistor space for all tree-level form factors of the stress tensor multiplet operator in $\\mathcal{N}=4$ 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.
The connected prescription for form factors in twistor space
Brandhuber, A.; Hughes, E.; Panerai, R.; Spence, B.; Travaglini, G.
2016-11-01
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.
Quaternionic (super)twistors extensions and general superspaces
Cirilo-Lombardo, Diego Julio
2016-01-01
In a attempt to treat a supergravity as a tensor representation, the 4-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors[14], with N = p + k: These quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and 4N odd- quaternionic coordinates where each coordinate is a quaternion composed by four C-felds (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case the number of felds of the supergravity is determined by the number of components of the tensor representation of the 4-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp (N) = Sp (N;HC) \\ U (N;HC) is elucidated from this theoretical context.
Rotating Black Hole, Twistor-String and Spinning Particle
Burinskii, A
2005-01-01
We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial {\\it real} stringy structure consisting of the Kerr circular string and an axial stringy system. We consider also the complex and twistorial structures of the Kerr geometry and show that there is a {\\it complex} twistor-string built of the complex N=2 chiral string with a twistorial $(x,\\theta)$ structure. By imbedding into the real Minkowski $\\bf M^4$, the N=2 supersymmetry is partially broken and string acquires the open ends. Orientifolding this string, we identify the chiral and antichiral structures. Target space of this string is equivalent to the Witten's `diagonal' of the $\\bf CP^3\\times CP^{*3}.$
Operator algebra of free conformal currents via twistors
Energy Technology Data Exchange (ETDEWEB)
Gelfond, O.A. [Institute of System Research of Russian Academy of Sciences, Nakhimovsky prospect 36-1, 117218 Moscow (Russian Federation); Vasiliev, M.A., E-mail: vasiliev@lpi.ru [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute, Leninsky prospect 53, 119991 Moscow (Russian Federation)
2013-11-21
Operator algebra of (not necessarily free) higher-spin conformal conserved currents in generalized matrix spaces, that include 3d Minkowski space–time as a particular case, is shown to be determined by an associative algebra M of functions on the twistor space. For free conserved currents, M is the universal enveloping algebra of the higher-spin algebra. Proposed construction greatly simplifies computation and analysis of correlators of conserved currents. Generating function for n-point functions of 3d (super)currents of all spins, built from N free constituent massless scalars and spinors, is obtained in a concise form of certain determinant. Our results agree with and extend earlier bulk computations in the HS AdS{sub 4}/CFT{sub 3} framework. Generating function for n-point functions of 4d conformal currents is also presented.
Twistor-Inspired Construction of Electroweak Vector Boson Currents
Bern, Z; Kosower, D A; Mastrolia, Pierpaolo; Bern, Zvi; Forde, Darren; Kosower, David A.; Mastrolia, Pierpaolo
2004-01-01
We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,\\gamma^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the non-abelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.
Renormalization of two-loop diagrams in scalar lattice field theory
Borasoy, B
2006-01-01
We present a method to calculate to very high precision the coefficients of the divergences occuring in two-loop diagrams for a massive scalar field on the lattice. The approach is based on coordinate space techniques and extensive use of the precisely known Green's function.
Sato, Yuji; Nakai, Chiaki; Wakeda, Masato; Ogata, Shigenobu
2017-08-03
Theoretical prediction of glass forming ability (GFA) of metallic alloys is a key process in exploring metallic alloy compositions with excellent GFA and thus with the ability to form a large-sized bulk metallic glass. Molecular dynamics (MD) simulation is a promising tool to achieve a theoretical prediction. However, direct MD prediction continues to be challenging due to the time-scale limitation of MD. With respect to practical bulk metallic glass alloys, the time necessary for quenching at a typical cooling rate is five or more orders of magnitude higher than that at the MD time-scale. To overcome the time-scale issue, this study proposes a combined method of classical nucleation theory and MD simulations. The method actually allows to depict the time-temperature-transformation (TTT) diagram of the bulk metallic glass alloys. The TTT directly provides a prediction of the critical cooling rate and GFA. Although the method assumes conventional classical nucleation theory, all the material parameters appearing in the theory were determined by MD simulations using realistic interatomic potentials. The method is used to compute the TTT diagrams and critical cooling rates of two Cu-Zr alloy compositions (Cu50Zr50 and Cu20Zr80). The results indicate that the proposed method reasonably predicts the critical cooling rate based on the computed TTT.
On the theory of ternary melt crystallization with a non-linear phase diagram
Toropova, L. V.; Dubovoi, G. Yu; Alexandrov, D. V.
2017-04-01
The present study is concerned with a theoretical analysis of unidirectional solidification process of ternary melts in the presence of a phase transition (mushy) layer. A new analytical solution of heat and mass transfer equations describing the steady-state crystallization scenario is found with allowance for a non-linear liquidus equation. The model under consideration takes into account the presence of two phase transition layers, namely, the primary and cotectic mushy regions. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.
Phase diagram of NaxCoO2 studied by Gutzwiller density-functional theory.
Wang, Guang-Tao; Dai, Xi; Fang, Zhong
2008-08-01
The ground state of NaxCoO2 (0.0Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated ab initio. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as (1) Stoner magnetic metal for x>0.6 due to a_{1g} van Hove singularity near the band top, (2) correlated nonmagnetic metal without e_{g};{'} pockets for 0.3
Phase diagram of rod-coil diblock copolymer melts by self-consistent field theory
Yan, Dadong; Tang, Jiuzhou; Jiang, Ying; Zhang, Xinghua; Chen, Jeff
A unified phase diagram is presented for rod-coil diblock copolymer melts in the isotropic phase regime as a function of the asymmetric parameter. The study is based on free-energy calculation, which incorporates three-dimensional spatial variations of the volume fraction with angular dependence. The wormlike-chain model is used in a self-consistent field treatment. Body-centered cubic, A15, hexagonal, gyroid, and lamellar structures where the rod segments are packed inside the convex rod-coil interface are found stable. As the conformational asymmetric parameter increases, the A15 phase region expands and the gyroid phase region reduces. The stability of the structures is analyzed by concepts such as packing frustration, spinodal limit, and interfacial curvature.
Jiang, Ying; Chen, Jeff Z. Y.
2013-10-01
This paper concerns establishing a theoretical basis and numerical scheme for studying the phase behavior of AB diblock copolymers made of wormlike chains. The general idea of a self-consistent field theory is the combination of the mean-field approach together with a statistical weight that describes the configurational properties of a polymer chain. In recent years, this approach has been extensively used for structural prediction of block copolymers, based on the Gaussian-model description of a polymer chain. The wormlike-chain model has played an important role in the description of polymer systems, covering the semiflexible-to-rod crossover of the polymer properties and the highly stretching regime, which the Gaussian-chain model has difficulties to describe. Although the idea of developing a self-consistent field theory for wormlike chains could be traced back to early development in polymer physics, the solution of such a theory has been limited due to technical difficulties. In particular, a challenge has been to develop a numerical algorithm enabling the calculation of the phase diagram containing three-dimensional structures for wormlike AB diblock copolymers. This paper describes a computational algorithm that combines a number of numerical tricks, which can be used for such a calculation. A phase diagram covering major parameter areas was constructed for the wormlike-chain system and reported by us, where the ratio between the total length and the persistence length of a constituent polymer is suggested as another tuning parameter for the microphase-separated structures; all detailed technical issues are carefully addressed in the current paper.
Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
Silvi, Pietro; Dalmonte, Marcello; Tschirsich, Ferdinand; Montangero, Simone
2016-01-01
We investigate the finite-density phase diagram of a non-abelian SU(2) lattice gauge theory, encoding Yang-Mills microscopical dynamics, in (1+1)-dimensions using tensor network methods. We numerically characterise the phase diagram as a function of the filling and of the matter-field coupling, individuating different phases, some of them appearing only at finite densities. At unit filling, we find a meson BCS liquid phase, which at strong coupling undergoes a phase transition to a charge density wave of single-site (spin-0) mesons via spontaneous chiral symmetry breaking. At finite densities, the chiral symmetry is restored almost everywhere, and the meson BCS liquid becomes a simple liquid at strong couplings, with the exception of filling two-thirds, where a charge density wave of mesons spreading over neighbouring sites appears. Finally, we individuate two tri-critical points between the chiral and the two liquid phases which are compatible with a SU(2)$_2$ Wess-Zumino-Novikov-Witten model.
Müller, Clemens; Stace, Thomas M.
2017-01-01
Motivated by correlated decay processes producing gain, loss, and lasing in driven semiconductor quantum dots [Phys. Rev. Lett. 113, 036801 (2014), 10.1103/PhysRevLett.113.036801; Science 347, 285 (2015), 10.1126/science.aaa2501; Phys. Rev. Lett. 114, 196802 (2015), 10.1103/PhysRevLett.114.196802], we develop a theoretical technique by using Keldysh diagrammatic perturbation theory to derive a Lindblad master equation that goes beyond the usual second-order perturbation theory. We demonstrate the method on the driven dissipative Rabi model, including terms up to fourth order in the interaction between the qubit and both the resonator and environment. This results in a large class of Lindblad dissipators and associated rates which go beyond the terms that have previously been proposed to describe similar systems. All of the additional terms contribute to the system behavior at the same order of perturbation theory. We then apply these results to analyze the phonon-assisted steady-state gain of a microwave field driving a double quantum dot in a resonator. We show that resonator gain and loss are substantially affected by dephasing-assisted dissipative processes in the quantum-dot system. These additional processes, which go beyond recently proposed polaronic theories, are in good quantitative agreement with experimental observations.
Universal Field-Induced Charge-Density-Wave Phase Diagram: Theory versus Experiment
Lebed, A. G.
2009-07-01
We suggest a theory of field-induced charge-density-wave phases, generated by high magnetic fields in quasi-low-dimensional conductors. We demonstrate that, in layered quasi-one-dimensional conductors, the corresponding critical magnetic field ratios are universal and do not depend on any fitting parameter. In particular, we find that H1/H0=0.73, H2/H0=0.59, H3/H0=0.49, and H4/H0=0.42, where Hn is a critical field of a phase transition between the field-induced charge-density-wave phases with numbers n and n+1. The suggested theory is in very good qualitative and quantitative agreement with the existing experimental data in α-(ET)2KHg(SCN)4 material.
Kastening
2000-04-01
The free energy of a multicomponent scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys nonlinear functional differential equations which are turned into recursion relations for the connected Green's functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Green's functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multiloop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are nonperturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.
Directory of Open Access Journals (Sweden)
Jae-Kwan Kim
2014-04-01
Full Text Available Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the twodimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr.
One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
Energy Technology Data Exchange (ETDEWEB)
Ellis, R. Keith [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Kunszt, Zoltan [Institute for Theoretical Physics (Switzerland); Melnikov, Kirill [Johns Hopkins Univ., Baltimore, MD (United States); Zanderighi, Giulia [Rudolf Peierls Centre for Theoretical Physics (United Kingdom)
2012-09-01
The success of the experimental program at the Tevatron re-inforced the idea that precision physics at hadron colliders is desirable and, indeed, possible. The Tevatron data strongly suggests that one-loop computations in QCD describe hard scattering well. Extrapolating this observation to the LHC, we conclude that knowledge of many short-distance processes at next-to-leading order may be required to describe the physics of hard scattering. While the field of one-loop computations is quite mature, parton multiplicities in hard LHC events are so high that traditional computational techniques become inefficient. Recently new approaches based on unitarity have been developed for calculating one-loop scattering amplitudes in quantum field theory. These methods are especially suitable for the description of multi-particle processes in QCD and are amenable to numerical implementations. We present a systematic pedagogical description of both conceptual and technical aspects of the new methods.
Cağlar, Tolga; Berker, A Nihat
2011-11-01
The roughening phase diagram of the d=3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d=2 Ising model for the full range of anisotropy, yielding no roughening transition.
Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams
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.
Institute of Scientific and Technical Information of China (English)
胡家文; 殷辉安; 唐明林
2000-01-01
A new easy method has been presented to calculate the variable intervals corresponding to the stable univariant curves and to discriminate the stabilities of invariant points. This method and the one reported previously constitute a simple and universal theory for the computer-plotting of the equilibriumphase diagrams of a multisystem——sign function matrix (SFM) discrimination method. Its main steps are:determining the stable univariant scheme according to the derivative (or difference) of △rGm; grouping the univariant curves by comparisons of the mutual relations among them; determining the existing intervals of the variables for the stable curves by comparisons of coordinate values of the curves about the invariant point; determining the stabilities of invariant points by comparisons of relations between the common curves and the invariant points. This method is suitable for any kind of phase diagram of closed or open systems in a phase diagram "space" with either 2 or more than 2 dimensions.
Feynman Diagrams for Beginners
Kumericki, Kresimir
2016-01-01
We give a short introduction to Feynman diagrams, with many exercises. Text is targeted at students who had little or no prior exposure to quantum field theory. We present condensed description of single-particle Dirac equation, free quantum fields and construction of Feynman amplitude using Feynman diagrams. As an example, we give a detailed calculation of cross-section for annihilation of electron and positron into a muon pair. We also show how such calculations are done with the aid of computer.
Twistor quantization of the space of half-differentiable vector functions on the circle revisited
Institute of Scientific and Technical Information of China (English)
SERGEEV; Armen
2009-01-01
We discuss the twistor quantization problem for the classical system(Vd,Ad),represented by the phase space Vd,identified with the Sobolev space H 1/2 0 (S1,Rd)of half-differentiable vector functions on the circle,and the algebra of observables Ad,identified with the semi-direct product of the Heisenberg algebra of Vd and the algebra Vect(S1)of tangent vector fields on the circle.
Yunus, Çağın; Renklioğlu, Başak; Keskin, Mustafa; Berker, A Nihat
2016-06-01
The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.
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
Engineering holographic phase diagrams
Chen, Jiunn-Wei; Dai, Shou-Huang; Maity, Debaprasad; Zhang, Yun-Long
2016-10-01
By introducing interacting scalar fields, we tried to engineer physically motivated holographic phase diagrams which may be interesting in the context of various known condensed matter systems. We introduce an additional scalar field in the bulk which provides a tunable parameter in the boundary theory. By exploiting the way the tuning parameter changes the effective masses of the bulk interacting scalar fields, desired phase diagrams can be engineered for the boundary order parameters dual to those scalar fields. We give a few examples of generating phase diagrams with phase boundaries which are strikingly similar to the known quantum phases at low temperature such as the superconducting phases. However, the important difference is that all the phases we have discussed are characterized by neutral order parameters. At the end, we discuss if there exists any emerging scaling symmetry associated with a quantum critical point hidden under the dome in this phase diagram.
Rose, Matthew
2004-01-01
Matthew Rose worked at the Naval Postgraduate School as a graphic designer from February 2002-November 2011. His work for NPS included logos, brochures, business packs, movies/presentations, posters, the CyberSiege video game and many other projects. This material was organized and provided by the artist, for inclusion in the NPS Archive, Calhoun. Includes these files: Plan_ver.ai; powerline.jpg; SCADA diagram.ai; SCADA diagram.pdf; SCADA diagramsmall.pdf; SCADA2.pdf
The Genesis of Feynman Diagrams
Wuthrich, Adrian
2011-01-01
In a detailed reconstruction of the genesis of Feynman diagrams the author reveals that their development was constantly driven by the attempt to resolve fundamental problems concerning the uninterpretable infinities that arose in quantum as well as classical theories of electrodynamic phenomena. Accordingly, as a comparison with the graphical representations that were in use before Feynman diagrams shows, the resulting theory of quantum electrodynamics, featuring Feynman diagrams, differed significantly from earlier versions of the theory in the way in which the relevant phenomena were concep
Scattering equations and Feynman diagrams
Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-09-01
We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in φ 3-theory. We also discuss the generalization to general scalar field theories with φ p interactions, corresponding to polygonal graphs involving vertices of order p. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.
Scattering Equations and Feynman Diagrams
Baadsgaard, Christian; Bourjaily, Jacob L; Damgaard, Poul H
2015-01-01
We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $\\phi^3$-theory. We also discuss the generalization to general scalar field theories with $\\phi^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.
Oostrom, V. van
2008-01-01
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 strat
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.
Djorgovski, S.; Murdin, P.
2000-11-01
Initially introduced as a way to demonstrate the expansion of the universe, and subsequently to determine the expansion rate (the HUBBLE CONSTANT H0), the Hubble diagram is one of the classical cosmological tests. It is a plot of apparent fluxes (usually expressed as magnitudes) of some types of objects at cosmological distances, against their REDSHIFTS. It is used as a tool to measure the glob...
D3-instantons, Mock Theta Series and Twistors
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2012-01-01
The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-i...
Institute of Scientific and Technical Information of China (English)
Bayram Devirena; Yasin Polatb; Mustafa Keskinc
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 antiferromagnetic 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,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.
Studies on instantons, twistor strings, and half-BPS geometries
Ricci, Riccardo
2006-12-01
In this Dissertation we discuss three different topics. We begin by studying supersymmetric instantons for Yang-Mills theories on non-anticommutative superspace. Performing an iterative expansion in the non-commutativity parameter C, we solve the equation of motions for U(2) Super Yang-Mills with and without matter. For pure Yang-Mills, we solve the equations exactly. In addition to the usual 't Hooft SU(2) instanton, the deformation turns on a non-trivial U(1) conncetion which depends on the fermionic collective coordinates and the deformation parameter C. In the Higgs phase on the other hand, we solve the equations of motion to leading order in the coupling constant. Even though the instanton effective action receives a contribution of order C 2, the gluino condensate and the non-perturbative Affleck-Dine-Seiberg superpotential remain as in N = 1 super Yang-Mills. The second topic is related to twister strings. Perturbative super Yang-Mills can be reinterpreted as a D-instanton expansion of the topological B-model on the supermanifold CP3|4 . We extend this contruction to N = 1 and N = 2 quiver gauge theories by contructing fermionic orbifolds of CP3|4 . Topological string suggest some efficient rules for computing Yang-Mills perturbative amplitudes. We consider possible extensions of these rules to gravity amplitudes. We conclude by analyzing some mathematical aspects of super Calabi-Yau manifolds. The final topic is devoted to the study of half-BPS type IIB supergravity solutions. The moduli space of these solutions can be associated to a one-dimensional, zero temperature fermion gas in a harmonic potential. We studied a natural generalization of the fermion-supergravity map, considering the fermions at non-zero temperature. We found that the ADM energy of the supergravity solution reproduces the thermal fermion energy. One important effect of the temperature is that the background develops a null singularity. This singularity is naked, that is not "covered" by
Tucker, J. W.; Balcerzak, T.; Gzik, M.; Sukiennicki, A.
1998-09-01
The complete global phase diagram for a magnetic spin-1 bilayer, whose interactions are described by the Blume Emery Griffiths model (BEG), is studied by cluster variational theory within the pair approximation. The results obtained, are also the exact results pertaining to the BEG model on a Bethe lattice having coordination number, z=5. Useful analytic expressions are derived for trajectories in phase space containing the second-order (continuous) phase boundaries. The physical existence of these second-order boundaries, together with the location of the first-order phase boundaries, are determined from a Gibbs free energy analysis. Detailed comparison of the results with those of other workers on this, and closely related systems, is made.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
According to the mass action law and the coexistence theory of metallic melts, the mass action concentrations of Cu-Mg, Bi-Tl and Ni-Al melts involving compound formation have been calculated. The calculated results show that, except the ultimate case of pure element, when two elements are present in the melts, all structural units (atoms and molecules) without exception will be present in the melts, i.e., their concentrations may change from great to small, but they will not vanish into nothing, and only under such conditions, the calculated results both agree with practice and obey the law of mass action. In view of that over considerable wide composition range, the activities of both elements of the three solid binary alloys mentioned above have been measured, this seems in contradiction with the present relevant phase diagrams, in which the structural units are determined by composition range, so the latter needs further investigation and consideration.
Diagramming Complex Activities
DEFF Research Database (Denmark)
Andersen, Peter Bøgh
2005-01-01
We increasingly live in heterogeneous ever-changing webs of activities where human actions are intertwined with events created by automatic machines. In order to make such webs understandable to its human participants, their structure should be represented by displays emphasizing their action as...... aspect. The paper suggests thematic roles as a semantics for actions, argues that a selection of well-known diagramming techniques can be defined within this theory, and uses the theory to discuss new issues related to process control and mobile technology....
A twistor formulation of the heterotic D=10 superstring with manifest (8,0) worldsheet supersymmetry
Delduc, F; Howe, Paul S; Sokatchev, Emery S
1993-01-01
We propose a new formulation of the heterotic $D=10$ Green-Schwarz superstring whose worldsheet is a superspace with two even and eight odd coordinates. The action is manifestly invariant under both target-space supersymmetry and a worldsheet reparametrisation supergroup. It contains only a finite set of auxiliary fields. The key ingredient are the commuting spinor (twistor) variables, which naturally arise as worldsheet superpartners of the target space Grassmann coordinates. These spinors parametrise the sphere $S^8$ regarded as a coset space of the $D=10$ Lorentz group. The sphere is associated with the lightlike vector of one of the string Virasoro constraints. The origin of the on-shell $D=10$ fermionic kappa symmetry of the standard Green-Schwarz formulation is explained. An essential and unusual feature is the appearance of the string tension only on shell as an integration constant.
A twistor-like D=10 superparticle action with manifest N=8 world-line supersymmetry
Galperin, A
1992-01-01
We propose a new formulation of the $D=10$ Brink-Schwarz superparticle which is manifestly invariant under both the target-space super-Poincar\\'e 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 $\\kappa$ 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.
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...
On pluri-half-anticanonical system of LeBrun twistor spaces
Honda, Nobuhiro
2009-01-01
In this note, we investigate pluri-half-anticanonical systems on the so called LeBrun twistor spaces. We determine its dimension, the base locus, structure of the associated rational map, and also structure of general members, in precise form. In particular, we show that if n>2 and m>1, the base locus of the system |mK^{-1/2}| on nCP^2 consists of two non-singular rational curves, along which any member has singularity, and that if we blow-up these curves, then the strict transform of a general members of |mK^{-1/2}| becomes an irreducible non-singular surface. We also show that if n>3 and m>n-2, then the last surface is a minimal surface of general type with vanishing irregularity. We also show that the rational map associated to the system |mK^{-1/2}| is birational if and only if m> n-2.
Resummation of Cactus Diagrams in Lattice QCD
Panagopoulos, H
1998-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, this expansion yields results remarkably close to corresponding nonperturbative estimates.
On twistor transformations and invariant differential operator of simple Lie group G2(2)
Wang, Wei
2013-01-01
The twistor transformations associated to the simple Lie group G2 are described explicitly. We consider the double fibration G_2/P_2 xleftarrow {η } {G_2/B} xrArr {tau }G_2/P_1, where P1 and P2 are two parabolic subgroups of G2 and B is a Borel subgroup, and its local version: H^*_2 xleftarrow {η } F xrArr {tau } H_1, where H_1 is the Heisenberg group of dimension 5 embedded in the coset space G2/P1, F = {CP}^1 × H_1 and H^*_2 contains the nilpotent Lie group H_2 of step three. The Baker-Campbell-Hausdorff formula is used to parametrize the coset spaces, coordinates charts, their transition functions and the fibers of the projection η as complex curves. We write down the relative De-Rham sequence on F along the fibers and push it down to H_1 to get a family of matrix-valued differential operators {D}_k. Then we establish a kind of Penrose correspondence for G2: the kernel of {D}_k is isomorphic to the first cohomology of the sheaf {O} (-k ) over H^*_2. We also give the Penrose-type integral transformation u = Pf for fin {O} (-k ), which gives solutions to equations {D}_ku=0. When restricted to the real Heisenberg group, the differential operators are invariant under the action of G2(2). Exchanging P1 and P2, we derive corresponding results on H_2.
Herzog, Franz; Ueda, Takahiro; Vermaseren, J A M; Vogt, Andreas
2016-01-01
We discuss a number of FORM features that are essential in the automatic processing of very large numbers of diagrams as used in the Forcer program for 4-loop massless propagator diagrams. Most of these features are new.
Extrinsic Curvature Embedding Diagrams
Lu, J L
2003-01-01
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.
All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Bern, Z; Kosower, D A; Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2004-01-01
We compute the next-to-MHV one-loop n-gluon amplitudes in N=4 super-Yang-Mills theory. These amplitudes contain three negative-helicity gluons and an arbitrary number of positive-helicity gluons, and are the first infinite series of amplitudes beyond the simplest, MHV, amplitudes. We also discuss some aspects of their twistor-space structure.
Phase Equilibria Diagrams Database
SRD 31 NIST/ACerS Phase Equilibria Diagrams Database (PC database for purchase) The Phase Equilibria Diagrams Database contains commentaries and more than 21,000 diagrams for non-organic systems, including those published in all 21 hard-copy volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program (formerly titled Phase Diagrams for Ceramists): Volumes I through XIV (blue books); Annuals 91, 92, 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics I. Materials covered include oxides as well as non-oxide systems such as chalcogenides and pnictides, phosphates, salt systems, and mixed systems of these classes.
DEFF Research Database (Denmark)
Duijm, Nijs Jan
2007-01-01
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......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...... analysis with operational safety management....
On-Shell Diagrams for N = 8 Supergravity Amplitudes
Heslop, Paul
2016-01-01
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.
Institute of Scientific and Technical Information of China (English)
LI Shichun
2004-01-01
Based on the Thomas-Fermi-Dirac-Cheng model, atomic phase diagram or electron density versus atomic radius diagram describing the interaction properties of atoms of different kinds in equilibrium state is developed. Atomic phase diagram is established based on the two-atoms model. Besides atomic radius, electron density and continuity condition for electron density on interfaces between atoms, the lever law of atomic phase diagram involving other physical parameters is taken into account, such as the binding energy, for the sake of simplicity.
Tian, Yiwei; Booth, Jonathan; Meehan, Elizabeth; Jones, David S; Li, Shu; Andrews, Gavin P
2013-01-07
Amorphous drug-polymer solid dispersions have the potential to enhance the dissolution performance and thus bioavailability of BCS class II drug compounds. The principle drawback of this approach is the limited physical stability of amorphous drug within the dispersion. Accurate determination of the solubility and miscibility of drug in the polymer matrix is the key to the successful design and development of such systems. In this paper, we propose a novel method, based on Flory-Huggins theory, to predict and compare the solubility and miscibility of drug in polymeric systems. The systems chosen for this study are (1) hydroxypropyl methylcellulose acetate succinate HF grade (HPMCAS-HF)-felodipine (FD) and (2) Soluplus (a graft copolymer of polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol)-FD. Samples containing different drug compositions were mixed, ball milled, and then analyzed by differential scanning calorimetry (DSC). The value of the drug-polymer interaction parameter χ was calculated from the crystalline drug melting depression data and extrapolated to lower temperatures. The interaction parameter χ was also calculated at 25 °C for both systems using the van Krevelen solubility parameter method. The rank order of interaction parameters of the two systems obtained at this temperature was comparable. Diagrams of drug-polymer temperature-composition and free energy of mixing (ΔG(mix)) were constructed for both systems. The maximum crystalline drug solubility and amorphous drug miscibility may be predicted based on the phase diagrams. Hyper-DSC was used to assess the validity of constructed phase diagrams by annealing solid dispersions at specific drug loadings. Three different samples for each polymer were selected to represent different regions within the phase diagram.
Covariant diagrams for one-loop matching
Zhang, Zhengkang
2016-01-01
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.
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.
Hammerl, Matthias
2011-01-01
We treat a non-normal Fefferman-type construction based on an inclusion $\\SL(n+1)\\embed\\Spin(n+1,n+1)$. The construction associates a split signature $(n,n)$-conformal spin structure to a projective structure of dimension $n$. For $n\\geq 3$ the induced conformal Cartan connection is shown to be normal if and only if it is flat. The main technical work of this article consists in showing that in the non-flat case the normalised conformal Cartan connection still allows a parallel (pure) spin-tractor and thus a corresponding (pure) twistor spinor on the conformal space. The Fefferman-type construction presented here is an alternative approach to study a construction of Dunajski-Tod
DEFF Research Database (Denmark)
Moeller, Jesper; Lichtenberg, Jacob; Andersen, Henrik Reif;
1999-01-01
This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form $x-y......This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form $x-y...
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.
Energy Technology Data Exchange (ETDEWEB)
Feinberg, Joshua [Physics Department, University of Haifa at Oranim, Tivon 36006 (Israel); Physics Department, Technion, Israel Institute of Technology, Haifa 32000 (Israel)
2006-08-11
I review aspects of work done in collaboration with A Zee and R Scalettar (1997 Nucl. Phys. B 504 579; 1997 Nucl. Phys. B 501 643; 2001 J. Math. Phys. 42 5718) on complex non-Hermitian random matrices. I open by explaining why the bag of tools used regularly in analysing Hermitian random matrices cannot be applied directly to analyse non-Hermitian matrices, and then introduce the method of Hermitization, which solves this problem. Then, for rotationally invariant ensembles, I derive a master equation for the average density of eigenvalues in the complex plane, in the limit of infinitely large matrices. This is achieved by resumming all the planar diagrams which appear in the perturbative expansion of the Hermitized Green function. Remarkably, this resummation can be carried out explicitly for any rotationally invariant ensemble. I prove that in the limit of infinitely large matrices, the shape of the eigenvalue distribution is either a disc or an annulus. This is the celebrated 'single-ring' theorem. Which of these shapes is realized is determined by the parameters (coupling constants) which determine the ensemble. By varying these parameters a phase transition may occur between the two possible shapes. I briefly discuss the universal features of this transition. As the analysis of this problem relies heavily on summation of planar Feynman diagrams, I make a special effort at presenting a pedagogical exposition of the diagrammatic method, which some readers may find useful.
Inductively generating Euler diagrams.
Stapleton, Gem; Rodgers, Peter; Howse, John; Zhang, Leishi
2011-01-01
Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of well-formedness conditions; we present a series of results that identify properties of cycles that correspond to the well-formedness conditions. This improves upon other contributions toward the automated generation of Euler diagrams which implicitly assume some fixed set of well-formedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed.
Phase diagram to design passive nanostructures
Lee, Jeng Yi
2015-01-01
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers. General physical bounds are naturally revealed based on the intrinsic power conservation in a passive scattering system, entailing power competitions among scattering, absorption, and extinction. Exotic scattering and absorption phenomena, from resonant scattering, invisible cloaking, coherent perfect absorber, and subwavelength superscattering can all be illustrated in this phase diagram. With electrically small core-shell scatterers as an example, we demonstrate a systematic method to design field-controllable structures based on the allowed trajectories in the phase diagram. The proposed phase diagram not only provides a simple tool to design optical devices but also promotes a deep understanding on Mie's scattering theory.
Herrmann, Enrico
2016-01-01
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, poles at infinity are present and loop amplitudes show special behavior on certain collinear cuts. We demonstrate on 1-loop and 2-loop examples that the behavior on collinear cuts is a highly non-trivial property which requires cancellations between all terms contributing to the amplitude.
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.
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.
Phase diagram distortion from traffic parameter averaging.
Stipdonk, H. Toorenburg, J. van & Postema, M.
2010-01-01
Motorway traffic congestion is a major bottleneck for economic growth. Therefore, research of traffic behaviour is carried out in many countries. Although well describing the undersaturated free flow phase as an almost straight line in a (k,q)-phase diagram, congested traffic observations and theori
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We 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 tautology checkin
Lindenbergh, R.C.
2002-01-01
The classic Voronoi diagram of a configuration of distinct points in the plane associates to each point that part of the plane that is closer to the point than to any other point in the configuration. In this thesis we no longer require all points to be distinct. After the introduction in
Equational binary decision diagrams
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
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Hansen, Esben Rune; Satti, Srinivasa Rao; Tiedemann, Peter
2008-01-01
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Rune Hansen, Esben; Srinivasa Rao, S.; Tiedemann, Peter
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Kneupper, Charles W.
1978-01-01
Responds to Charles Willard's recommendations (in an article in "Communication Monographs," November 1976) that argument be viewed as an attempt to establish formal relationships among symbolic structures. Demonstrates flaws in this redefinition and shows argument diagrams to be theoretically and practically justifiable. (JMF)
Compressing Binary Decision Diagrams
DEFF Research Database (Denmark)
Hansen, Esben Rune; Satti, Srinivasa Rao; Tiedemann, Peter
2008-01-01
The paper introduces a new technique for compressing Binary Decision Diagrams in those cases where random access is not required. Using this technique, compression and decompression can be done in linear time in the size of the BDD and compression will in many cases reduce the size of the BDD to 1...
Equational binary decision diagrams
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 tauto
Lectures on Higher Structures in M-Theory
Saemann, Christian
2016-01-01
These are notes for four lectures on higher structures in M-theory as presented at workshops at the Erwin Schroedinger Institute and Tohoku University. The first lecture gives an overview of systems of multiple M5-branes and introduces the relevant mathematical structures underlying a local description of higher gauge theory. In the second lecture, we develop the corresponding global picture. A construction of non-abelian superconformal gauge theories in six dimensions using twistor spaces is discussed in the third lecture. The last lecture deals with the problem of higher quantization and its relation to loop space. An appendix summarizes the relation between 3-Lie algebras and Lie 2-algebras.
Jian, Yu-Cin; Wu, Chao-Jung
2015-02-01
We investigated strategies used by readers when reading a science article with a diagram and assessed whether semantic and spatial representations were constructed while reading the diagram. Seventy-one undergraduate participants read a scientific article while tracking their eye movements and then completed a reading comprehension test. Our results showed that the text-diagram referencing strategy was commonly used. However, some readers adopted other reading strategies, such as reading the diagram or text first. We found all readers who had referred to the diagram spent roughly the same amount of time reading and performed equally well. However, some participants who ignored the diagram performed more poorly on questions that tested understanding of basic facts. This result indicates that dual coding theory may be a possible theory to explain the phenomenon. Eye movement patterns indicated that at least some readers had extracted semantic information of the scientific terms when first looking at the diagram. Readers who read the scientific terms on the diagram first tended to spend less time looking at the same terms in the text, which they read after. Besides, presented clear diagrams can help readers process both semantic and spatial information, thereby facilitating an overall understanding of the article. In addition, although text-first and diagram-first readers spent similar total reading time on the text and diagram parts of the article, respectively, text-first readers had significantly less number of saccades of text and diagram than diagram-first readers. This result might be explained as text-directed reading.
Asteroseismology Across the HR Diagram
Thompson, M. J.; Cunha, M. S.; Monteiro, M. J. P. F. G.
2003-05-01
Ground-based observations have detected solar-like oscillations on Sun-like stars, and diagnostics similar to those used in helioseismology are now being used to test and constrain the physics and evolutionary state of these stars. Multi-mode oscillations are being observed in an abundance of other stars, including slowly pulsating B stars (SPB stars), delta-Scuti stars, Ap stars and the pulsating white dwarfs. New classes of pulsators continue to be discovered across the Herzsprung-Russell diagram. Yet the chances still to be faced to make asteroseismology across the HR diagram a reality are formidable. Observation, data analysis and theory all pose hard problems to be overcome. This book, reflecting the goal of the meeting, aims to facilitate a cross-fertilisation of ideas and approaches between fields covering different pulsators and with different areas of expertise. The book successfully covers most known types of pulsators, reflecting a highly productive and far reaching interchange of ideas which we believe is conveyed by the papers and posters published, making it a reference for researchers and postgraduate students working on stellar structure and evolution. Link: http://www.wkap.nl/prod/b/1-4020-1173-3
Lobato, Joanne; Hohensee, Charles; Diamond, Jaime Marie
2014-09-01
Despite recent research interest in student-created diagrams, little research has systematically investigated students' diagram- construction processes, meaning the order and manner in which students create markings as they physically generate diagrams. In this study, we characterize the various processes students use to create diagrams that represent a quadratic motion situation involving increasing speed, and we explore how these diagram-construction processes are related to students' conceptions of speed as inferred from their explanations with their completed diagrams. Previous literature suggests contrasting predictions regarding whether or not students' diagram-construction processes are closely related (from our perspective as researchers) to students' inferred conceptions. We see the study as having value for research and practice by raising new questions related to diagram-construction processes, pointing to the potential formative assessment value of attending to diagram-construction processes, and demonstrating the need for the development of theory to explain the relationships identified by this study.
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.
Partition functions of web diagrams with an O7$^-$-plane
Hayashi, Hirotaka
2016-01-01
We consider the computation of the topological string partition function for 5-brane web diagrams with an O7$^-$-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.
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
2002-01-01
This paper presents a new data structure called boolean expression diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of binary decision diagrams (BDDs) which can represent any Boolean circuit in linear space. Two algorithms are described for transforming...... a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two different circuit implementations of a 16-bit multiplier implement the same...... Boolean function. Using BEDs, this verification problem is solved efficiently, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small. Moreover, using operators...
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
1997-01-01
This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable...... properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying...... that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using...
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....
Energy Technology Data Exchange (ETDEWEB)
Wilms, R Scott [Los Alamos National Laboratory; Carlson, Bryan [Los Alamos National Laboratory; Coons, James [Los Alamos National Laboratory; Kubic, William [Los Alamos National Laboratory
2008-01-01
This presentation describes the development of the proposed Process Flow Diagram (PFD) for the Tokamak Exhaust Processing System (TEP) of ITER. A brief review of design efforts leading up to the PFD is followed by a description of the hydrogen-like, air-like, and waterlike processes. Two new design values are described; the mostcommon and most-demanding design values. The proposed PFD is shown to meet specifications under the most-common and mostdemanding design values.
Energy Technology Data Exchange (ETDEWEB)
Rudin, M.J. [Univ. of Nevada, Las Vegas NV (United States); O`Brien, M.C. [Univ. of Arizona, Tucson, AZ (United States)
1995-04-01
A planning and management tool was developed that relates environmental restoration and waste management problems to technologies that can be used to remediate these problems. Although the Technology Logic Diagram has been widely used within the US Department of Energy`s Office of Environmental Restoration and Waste Management, it can be modified for use during the planning of any waste management and environmental cleanup effort.
The Massive Thermal Basketball Diagram
Andersen, J O; Strickland, Michael T; Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-01-01
The "basketball diagram" is a three-loop vacuum diagram for a scalar fieldtheory that cannot be expressed in terms of one-loop diagrams. We calculatethis diagram for a massive scalar field at nonzero temperature, reducing it toexpressions involving three-dimensional integrals that can be easily evaluatednumerically. We use this result to calculate the free energy for a massivescalar field with a phi^4 interaction to three-loop order.
Feynman diagram drawing made easy
Baillargeon, Marc; Nogueira, P.
1997-02-01
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.
Voronoi diagrams on the sphere
Na, H.-S.; Lee, C.-N.; Cheong, O.
2001-01-01
Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthest-site Voronoi diagram can always be obtained as a portion of a
Spin wave Feynman diagram vertex computation package
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.
Knot probabilities in random diagrams
Cantarella, Jason; Chapman, Harrison; Mastin, Matt
2016-10-01
We consider a natural model of random knotting—choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 10 and fewer crossings are unknots (about 78% of the roughly 1.6 billion 10 crossing diagrams). For these crossing numbers, the unknot fraction is mostly explained by the prevalence of ‘tree-like’ diagrams which are unknots for any assignment of over/under information at crossings. The data shows a roughly linear relationship between the log of knot type probability and the log of the frequency rank of the knot type, analogous to Zipf’s law for word frequency. The complete tabulation and all knot frequencies are included as supplementary data.
Phase diagrams of binary crystalline-crystalline polymer blends.
Matkar, Rushikesh A; Kyu, Thein
2006-08-17
A thermodynamically self-consistent theory has been developed to establish binary phase diagrams for two-crystalline polymer blends by taking into consideration all interactions including amorphous-amorphous, crystal-amorphous, amorphous-crystal, and crystal-crystal interactions. The present theory basically involves combination of the Flory-Huggins free energy for amorphous-amorphous isotropic mixing and the Landau free energy of polymer solidification (e.g., crystallization) of the crystalline constituents. The self-consistent solution via minimization of the free energy of the mixture affords determination of eutectic, peritectic, and azeotrope phase diagrams involving various coexistence regions such as liquid-liquid, liquid-solid, and solid-solid coexistence regions bound by liquidus and solidus lines. To validate the present theory, the predicted eutectic phase diagrams have been compared with the reported experimental binary phase diagrams of blends such as polyethylene fractions as well as polycaprolactone/trioxane mixtures.
Perturbation Series in Light-Cone Diagrams of Green Function of String Field
Li, Am-Gil; Li, Chol-Man; Im, Song-Jin
2016-01-01
In this paper, we proved the correspondence between Feynman diagrams in space-time and light-cone diagrams in world-sheet by using only path integral representation on free Green function in the first quantization theory. We also obtained general representation on perturbation series of light-cone diagrams describing split and join of strings.
Collective neurodynamics: Phase diagram
Ovchinnikov, Igor V.; Li, Wenyuan; Schwartz, Robert N.; Hudson, Andrew E.; Meier, Karlheinz; Wang, Kang L.
2016-01-01
Here, we conceptualize the phase diagram of collective short-term bio-chemo-electric component of neurodynamics (S-ND) on the parameter space of externally, e.g., pharmacologically, controllable single-neuron parameters such as the resting potential and/or firing threshold, repolarization time, etc. This concept may become a useful tool for the systematization of knowledge in anesthesiology and provide a fruitful venue for future studies of the high-level S-ND functionalities such as short-te...
Smolec, Radoslaw; Dziembowski, Wojciech; Moskalik, Pawel; Netzel, Henryka; Prudil, Zdenek; Skarka, Marek; Soszynski, Igor
2017-09-01
Over the recent years, the Petersen diagram for classical pulsators, Cepheids and RR Lyr stars, populated with a few hundreds of new multiperiodic variables. We review our analyses of the OGLE data, which resulted in a significant extension of the known, and in the discovery of a few new and distinct forms of multiperiodic pulsation. The showcase includes not only radial mode pulsators, but also radial-non-radial pulsators and stars with significant modulation observed on top of the beat pulsation. First theoretical models explaining the new forms of stellar variability are briefly discussed.
Enriched model categories and diagram categories
Guillou, Bertrand
2011-01-01
We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. One twist is a new perspective on equivariant model categories. A central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between a given V-model category and a category of diagrams in V, where V is any good enriching category. From this perspective, we rederive the result of Schwede and Shipley that reasonable stable model categories are Quillen equivalent to diagram categories of spectra (alias categories of module spectra). The general theory will be applied to G-spectra in a sequel, and for that we need quite a few technical improvements and modifications of general model categorical results. We collect those here. They are bound to have applications in a variety of other contexts.
A pseudo-haptic knot diagram interface
Zhang, Hui; Weng, Jianguang; Hanson, Andrew J.
2011-01-01
To make progress in understanding knot theory, we will need to interact with the projected representations of mathematical knots which are of course continuous in 3D but significantly interrupted in the projective images. One way to achieve such a goal would be to design an interactive system that allows us to sketch 2D knot diagrams by taking advantage of a collision-sensing controller and explore their underlying smooth structures through a continuous motion. Recent advances of interaction techniques have been made that allow progress to be made in this direction. Pseudo-haptics that simulates haptic effects using pure visual feedback can be used to develop such an interactive system. This paper outlines one such pseudo-haptic knot diagram interface. Our interface derives from the familiar pencil-and-paper process of drawing 2D knot diagrams and provides haptic-like sensations to facilitate the creation and exploration of knot diagrams. A centerpiece of the interaction model simulates a "physically" reactive mouse cursor, which is exploited to resolve the apparent conflict between the continuous structure of the actual smooth knot and the visual discontinuities in the knot diagram representation. Another value in exploiting pseudo-haptics is that an acceleration (or deceleration) of the mouse cursor (or surface locator) can be used to indicate the slope of the curve (or surface) of whom the projective image is being explored. By exploiting these additional visual cues, we proceed to a full-featured extension to a pseudo-haptic 4D visualization system that simulates the continuous navigation on 4D objects and allows us to sense the bumps and holes in the fourth dimension. Preliminary tests of the software show that main features of the interface overcome some expected perceptual limitations in our interaction with 2D knot diagrams of 3D knots and 3D projective images of 4D mathematical objects.
Worldline Green functions for multiloop diagrams
Schmidt, M G
1994-01-01
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.
Phase diagram of elastic spheres.
Athanasopoulou, L; Ziherl, P
2017-02-15
Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant-Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.
Calculation of Gallium-metal-Arsenic phase diagrams
Scofield, J. D.; Davison, J. E.; Ray, A. E.; Smith, S. R.
1991-01-01
Electrical contacts and metallization to GaAs solar cells must survive at high temperatures for several minutes under specific mission scenarios. The determination of which metallizations or alloy systems that are able to withstand extreme thermal excursions with minimum degradation to solar cell performance can be predicted by properly calculated temperature constitution phase diagrams. A method for calculating a ternary diagram and its three constituent binary phase diagrams is briefly outlined and ternary phase diagrams for three Ga-As-X alloy systems are presented. Free energy functions of the liquid and solid phase are approximated by the regular solution theory. Phase diagrams calculated using this method are presented for the Ga-As-Ge and Ga-As-Ag systems.
Program Synthesizes UML Sequence Diagrams
Barry, Matthew R.; Osborne, Richard N.
2006-01-01
A computer program called "Rational Sequence" generates Universal Modeling Language (UML) sequence diagrams of a target Java program running on a Java virtual machine (JVM). Rational Sequence thereby performs a reverse engineering function that aids in the design documentation of the target Java program. Whereas previously, the construction of sequence diagrams was a tedious manual process, Rational Sequence generates UML sequence diagrams automatically from the running Java code.
Linkage intensity learning approach with genetic algorithm for causality diagram
Institute of Scientific and Technical Information of China (English)
WANG Cheng-liang; CHEN Juan-juan
2007-01-01
The causality diagram theory, which adopts graphical expression of knowledge and direct intensity of causality, overcomes some shortages in belief network and has evolved into a mixed causality diagram methodology for discrete and continuous variable. But to give linkage intensity of causality diagram is difficult, particularly in many working conditions in which sampling data are limited or noisy. The classic learning algorithm is hard to be adopted. We used genetic algorithm to learn linkage intensity from limited data. The simulation results demonstrate that this algorithm is more suitable than the classic algorithm in the condition of sample shortage such as space shuttle's fault diagnoisis.
Linearly recursive sequences and Dynkin diagrams
Reutenauer, Christophe
2012-01-01
Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\\em frieze}; these sequences are given by nonlinear recursions (with division), and the fact that they are integers is a consequence of the Laurent phenomenon of Fomin and Zelevinsky. If the sequences satisfy a linear recursion with constant coefficients, then the graph must be a Dynkin diagram or an extended Dynkin diagram, with an acyclic orientation. The converse also holds: the sequences of the frieze associated to an oriented Dynkin or Euclidean diagram satisfy linear recursions, and are even $\\mathbb N$-rational. One uses in the proof objects called $SL_2$-{\\em tilings of the plane}, which are fillings of the discrete plane such that each adjacent 2 by 2 minor is equal to 1. These objects, which have applications in the theory of cluster algebras, are interesting for themselves. S...
Collins Model and Phase Diagram of 2D Ternary System
Institute of Scientific and Technical Information of China (English)
XIE Chuan-Mei; CHEN Li-Rong
2004-01-01
The Collins model is introduced into the two-dimensional (2D) alternative ternary system having the Lennard-Jones (L-J) potential. The Gibbs free energy of this ternary system is calculated, and according to thermodynamic theory, a group of equations that determine the solid-liquid diagram of ternary system are derived, some isothermal sectional diagrams of the 2D ternary system are obtained. The results are quite similar to the behavior of three-dimensional substances.
Diagonal Slices of 3D Young Diagrams in the Approach of Maya Diagrams
Cai, Li-Qiang; Wang, Li-Fang; Wu, Ke; Yang, Jie
2014-09-01
According to the correspondence between 2D Young diagrams and Maya diagrams and the relation between 2D and 3D Young diagrams, we construct 3D Young diagrams in the approach of Maya diagrams. Moreover, we formulate the generating function of 3D Young diagrams, which is the MacMahon function in terms of Maya diagrams.
Students' different understandings of class diagrams
Boustedt, Jonas
2012-03-01
The software industry needs well-trained software designers and one important aspect of software design is the ability to model software designs visually and understand what visual models represent. However, previous research indicates that software design is a difficult task to many students. This article reports empirical findings from a phenomenographic investigation on how students understand class diagrams, Unified Modeling Language (UML) symbols, and relations to object-oriented (OO) concepts. The informants were 20 Computer Science students from four different universities in Sweden. The results show qualitatively different ways to understand and describe UML class diagrams and the "diamond symbols" representing aggregation and composition. The purpose of class diagrams was understood in a varied way, from describing it as a documentation to a more advanced view related to communication. The descriptions of class diagrams varied from seeing them as a specification of classes to a more advanced view, where they were described to show hierarchic structures of classes and relations. The diamond symbols were seen as "relations" and a more advanced way was seeing the white and the black diamonds as different symbols for aggregation and composition. As a consequence of the results, it is recommended that UML should be adopted in courses. It is briefly indicated how the phenomenographic results in combination with variation theory can be used by teachers to enhance students' possibilities to reach advanced understanding of phenomena related to UML class diagrams. Moreover, it is recommended that teachers should put more effort in assessing skills in proper usage of the basic symbols and models and students should be provided with opportunities to practise collaborative design, e.g. using whiteboards.
6d SCFTs, 5d Dualities and Tao Web Diagrams
Hayashi, Hirotaka; Lee, Kimyeong; Yagi, Futoshi
2015-01-01
We propose 5d descriptions of 6d ${\\cal N}=(1,0)$ superconformal field theories arising from Type IIA brane configurations with an $O8^-$-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two $O7^-$-planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two $O7^-$-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the $SL(2,\\mathbb{Z})$ duality of Type IIB string theory, leading to completely differen...
Mineev, V. P.
2017-03-01
The temperature-pressure phase diagram of ferromagnetic superconductor UCoGe includes four phase transitions. They are between the paramagnetic and the ferromagnetic states with the subsequent transition in the superconducting ferromagnetic state and between the normal and the superconducting states after which the transition to the superconducting ferromagnetic state has to occur. Here we have developed the Landau theory description of the phase diagram and established the specific ordering arising at each type of transition. The phase transitions to the ferromagnetic superconducting state are inevitably accompanied by the emergence of screening currents. The corresponding magnetostatics considerations allow for establishing the significant difference between the transition from the ferromagnetic to the ferromagnetic superconducting state and the transition from the superconducting to the ferromagnetic superconducting state.
Diagrams and Proofs in Analysis
DEFF Research Database (Denmark)
Carter, Jessica M H Grund
2010-01-01
The article discusses the role of diagrams in mathematical reasoning based on a case study in analysis. In the presented example certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures are replaced by reasoning about permutation groups...
Modeling process flow using diagrams
Kemper, B.; de Mast, J.; Mandjes, M.
2010-01-01
In the practice of process improvement, tools such as the flowchart, the value-stream map (VSM), and a variety of ad hoc variants of such diagrams are commonly used. The purpose of this paper is to present a clear, precise, and consistent framework for the use of such flow diagrams in process
Modeling process flow using diagrams
Kemper, B.; de Mast, J.; Mandjes, M.
2010-01-01
In the practice of process improvement, tools such as the flowchart, the value-stream map (VSM), and a variety of ad hoc variants of such diagrams are commonly used. The purpose of this paper is to present a clear, precise, and consistent framework for the use of such flow diagrams in process improv
Genus Ranges of Chord Diagrams.
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.
Farthest-Polygon Voronoi Diagrams
Cheong, Otfried; Glisse, Marc; Gudmundsson, Joachim; Hornus, Samuel; Lazard, Sylvain; Lee, Mira; Na, Hyeon-Suk
2010-01-01
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region.
Phase Diagrams for Systems Containing Hyperbranched Polymers
Directory of Open Access Journals (Sweden)
Tim Zeiner
2012-01-01
Full Text Available Hyperbranched polymers show an outstanding potential for applications ranging from chemistry over nanotechnology to pharmacy. In order to take advantage of this potential, the underlying phase behaviour must be known. From the thermodynamic point of view, the modelling of these phase diagrams is quite challenging, because the thermodynamic properties depend on the architecture of the hyperbranched polymer as well as on the number and kind of present functional end groups. The influence of architecture can be taken into account via the lattice cluster theory (LCT as an extension of the well-known Flory–Huggins theory. Whereas the Flory–Huggins theory is limited to linear polymer chains, the LCT can be applied to an arbitrary chain architecture. The number and the kind of functional groups can be handled via the Wertheim perturbation theory, applicable for directed forces between the functional groups and the surrounding solvent molecules. The combination of the LCT and the Wertheim theory can be established for the modelling or even prediction of the liquid-liquid equilibria (LLE of polymer solutions in a single solvent or in a solvent mixture or polymer blends, where the polymer can have an arbitrary structure. The applied theory predicts large demixing regions for mixtures of linear polymers and hyperbranched polymers, as well as for mixtures made from two hyperbranched polymers. The introduction of empty lattice sites permits the theoretical investigation of pressure effects on phase behaviour. The calculated phase diagrams were compared with own experimental data or to experimental data taken from literature.
Phase diagram of quantum square ice
Henry, Louis-Paul; Holdsworth, Peter; Mila, Frederic; Roscilde, Tommaso
2013-03-01
We have investigated the ground-state and finite-temperature phase diagram of quantum square ice - realized by the transverse-field Ising model on a checkerboard lattice - using both linear spin-wave (LSW) theory and quantum Monte Carlo (QMC). We generalize the model with different couplings between nearest (J1) and next-to-nearest (J2) neighbors on the checkerboard lattice. Our QMC approach generalizes the loop algorithm - very efficient in the study of constrained classical systems - to a ``brane algorithm'' for quantum systems. At the LSW level the vast degeneracy of the ground-state for J1 =J2 and J2 >J1 remains intact; moreover LSW theory breaks down in extended regions of the phase diagram, pointing at non-classical states. Our QMC study goes beyond perturbative schemes and addresses directly the nature of the low-temperature phases. We have critically examined the possibility of a resonating-plaquette state for J1 =J2 , suggested by degenerate perturbation theory on the ice-rule manifold for weak fields. Our QMC results for finite fields confirm the absence of Néel or collinear order, but they do not confirm the presence of resonating-plaquette order, pointing at a possibly more complex non-classical state.
Particles, Feynman Diagrams and All That
Daniel, Michael
2006-01-01
Quantum fields are introduced in order to give students an accurate qualitative understanding of the origin of Feynman diagrams as representations of particle interactions. Elementary diagrams are combined to produce diagrams representing the main features of the Standard Model.
Resistance of Feynman diagrams and the percolation backbone dimension.
Janssen, H K; Stenull, O; Oerding, K
1999-06-01
We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... .
A Finite Temperature Phase Diagram in Rotating Bosonic Optical Lattices
Institute of Scientific and Technical Information of China (English)
HUANG Bei-Bing; WAN Shao-Long
2011-01-01
A finite temperature phase diagram of the rotating Bose-Hubbard model, including the crossover between Mott insulator and the normal state, is derived on the frame of the Gutzwiller mean-field theory. In addition, we calculate the critical temperature of superBuid-normal phase transition.%@@ A finite temperature phase diagram of the rotating Bose-Hubbard model, including the crossover between Mort insulator and the normal state, is derived on the frame of the Gutzwiller mean-field theory.In addition, we calculate the critical temperature of superfluid-normal phase transition.
Heuristic Diagrams as a Tool to Teach History of Science
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.
The Compressibility of Checkerboard Surfaces of Link Diagrams
Institute of Scientific and Technical Information of China (English)
Zhi Qiang BAO
2007-01-01
Consider the checkerboard surfaces defined by some link diagrams. When they are notorientable, one considers the boundary surfaces of small regular neighborhoods of them. This articlestudies the compressibility problem of these kinds of surfaces in the link complements. The problemis solved by devising a normalization theory for the compressing discs, which brings up an algorithmto read out compressibility directly from the link diagrams. As an application of the algorithm, thecompressibility changes under Reidermeister moves are studied. Diagrams from the knot tables arealso studied, and surprisingly, some of them are shown to define completely compressible surfaces ofthis kind. Infinitely many examples of non-alternating knot diagrams with incompressible surfaces ofthis kind are also constructed.
Causal diagrams for physical models
Kinsler, Paul
2015-01-01
I present a scheme of drawing causal diagrams based on physically motivated mathematical models expressed in terms of temporal differential equations. They provide a means of better understanding the processes and causal relationships contained within such systems.
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
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...
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....
Lau, S. S.; Liu, B. X.; Nicolet, M.-A.
1983-05-01
Interactions induced by ion irradiation are generally considered to be non-equilibrium processes, whereas phase diagrams are determined by phase equilibria. These two entities are seemingly unrelated. However, if one assumes that quasi-equilibrium conditions prevail after the prompt events, subsequent reactions are driven toward equilibrium by thermodynamical forces. Under this assumption, ion-induced reactions are related to equilibrium and therefore to phase diagrams. This relationship can be seen in the similarity that exists in thin films between reactions induced by ion irradiation and reactions induced by thermal annealing. In the latter case, phase diagrams have been used to predict the phase sequence of stable compound formation, notably so in cases of silicide formation. Ion-induced mixing not only can lead to stable compound formation, but also to metastable alloy formation. In some metal-metal systems, terminal solubilities can be greatly extended by ion mixing. In other cases, where the two constituents of the system have different crystal structures, extension of terminal solubility from both sides of the phase diagram eventually becomes structurally incompatible and a glassy (amorphous) mixture can form. The composition range where this bifurcation is likely to occur is in the two-phase regions of the phase diagram. These concepts are potentially useful guides in selecting metal pairs that from metallic glasses by ion mixing. In this report, phenomenological correlation between stable (and metastable) phase formation and phase diagram is discussed in terms of recent experimental data.
de las Heras, Daniel; Schmidt, Matthias
2015-05-20
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.
The limit shape problem for ensembles of Young diagrams
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
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.
Perfect orderings on Bratteli diagrams
Bezuglyi, Sergey; Yassawi, Reem
2012-01-01
Given a Bratteli diagram B, we study the set O(B) of all possible orderings w on a Bratteli diagram B and its subset P(B) consisting of `perfect' orderings that produce Bratteli-Vershik dynamical systems (Vershik maps). We give necessary and sufficient conditions for w to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths affects significantly the values of the entries of the incidence matrices and the structure of the diagram B. Endowing the set O(B) with product measure, we prove that there is some j such that almost all orderings on B have j maximal and minimal paths, and that if j is strictly greater than the number of minimal components that B has, then almost all orderings are imperfect.
Improving modeling with layered UML diagrams
DEFF Research Database (Denmark)
Störrle, Harald
2013-01-01
Layered diagrams are diagrams whose elements are organized into sets of layers. Layered diagrams are routinely used in many branches of engineering, except Software Engineering. In this paper, we propose to add layered diagrams to UML modeling tools, and elaborate the concept by exploring usage...
Nonabelian cut diagrams and their applications
Lam, C S
1996-01-01
A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both the real and the imaginary parts of Feynman diagrams related by permutations. Several applications of the technique are reported, including a resolution of the apparent inconsistency of the baryon problem in large-N_c QCD, a simplified calculation of high-energy low-order QCD diagrams, and progress made with this technique on the unitarization of the BFKL equation.
Applications Of Nonclassical Geometry To String Theory
Zunger, Y
2003-01-01
String theory is built on a foundation of geometry. This thesis examines several applications of geometry beyond the classical Riemannian geometry of curved surfaces. The first part considers the use of extended spaces with internal dimensions to each point (“twistors”) to probe systems with a great deal of symmetry but complicated dynamics. These systems are of critical interest in understanding holographic phenomena in string theory and the origins of entropy. We develop a twistor formulation of coset spaces and use this to write simplified actions for particles and strings on anti-de Sitter space, which are easier to quantize than the ordinary (highly nonlinear) actions. In the second part, we consider two aspects of noncommutative geometry, a generalization of ordinary geometry where points are “fuzzed out” and functions of space become noncommuting operators. We first examine strings with one endpoint on a D-brane in a background magnetic field. (Strings with both ...
Visualizing spacetimes via embedding diagrams
Hledik, Stanislav; Cipko, Alois
2016-01-01
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an intuitive insight into the gravitational field rendered into a curved spacetime, and to assess the influence of parameters like electric charge and spin of a black hole, magnetic field or cosmological constant. Optical reference geometry and related inertial forces and their relationship to embedding diagrams are particularly useful for investigation of test particles motion. Embedding diagrams of static and spherically symmetric, or stationary and axially symmetric black-hole and naked-singularity spacetimes thus present a useful concept for intuitive understanding of these spacetimes' nature. We concentrate on general way of embedding into 3-dimensional Euclidean space, and give a set of illustrative examples.
The Traders' Cross: Identifying Traders' Surpluses in the Traditional Edgeworth Exchange Diagram
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…
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
Electrical elementary diagrams and operators
Energy Technology Data Exchange (ETDEWEB)
Patterson, B.K. [Human Factors Practical Inc., Dipper Harbour, New Brunswick (Canada)]. E-mail: HumanFactors@netscape.ca
2005-07-01
After 40 years of reading and interrupting electrical elementary logic drawings, I have concluded that we need to make a change. We need to write and express our nuclear power plant logic in some other language than relay ladder logic, solid state logic or computer mnemonics. The language should be English, or your native language, and the format should be Descriptive Block Diagrams. (author)
The diagram for phyllotactic series
Directory of Open Access Journals (Sweden)
Joanna Szymanowska-Pułka
2014-01-01
Full Text Available Many authors studying phyllotaxis in various plant species have reported the occurrence of many different numbers of contact parastichy pairs that are members of different Fibonacci-like series. On the basis of these reports a diagram was constructed in which any theoretically possible series was represented by the two first members of a given series.
BIHOURLY DIAGRAMS OF FORBUSH DECREASES
Bihourly diagrams were made of Forbush decreases of cosmic ray intensity as observed at Uppsala from 31 Aug 56 to 31 Dec 59, at Kiruna from Nov 56 to 31 Dec 59, and at Murchison Bay from 26 Aug 57 to 30 Apr 59. (Author)
Phase diagram of Hertzian spheres
Pàmies, J.C.; Cacciuto, A.; Frenkel, D.
2009-01-01
We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of wea
Bayesian Networks and Influence Diagrams
DEFF Research Database (Denmark)
Kjærulff, Uffe Bro; Madsen, Anders Læsø
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new...
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...
Multi-currency Influence Diagrams
DEFF Research Database (Denmark)
Nielsen, Søren Holbech; Nielsen, Thomas Dyhre; Jensen, Finn Verner
2004-01-01
that the converted problem is equivalent to the original one. In this paper we present an extension of the Influence Diagram framework, which allows for these decision problems to be modelled in their original form. We present an algorithm that, given a conversion function between the currencies, discovers...
The Coulomb Branch of 3d N= 4 Theories
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.
Basic principles of Hasse diagram technique in chemistry.
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.
Resummation of Cactus Diagrams in Lattice QCD, to all Orders
Panagopoulos, H
2000-01-01
We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.
Revised Phase Diagram of the Gross-Neveu Model
Thies, M; Thies, Michael; Urlichs, Konrad
2003-01-01
We confirm earlier hints that the conventional phase diagram of the discrete chiral Gross-Neveu model in the large N limit is deficient at non-zero chemical potential. We present the corrected phase diagram constructed in mean field theory. It has three different phases, including a kink-antikink crystal phase. All transitions are second order. The driving mechanism for the new structure of baryonic matter in the Gross-Neveu model is an Overhauser type instability with gap formation at the Fermi surface.
Invariants in the Yukawa system’s thermodynamic phase diagram
DEFF Research Database (Denmark)
Veldhorst, Arno; Schrøder, Thomas; Dyre, Jeppe C.
2015-01-01
phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method...... of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas...
Phase diagram of twisted mass lattice QCD
Sharpe, Stephen R.; Wu, Jackson M.
2004-11-01
We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m2π/(4πfπ)2˜aΛ (a being the lattice spacing, and Λ=ΛQCD). We then focus on the region where m2π/(4πfπ)2˜(aΛ)2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is nonvanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transition extends into the twisted mass plane, ending with two symmetrical second order points at which the mass of the neutral pion vanishes. We provide graphs of the condensate and pion masses for both scenarios, and note a simple mathematical relation between them. These results may be of importance to numerical simulations.
Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective
Textor, Johannes
2012-01-01
Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.
QCD phase diagram with isospin chemical potential
Brandt, Bastian B
2016-01-01
In this contribution we investigate the phase diagram of QCD in the presence of an isospin chemical potential. To alleviate the infrared problems of the theory associated with pion condensation, we introduce the pionic source as an infrared regulator. We discuss various methods to extrapolate the results to vanishing pionic source, including a novel method based on the singular value spectrum of the massive Dirac operator, a leading-order reweighting and a spline Monte-Carlo fit. Our main results concern the phase transition boundary between the normal and the pion condensation phases and the chiral/deconfinement transition temperature as a function of the chemical potential. In addition, we perform a quantitative comparison between our direct results and a Taylor-expansion obtained at zero chemical potential to assess the applicability range of the latter.
Hero's journey in bifurcation diagram
Monteiro, L. H. A.; Mustaro, P. N.
2012-06-01
The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films.
Anatomy of geodesic Witten diagrams
Chen, Heng-Yu; Kuo, En-Jui; Kyono, Hideki
2017-05-01
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.
Hubble's diagram and cosmic expansion
Kirshner, Robert P.
2003-01-01
Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168–173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velo...
Hubble's diagram and cosmic expansion
Kirshner, Robert P.
2003-01-01
Edwin Hubble's classic article on the expanding universe appeared in PNAS in 1929 [Hubble, E. P. (1929) Proc. Natl. Acad. Sci. USA 15, 168–173]. The chief result, that a galaxy's distance is proportional to its redshift, is so well known and so deeply embedded into the language of astronomy through the Hubble diagram, the Hubble constant, Hubble's Law, and the Hubble time, that the article itself is rarely referenced. Even though Hubble's distances have a large systematic error, Hubble's velo...
Reliability computation from reliability block diagrams
Chelson, P. O.; Eckstein, E. Y.
1975-01-01
Computer program computes system reliability for very general class of reliability block diagrams. Four factors are considered in calculating probability of system success: active block redundancy, standby block redundancy, partial redundancy, and presence of equivalent blocks in the diagram.
Phase diagram of crushed powders
Bodard, Sébastien; Jalbaud, Olivier; Saurel, Richard; Burtschell, Yves; Lapebie, Emmanuel
2016-12-01
Compression of monodisperse powder samples in quasistatic conditions is addressed in a pressure range such that particles fragmentation occurs while the solid remains incompressible (typical pressure range of 1-300 MPa for glass powders). For a granular bed made of particles of given size, the existence of three stages is observed during compression and crush up. First, classical compression occurs and the pressure of the granular bed increases along a characteristic curve as the volume decreases. Then, a critical pressure is reached for which fragmentation begins. During the fragmentation process, the granular pressure stays constant in a given volume range. At the end of this second stage, 20%-50% of initial grains are reduced to finer particles, depending on the initial size. Then the compression undergoes the third stage and the pressure increases along another characteristic curve, in the absence of extra fragmentation. The present paper analyses the analogies between the phase transition in liquid-vapour systems and powder compression with crush-up. Fragmentation diagram for a soda lime glass is determined by experimental means. The analogues of the saturation pressure and latent heat of phase change are determined. Two thermodynamic models are then examined to represent the crush-up diagram. The first one uses piecewise functions while the second one is of van der Waals type. Both equations of state relate granular pressure, solid volume fraction, and initial particle diameter. The piecewise functions approach provides reasonable representations of the phase diagram while the van der Waals one fails.
Scheil-Gulliver Constituent Diagrams
Pelton, Arthur D.; Eriksson, Gunnar; Bale, Christopher W.
2017-03-01
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.
Operations space diagram for ECRH and ECCD
DEFF Research Database (Denmark)
Bindslev, H.
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...
Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams
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…
Diagram, a Learning Environment for Initiation to Object-Oriented Modeling with UML Class Diagrams
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…
Puente, Elsa
2011-01-01
For $n \\geq 1$, the twistor space $\\mathfrak{Z}(\\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\\mathbf{G}(n+1, 2n+2)$, of the set of graphs of skew-symmetric linear endomorphism of $\\mathbb{C}^{n+1}$. We use this fact to describe a natural stratification of the twistor space $\\mathfrak{Z}(\\mathbb{S}^{2n})$ with $n \\geq 3$, in terms of what we have called {\\it generalised complex orthogonal Stiefel manifolds} of $\\mathbb{C}^{n+1}$. In particular, the twistor space $\\mathfrak{Z}(\\mathbb{S}^{6})$ is biholomorphic to a non-singular complex quadric hypersurface in $\\mathbb{P}^{7}$. We explicitly construct a real-analytic foliation, by linear 3-folds, of this quadric hypersurface such that the quotient space is isomorphic to the 6-sphere with its standard metric. This foliation is Riemannian with respect to the Fubini-Study metric and isometrically equivalent to the twistor fibration over the 6-sphere.
Origin and use of crystallization phase diagrams.
Rupp, Bernhard
2015-03-01
Crystallization phase diagrams are frequently used to conceptualize the phase relations and also the processes taking place during the crystallization of macromolecules. While a great deal of freedom is given in crystallization phase diagrams owing to a lack of specific knowledge about the actual phase boundaries and phase equilibria, crucial fundamental features of phase diagrams can be derived from thermodynamic first principles. Consequently, there are limits to what can be reasonably displayed in a phase diagram, and imagination may start to conflict with thermodynamic realities. Here, the commonly used `crystallization phase diagrams' are derived from thermodynamic excess properties and their limitations and appropriate use is discussed.
Using Affinity Diagrams to Evaluate Interactive Prototypes
DEFF Research Database (Denmark)
Lucero, Andrés
2015-01-01
Affinity diagramming is a technique used to externalize, make sense of, and organize large amounts of unstructured, far-ranging, and seemingly dissimilar qualitative data. HCI and interaction design practitioners have adopted and used affinity diagrams for different purposes. This paper discusses...... 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...
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...
Topologically distinct Feynman diagrams for mass operator in electron-phonon interaction
Directory of Open Access Journals (Sweden)
C.C. Tovstyuk
2009-01-01
Full Text Available The new method for designing topologically distinct Feynman diagrams for electron's mass operator in electron-phonon interaction is developed using the permutation group theory. The carried out classification of DPs allows to choose the classes, corresponding to disconnected diagrams, to singly connected diagrams, direct ("tadpole" diagrams, to diagrams corresponding to phonon Green functions. After this classification the set of considered double permutations is reduced to one class since only these are relevant to mass operator. We derive analytical expressions which allow to identify the DP, and to choose the phonon components, which are not accepted in every type. To avoid repetition of asymmetric diagrams, which correspond to the same analytical expression, we introduce the procedure of inversion in phonon component, and identify symmetric as well as a pair of asymmetric phonon components. For every type of DP (denoted by its digital encoding, taking into account its symmetry, we perform a set of transformations on this DP, list all DPs of the type and all the corresponding Feynman diagrams of mass operator automatically. It is clear that no more expressions (diagrams for the relevant order of perturbation theory for mass operator can be designed.
Grid diagrams and Khovanov homology
DEFF Research Database (Denmark)
Droz, Jean-Marie; Wagner, Emmanuel
2009-01-01
We explain how to compute the Jones polynomial of a link from one of its grid diagrams and we observe a connection between Bigelow’s homological definition of the Jones polynomial and Kauffman’s definition of the Jones polynomial. Consequently, we prove that the Maslov grading on the Seidel......–Smith symplectic link invariant coincides with the difference between the homological grading on Khovanov homology and the Jones grading on Khovanov homology. We give some evidence for the truth of the Seidel–Smith conjecture....
Phase diagram of colloid-rod system
Lai, S. K.; Xiao, Xuhui
2010-01-01
The semigrand ensemble theory [H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren, Europhys. Lett. 20, 559 (1992)] in conjunction with the fundamental measure density functional theory [V. B. Warshavsky and X. Song, Phys. Rev. E 69, 061113 (2004)] are used to construct the Helmholtz free energy densities of a mixture of uncharged colloidal hard spheres and colloidal rods in its solid and liquid phases. Given these free energy density functions, we apply the free energy density minimization method [G. F. Wang and S. K. Lai, Phys. Rev. E 70, 051402 (2004)] to crosshatch the system's regions of phases in coexistence. The calculated results show that the triangular area bounded by gas-liquid, gas-solid, and liquid-solid coexisting two phases which has been called the coexistence region of gas-liquid-solid corresponds in fact to sets of two phases in coexistence. The phase boundaries which define our calculated coexistence domains compare very well with previous theoretical calculations. The relevance of the phase-diagram domains to three phases in coexistence will be discussed.
Phase Diagrams of Nuclear Pasta
Caplan, Matthew; Horowitz, Chuck; Berry, Don; da Silva Schneider, Andre
2016-03-01
In the inner crust of neutrons stars, where matter is near the saturation density, protons and neutrons arrange themselves into complex structures called nuclear pasta. Early theoretical work predicted a simple graduated hierarchy of pasta phases, consisting of spheres, cylinders, slabs, and uniform matter with voids. Previous work has simulated these phases with a simple classical model and has shown that the formation of these structures is dependent on the temperature, density, and proton fraction. However, previous work only studied a limited range of these parameters due to computational limitations. Thanks to recent advances in computing it is now possible to survey the structure of nuclear pasta for a larger range of parameters. By simulating nuclear pasta with constant temperature and proton fraction in an expanding simulation volume we are able to study the phase transitions in nuclear pasta, and thus produce a set of phase diagrams. We report on these phase diagrams as well as newly identified phases of nuclear pasta and discuss their implications for neutron star observables.
Massless scalar Feynman diagrams: five loops and beyond
Broadhurst, David J
2016-01-01
Several powerful techniques for evaluating massless scalar Feynman diagrams are developed, viz: the solution of recurrence relations to evaluate diagrams with arbitrary numbers of loops in $n=4-2\\omega$ dimensions; the discovery and use of symmetry properties to restrict and compute Taylor series in $\\omega$; the reduction of triple sums over Chebyshev polynomials to products of Riemann zeta functions; the exploitation of conformal invariance to avoid four-dimensional Racah coefficients. As an example of the power of these techniques we evaluate all of the 216 diagrams, with 5 loops or less, which give finite contributions of order $1/k^2$ or $1/k^4$ to a propagator of momentum $k$ in massless four-dimensional scalar field theories. Remarkably, only 5 basic numbers are encountered: $\\zeta(3)$, $\\zeta(5)$, $\\zeta(7)$, $\\zeta(9)$ and the value of the most symmetrical diagram, which is calculated to 14 significant figures. It is conceivable that these are the only irrationals appearing in 6-loop beta functions. ...
Continuation of point clouds via persistence diagrams
Gameiro, Marcio; Hiraoka, Yasuaki; Obayashi, Ippei
2016-11-01
In this paper, we present a mathematical and algorithmic framework for the continuation of point clouds by persistence diagrams. A key property used in the method is that the persistence map, which assigns a persistence diagram to a point cloud, is differentiable. This allows us to apply the Newton-Raphson continuation method in this setting. Given an original point cloud P, its persistence diagram D, and a target persistence diagram D‧, we gradually move from D to D‧, by successively computing intermediate point clouds until we finally find a point cloud P‧ having D‧ as its persistence diagram. Our method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.
Mathematical review on source-type diagrams
Aso, Naofumi; Ohta, Kazuaki; Ide, Satoshi
2016-03-01
A source-type diagram is a visualization tool used to display earthquake sources, including double-couples, compensated linear vector dipoles, and isotropic deformation. Together with recent observations of non-double-couple events in a variety of tectonic settings, it is important to be able to recognize the source type intuitively from a representative diagram. Since previous works have proposed diagrams created using a range of projections, we review these diagrams in the framework of the moment tensor eigenvalue space. For further applications, we also provide complete formulas for conversion between moment tensor representation and the coordinate system of each diagram style. Using both a global catalog and synthetic data, we discuss differences between types of diagrams and the relative effectiveness of each.
Retrospect and Prospect of the Influence Diagram
Institute of Scientific and Technical Information of China (English)
LiuYanqiong; ShenYongping; ChenYingwu
2005-01-01
The evaluation algorithm and the application of the influence diagram were surveyed, which argues that to construct an explicit,compact and objective influence diagram is of the most importance. There are two suggested ways for realization of the influence diagram: introducing the achievements of the modern psychology, cognitive science, behavior science, and so on to represent and solve uncertainty to build a well-constructed influence diagram; based on the observed data to build an influence diagram. Also, the limitations of the influence diagram were analyzed, such as that it cannot deal with asynunetric problems efficiently, cannot picture dynamic problems,cannot model the problems with a limitless horizon, and ther is no highly efficient algorithm. And some potential methods to overcome these limitations were pointed out.
Rajagopal, K
1999-01-01
The QCD vacuum in which we live, which has the familiar hadrons as its excitations, is but one phase of QCD, and far from the simplest one at that. One way to better understand this phase and the nonperturbative dynamics of QCD more generally is to study other phases and the transitions between phases. We are engaged in a voyage of exploration, mapping the QCD phase diagram as a function of temperature T and baryon number chemical potential mu . Because of asymptotic freedom, the high temperature and high baryon density phases of QCD are more simply and more appropriately described in terms of quarks and gluons as degrees of freedom, rather than hadrons. The chiral symmetry breaking condensate which characterizes the vacuum phase melts away. At high densities, quarks form Cooper pairs and new condensates develop. The formation of such superconducting phases requires only weak attractive interactions; these phases may nevertheless break chiral symmetry and have excitations which are indistinguishable from thos...
Solving Limited Memory Influence Diagrams
Mauá, Denis Deratani; Zaffalon, Marco
2011-01-01
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and $10^{64}$ solutions. We show that the problem is NP-hard even if the underlying graph structure of the problem has small treewidth and the variables take on a bounded number of states, but that a fully polynomial time approximation scheme exists for these cases. Moreover, we show that the bound on the number of states is a necessary condition for any efficient approximation scheme.
Phase diagram of ammonium nitrate
Dunuwille, M.; Yoo, C. S.
2014-05-01
Ammonium Nitrate (AN) has often subjected to uses in improvised explosive devices, due to its wide availability as a fertilizer and its capability of becoming explosive with slight additions of organic and inorganic compounds. Yet, the origin of enhanced energetic properties of impure AN (or AN mixtures) is neither chemically unique nor well understood -resulting in rather catastrophic disasters in the past1 and thereby a significant burden on safety in using ammonium nitrates even today. To remedy this situation, we have carried out an extensive study to investigate the phase stability of AN at high pressure and temperature, using diamond anvil cells and micro-Raman spectroscopy. The present results confirm the recently proposed phase IV-to-IV' transition above 17 GPa2 and provide new constraints for the melting and phase diagram of AN to 40 GPa and 400 °C.
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.
Process Flow Diagrams for Training and Operations
Venter, Jacobus
This paper focuses on the use of process flow diagrams for training first responders who execute search and seizure warrants at electronic crime scenes. A generic process flow framework is presented, and the design goals and layout characteristics of process flow diagrams are discussed. An evaluation of the process flow diagrams used in training courses indicates that they are beneficial to first responders performing searches and seizures, and they speed up investigations, including those conducted by experienced personnel.
The spectroscopic Hertzsprung-Russell diagram
Langer, N
2014-01-01
The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. ...
Hofstadter Butterfly Diagram in Noncommutative Space
Takahashi, H; Takahashi, Hidenori; Yamanaka, Masanori
2006-01-01
We study an energy spectrum of electron moving under the constant magnetic field in two dimensional noncommutative space. It take place with the gauge invariant way. The Hofstadter butterfly diagram of the noncommutative space is calculated in terms of the lattice model which is derived by the Bopp's shift for space and by the Peierls substitution for external magnetic field. We also find the fractal structure in new diagram. Although the global features of the new diagram are similar to the diagram of the commutative space, the detail structure is different from it.
The origins of Penrose diagrams in physics, art, and the psychology of perception, 1958-62.
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.
Stage line diagram: An age-conditional reference diagram for tracking development
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.
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
The phase diagram of water at negative pressures: virtual ices.
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.
Calculated Phase Diagram for the γ⇌α Transition in Ce
DEFF Research Database (Denmark)
Johansson, Børje; Abrikosov, I. A.; Aldén, Magnus
1995-01-01
We have calculated the pressure-temperature phase diagram of the γ⇌α isostructural transition in Ce on the basis of the Mott transition model. The theory correctly describes the linear variation of the transition temperature with pressure and the existence of a critical point. The quantitative...... agreement with the experimental diagram is good. The influence of different free energy contributions (configurational, magnetic, and vibrational) on the phase transition in Ce is discussed....
Phase Diagrams and Tricritical Behaviour of the Spin-2 Ising Model in a Longitudinal Random Field
Institute of Scientific and Technical Information of China (English)
LIANG Ya-Qiu; WEI Guo-Zhu; ZHANG Qi; SONG Guo-Li
2004-01-01
@@ Within the framework of the effective-field theory with correlations, we study the ferromagnetic spin-2 randomfield Ising model (RFIM) in the presence of a crystal field on honeycomb (z = 3), square (z = 4) and simple cubic (z = 6) lattices. The effects of the crystal field and the longitudinal random field on the phase diagrams are investigated. Some characteristic features of the phase diagrams, such as the tricritical phenomena, reentrant phenomena and existence of two tricritical points, are found.
Phase Diagram of Wilson and Twisted Mass Fermions at finite isospin chemical potential
Kieburg, M; Verbaarschot, J J M; Zafeiropoulos, S
2014-01-01
Wilson Fermions with untwisted and twisted mass are widely used in lattice simulations. Therefore one important question is whether the twist angle and the lattice spacing affect the phase diagram. We briefly report on the study of the phase diagram of QCD in the parameter space of the degenerate quark masses, isospin chemical potential, lattice spacing, and twist angle by employing chiral perturbation theory. Moreover we calculate the pion masses and their dependence on these four parameters.
Darwin's diagram of divergence of taxa as a causal model for the origin of species.
Bouzat, Juan L
2014-03-01
On the basis that Darwin's theory of evolution encompasses two logically independent processes (common descent and natural selection), the only figure in On the Origin of Species (the Diagram of Divergence of Taxa) is often interpreted as illustrative of only one of these processes: the branching patterns representing common ancestry. Here, I argue that Darwin's Diagram of Divergence of Taxa represents a broad conceptual model of Darwin's theory, illustrating the causal efficacy of natural selection in producing well-defined varieties and ultimately species. The Tree Diagram encompasses the idea that natural selection explains common descent and the origin of organic diversity, thus representing a comprehensive model of Darwin's theory on the origin of species. I describe Darwin's Tree Diagram in relation to his argumentative strategy under the vera causa principle, and suggest that the testing of his theory based on the evidence from the geological record, the geographical distribution of organisms, and the mutual affinities of organic beings can be framed under the hypothetico-deductive method. Darwin's Diagram of Divergence of Taxa therefore represents a broad conceptual model that helps understanding the causal construction of Darwin's theory of evolution, the structure of his argumentative strategy, and the nature of his scientific methodology.
Phase diagram of hot QCD in an external magnetic field
Energy Technology Data Exchange (ETDEWEB)
Fraga, Eduardo; Mizher, Ana Julia [Instituto de Fisica, Universidade Federal do Rio de Janeiro, CP 68528, Rio de Janeiro, 21945-970 RJ (Brazil); Chernodub, Maxim [Laboratoire de Mathematiques et Physique Theorique - LMPT, CNRS UMR 6083 Tours, Federation Denis Poisson, Faculte des Sciences et Techniques, Universite Francois Rabelais, Parc de Grandmont, 37200 Tours (France)
2010-07-01
The structure of the phase diagram for strong interactions becomes richer in the presence of a magnetic background, which enters as a new control parameter for the thermodynamics, and can exhibit new phases and interesting features. Motivated by the relevance of this physical setting for current and future high-energy heavy ion collision experiments and for the cosmological QCD transitions, we use the linear sigma model coupled to quarks and to Polyakov loops as an effective theory to investigate how the chiral and the deconfining transitions are affected, and present a general picture for the temperature-magnetic field phase diagram. We compute and discuss each contribution to the effective potential for the approximate order parameters, and uncover new phenomena such as the para-magnetically-induced breaking of Z(3). (authors)
Complete Phase Diagrams for a Holographic Superconductor/Insulator System
Horowitz, Gary T
2010-01-01
The gravitational dual of an insulator/superconductor transition driven by increasing the chemical potential has recently been constructed. However, the system was studied in a probe limit and only a part of the phase diagram was obtained. We include the backreaction and construct the complete phase diagram for this system. For fixed chemical potential there are typically two phase transitions as the temperature is lowered. Surprisingly, for a certain range of parameters, the system first becomes a superconductor and then becomes an insulator as the temperature approaches zero. As a byproduct of our analysis, we also construct the gravitational dual of a Bose-Einstein condensate of glueballs in a confining gauge theory.
One-loop diagrams in the random Euclidean matching problem
Lucibello, Carlo; Parisi, Giorgio; Sicuro, Gabriele
2017-01-01
The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e., the optimal matching problem between points randomly distributed on a d -dimensional Euclidean space, where the cost to minimize depends on the points' pairwise distances. Using Mayer's cluster expansion we write a formal expression for the replicated action that is suitable for a saddle point computation. We give the diagrammatic rules for each term of the expansion, and we analyze in detail the one-loop diagrams. A characteristic feature of the theory, when diagrams are perturbatively computed around the mean field part of the action, is the vanishing of the mass at zero momentum. In the non-Euclidean case of uncorrelated costs instead, we predict and numerically verify an anomalous scaling for the sub-sub-leading correction to the asymptotic average cost.
Formal verification of Simulink/Stateflow diagrams a deductive approach
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.
Phase diagram of hydrogen adsorbed on Ni(111)
Nagai, Kiyoshi; Ohno, Yuichi; Nakamura, Takashi
1984-08-01
The phase diagram for the H/Ni(111) system is calculated by treating a lattice gas on a honeycomb lattice through the position-space renormalization-group theory with prefacing transformation. The following interparticle interactions are considered: (A) nearest-neighbor exclusion, second-neighbor repulsion, and third-neighbor attraction, which was previously proposed by Domany et al.; (B) nearest-neighbor exclusion, second- and third-neighbor repulsions, and further-neighbor interactions up to the sixth-neighbor one. When the interaction parameters involved are suitably adjusted, both the interactions (A) and (B) lead to the phase diagrams in good agreement with the experimental one by Christmann et al. The change of the isosteric heat of hydrogen adsorption with the adsorbed amount is also calculated. The result obtained from interaction (B) is consistent with experiment, whereas that from interaction (A) is not.
Lubrication modes and the IRG transition diagram
Schipper, D.J.; Gee, de A.W.J.
1995-01-01
The relationship between a Lubrication Mode Diagram (LMD) for concentrated contacts (LCC's) and the IRG transition diagram has been studied. In addition, scuffing results, obtained by the IRG (International Research Group) have been analysed, as well as the results of scuffing tests performed by dif
Comprehending process diagrams in biology education
Kragten, M.
2015-01-01
Students in secondary Science education seem to have difficulties with comprehending diagrams. Process diagrams are an important type of representation in Biology for explaining processes like protein synthesis, compound cycles, etc. In this thesis, we aimed at getting deeper insight into students’
Ferroelectric phase diagram of PVDF:PMMA
Li, M.; Stingelin, N.; Michels, J.J.; Spijkman, M.-J.; Asadi, K.; Feldman, K.; Blom, P.W.M.; Leeuw, D.M. de
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 α- and β-phase PVDF was identified. Ferroelectric β-PVDF:PMMA blend films were made b
Ferroelectric Phase Diagram of PVDF : PMMA
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 w
Automatically extracting class diagrams from spreadsheets
Hermans, F.; Pinzger, M.; Van Deursen, A.
2010-01-01
The use of spreadsheets to capture information is widespread in industry. Spreadsheets can thus be a wealthy source of domain information. We propose to automatically extract this information and transform it into class diagrams. The resulting class diagram can be used by software engineers to under
Structural Controllability and Observability in Influence Diagrams
Chan, Brian Y.; Shachter, Ross D.
2013-01-01
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are fundamental concepts in dynamic systems (Luenberger 1979). Controllability corresponds to the ability to control a system while observability a...
Automatic fitting procedure for the fundamental diagram
Knoop, V.L.; Daamen, W.
2014-01-01
The fundamental diagram of a road, including free flow capacity and queue discharge rate, is very important for traffic engineering purposes. In the real word, most traffic measurements come from stationary loop detectors. This paper proposes a method to fit Wu’s fundamental diagram to loop detector
Persistence Diagrams and the Heat Equation Homotopy
Fasy, Brittany Terese
2010-01-01
Persistence homology is a tool used to measure topological features that are present in data sets and functions. Persistence pairs births and deaths of these features as we iterate through the sublevel sets of the data or function of interest. I am concerned with using persistence to characterize the difference between two functions f, g : M -> R, where M is a topological space. Furthermore, I formulate a homotopy from g to f by applying the heat equation to the difference function g-f. By stacking the persistence diagrams associated with this homotopy, we create a vineyard of curves that connect the points in the diagram for f with the points in the diagram for g. I look at the diagrams where M is a square, a sphere, a torus, and a Klein bottle. Looking at these four topologies, we notice trends (and differences) as the persistence diagrams change with respect to time.
Free-Body Diagrams: Necessary or Sufficient?
Rosengrant, David; Van Heuvelen, Alan; Etkina, Eugenia
2005-09-01
The Rutgers PAER group is working to help students develop various scientific abilities. One of the abilities is to create, understand and learn to use for qualitative reasoning and problem solving different representations of physical processes such as pictorial representations, motion diagrams, free-body diagrams, and energy bar charts. Physics education literature indicates that using multiple representations is beneficial for student understanding of physics ideas and for problem solving. We developed a special approach to construct and utilize free-body diagrams for representing physical phenomena and for problem solving. We will examine whether students draw free-body diagrams in solving problems when they know they will not receive credit for it; the consistency of their use in different conceptual areas; and if students who use free-body diagrams while solving problems in different areas of physics are more successful then those who do not.
Faceting diagram for sticky steps
Directory of Open Access Journals (Sweden)
Noriko Akutsu
2016-03-01
Full Text Available Faceting diagrams for the step-faceting zone, the step droplet zone, and the Gruber-Mullins-Pokrovsky-Talapov (GMPT zone for a crystal surface are obtained by using the density matrix renormalization group method to calculate the surface tension. The model based on these calculations is the restricted solid-on-solid (RSOS model with a point-contact-type step-step attraction (p-RSOS model on a square lattice. The point-contact-type step-step attraction represents the energy gain obtained by forming a bonding state with orbital overlap at the meeting point of the neighboring steps. In the step-faceting zone, disconnectedness in the surface tension leads to the formation of a faceted macrostep on a vicinal surface at equilibrium. The disconnectedness in the surface tension also causes the first-order shape transition for the equilibrium shape of a crystal droplet. The lower zone boundary line (ZBL, which separates the step-faceting zone and the step droplet zone, is obtained by the condition γ 1 = lim n → ∞ γ n / n , where γn is the step tension of the n-th merged step. The upper ZBL, which separates the GMPT zone and the step droplet zone, is obtained by the condition Aq,eff = 0 and Bq,eff = 0, where Aq,eff and Bq,eff represent the coefficients for the | q → | 2 term and the | q → | 3 term, respectively, in the | q → | -expanded form of the surface free energy f eff ( q → . Here, q → is the surface gradient relative to the (111 surface. The reason why the vicinal surface inclined in the 〈101〉 direction does not exhibit step-faceting is explained in terms of the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero.
Topological M-theory as Unification of Form Theories of Gravity
Dijkgraaf, R; Neitzke, A; Vafa, C; Dijkgraaf, Robbert; Gukov, Sergei; Neitzke, Andrew; Vafa, Cumrun
2004-01-01
We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory one can classically obtain 6-dimensional topological A and B models, the topological sector of loop quantum gravity in 4 dimensions, and Chern-Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective we find hints of an intriguing holographic link between non-supersymmetric Yang-Mills in 4 dimensions and A model topological strings on twistor...
Breviz: Visualizing Spreadsheets using Dataflow Diagrams
Hermans, Felienne; van Deursen, Arie
2011-01-01
Spreadsheets are used extensively in industry, often for business critical purposes. In previous work we have analyzed the information needs of spreadsheet professionals and addressed their need for support with the transition of a spreadsheet to a colleague with the generation of data flow diagrams. In this paper we describe the application of these data flow diagrams for the purpose of understanding a spreadsheet with three example cases. We furthermore suggest an additional application of the data flow diagrams: the assessment of the quality of the spreadsheet's design.
Modeling Workflow Using UML Activity Diagram
Institute of Scientific and Technical Information of China (English)
Wei Yinxing(韦银星); Zhang Shensheng
2004-01-01
An enterprise can improve its adaptability in the changing market by means of workflow technologies. In the build time, the main function of Workflow Management System (WFMS) is to model business process. Workflow model is an abstract representation of the real-world business process. The Unified Modeling Language (UML) activity diagram is an important visual process modeling language proposed by the Object Management Group (OMG). The novelty of this paper is representing workflow model by means of UML activity diagram. A translation from UML activity diagram to π-calculus is established. Using π-calculus, the deadlock property of workflow is analyzed.
Shock dynamics of phase diagrams
Moro, Antonio
2014-01-01
A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the simplest model that predicts the occurrence of a critical point associated with the gas-liquid phase transition. Nevertheless, below the critical temperature, theoretical predictions of the van der Waals theory significantly depart from the observed physical behaviour. We develop a novel approach to classical thermodynamics based on the solution of Maxwell relations for a generalised family of nonlocal entropy functions. This theory provides an exact mathematical description of discontinuities of the order parameter within the phase transition region, it explains the universal form of the equations of state and the occurrence of triple points in terms of the dynamics of nonlinear shock wave fronts.
Phase diagrams for surface alloys
DEFF Research Database (Denmark)
Christensen, Asbjørn; Ruban, Andrei; Stoltze, Per
1997-01-01
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...... in detail the cases Ag/Cu(100), Pt/Cu(111), Ag/Pt(111), Co/Cu(111), Fe/Cu(111), and Pd/Cu(110) in connection with available experimental results....
Phase diagram of the triangular-lattice Potts antiferromagnet
Lykke Jacobsen, Jesper; Salas, Jesús; Scullard, Christian R.
2017-08-01
We study the phase diagram of the triangular-lattice Q-state Potts model in the real (Q, v) -plane, where v=e^J-1 is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding Ap-1 RSOS model on the torus, for integer p=4, 5, \\ldots, 8 . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.
Phase Diagrams of Electric-Fduced Aggregation in Conducting Colloids
Khusid, B.; Acrivos, A.
1999-01-01
Under the application of a sufficiently strong electric field, a suspension may undergo reversible phase transitions from a homogeneous random arrangement of particles into a variety of ordered aggregation patterns. The surprising fact about electric-field driven phase transitions is that the aggregation patterns, that are observed in very diverse systems of colloids, display a number of common structural features and modes of evolution thereby implying that a universal mechanism may exist to account for these phenomena. It is now generally believed that this mechanism emanates from the presence of the long-range anisotropic interactions between colloidal particles due to their polarization in an applied field. But, in spite of numerous applications of the electric-field-driven phenomena in biotechnology, separation, materials engineering, chemical analysis, etc. our understanding of these phenomena is far from complete. Thus, it is the purpose of the proposed research to develop a theory and then test experimentally, under normal- and low-gravity conditions, the accuracy of the theoretical predictions regarding the effect of the synergism of the interparticle electric and hydrodynamic interactions on the phase diagram of a suspension. The main results from our theoretical studies performed to-date enable one to trace how the variations of the electrical properties of the constituent materials influence the topology of the suspension phase diagram and then, by using an appropriate phase diagram, to evaluate how the electric-field-induced transformations will depend on the frequency and the strength of the applied field.
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.
Between Analogue and Digital Diagrams
Directory of Open Access Journals (Sweden)
Zoltan Bun
2012-10-01
Full Text Available This essay is about the interstitial. About how the diagram, as a method of design, has lead fromthe analogue deconstruction of the eighties to the digital processes of the turn of the millennium.Specifically, the main topic of the text is the interpretation and the critique of folding (as a diagramin the beginning of the nineties. It is necessary then to unfold its relationship with immediatelypreceding and following architectural trends, that is to say we have to look both backwards andforwards by about a decade. The question is the context of folding, the exchange of the analogueworld for the digital. To understand the process it is easier to investigate from the fields of artand culture, rather than from the intentionally perplicated1 thoughts of Gilles Deleuze. Both fieldsare relevant here because they can similarly be used as the yardstick against which the era itselfit measured. The cultural scene of the eighties and nineties, including performing arts, movies,literature and philosophy, is a wide milieu of architecture. Architecture responds parallel to itsera; it reacts to it, and changes with it and within it. Architecture is a medium, it has always beena medium, yet the relations are transformed. That’s not to say that technical progress, for exampleusing CAD-software and CNC-s, has led to the digital thinking of certain movements ofarchitecture, (it is at most an indirect tool. But the ‘up-to-dateness’ of the discipline, however,a kind of non-servile reading of an ‘applied culture’ or ‘used philosophy’2 could be the key.(We might recall here, parenthetically, the fortunes of the artistic in contemporary mass society.The proliferation of museums, the magnification of the figure of the artist, the existence of amassive consumption of printed and televised artistic images, the widespread appetite for informationabout the arts, all reflect, of course, an increasingly leisured society, but also relateprecisely to the fact
Quantum Bubble Nucleation beyond WKB Resummation of Vacuum Bubble Diagrams
Suzuki, H; Suzuki, Hiroshi; Yasuta, Hirofumi
1998-01-01
On the basis of Borel resummation, we propose a systematical improvement of bounce calculus of quantum bubble nucleation rates. We study a metastable super-renormalizable field theory, D dimensional O(N) symmetric \\phi^4 model (D<4) with an attractive interaction. The validity of our proposal is tested in D=1 (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in D=2 based on an explicit calculation of vacuum bubble diagrams to five loop orders.
5d $E_n$ Seiberg-Witten curve via toric-like diagram
Kim, Sung-Soo
2014-01-01
We consider 5d Sp(1) gauge theory with $E_{N_f+1}$ global symmetries based on toric(-like) diagram constructed from (p,q)-web with 7-branes. We propose a systematic procedure to compute the Seiberg-Witten curve for generic toric-like diagram. For $N_f=6,7$ flavors, we explicitly compute the Seiberg-Witten curves for 5d Sp(1) gauge theory, and show that these Seiberg-Witten curves agree with already known $E_{7,8}$ results. We also discuss a generalization of the Seiberg-Witten curve to rank-N cases.
Relaxation time diagram for identifying heat generation mechanisms in magnetic fluid hyperthermia
Energy Technology Data Exchange (ETDEWEB)
Lima, Enio, E-mail: lima@cab.cnea.gov.ar; De Biasi, Emilio; Zysler, Roberto D.; Vasquez Mansilla, Marcelo; Mojica-Pisciotti, Mary L. [Centro Atómico Bariloche/CONICET (Argentina); Torres, Teobaldo E.; Calatayud, M. Pilar; Marquina, C.; Ricardo Ibarra, M.; Goya, Gerardo F. [Universidad de Zaragoza, Instituto de Nanociencia de Aragón INA (Spain)
2014-12-15
We present a versatile diagram to envisage the dominant relaxation mechanism of single-domain magnetic nanoparticles (MNPs) under alternating magnetic fields, as those used in magnetic fluid hyperthermia (MFH). The diagram allows estimating the heating efficiency, measured by the Specific Power Absorption (SPA), originated in the magnetic and viscous relaxation times of single-domain MNPs for a given frequency of the ac magnetic field (AFM). The diagram has been successfully applied to different colloids, covering a wide variety of MNPs with different magnetic anisotropy and particle size, and dispersed in different viscous liquid carriers. From the general diagram, we derived a specific chart based on the Linear Response Theory in order to easily estimate the experimental condition for the optimal SPA values of most colloids currently used in MFH.
Stones, Catherine; Cole, Frances
2014-01-01
The persistent pain cycle diagram is a common feature of pain management literature. but how is it designed and is it fulfilling its potential in terms of providing information to motivate behavioral change? This article examines on-line persistent pain diagrams and critically discusses their purpose and design approach. By using broad information design theories by Karabeg and particular approaches to dialogic visual communications in business, this article argues the need for motivational as well as cognitive diagrams. It also outlines the design of a new persistent pain cycle that is currently being used with chronic pain patients in NHS Bradford, UK. This new cycle adopts and then visually extends an established verbal metaphor within acceptance and commitment therapy (ACT) in an attempt to increase the motivational aspects of the vicious circle diagram format.
Relation among C-curve characterization diagrams
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
As three control points are fixed and the fourth control point varies, the planar cubic C-curve may take on a loop, a cusp, or zero to two inflection points, depending on the position of the moving point. The plane can, therefore, be partitioned into regions labelled according to the characterization of the curve when the fourth point is in each region. This partitioned plane is called a "characterization diagram". By moving one of the control points but fixing the rest, one can induce different characterization diagrams. In this paper, we investigate the relation among all different characterization diagrams of cubic C-curves based on the singularity conditions proposed by Yang and Wang (2004). We conclude that, no matter what the C-curve type is or which control point varies, the characterization diagrams can be obtained by cutting a common 3D characterization space with a corresponding plane.
Revised Diagnostic Diagrams for Planetary Nebulae
Riesgo, H
2006-01-01
Diagnostic diagrams of electron density - excitation for a sample of 613 planetary nebulae are presented. The present extensive sample allows the definition of new statistical limits for the distribution of planetary nebulae in the log [Ha/[SII
A Smart Thermal Block Diagram Tool
Tsuyuki, Glenn; Miyake, Robert; Dodge, Kyle
2008-01-01
The presentation describes a Smart Thermal Block Diagram Tool. It is used by JPL's Team X in studying missions during the Pre-Phase A. It helps generate cost and mass estimates using proprietary data bases.
Atomic energy levels and Grotrian diagrams
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.
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 ...
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.
QCD Phase Diagram with Imaginary Chemical Potential
Directory of Open Access Journals (Sweden)
Nakamura Atsushi
2012-02-01
Full Text Available We report our recent results on the QCD phase diagram obtained from the lattice QCD simulation. The location of the phase boundary between hadronic and QGP phases in the two-flavor QCD phase diagram is investigated. The imaginary chemical potential approach is employed, which is based on Monte Carlo simulations of the QCD with imaginary chemical potential and analytic continuation to the real chemical potential region.
ISS EPS Orbital Replacement Unit Block Diagrams
Schmitz, Gregory V.
2001-01-01
The attached documents are being provided to Switching Power Magazine for information purposes. This magazine is writing a feature article on the International Space Station Electrical Power System, focusing on the switching power processors. These units include the DC-DC Converter Unit (DDCU), the Bi-directional Charge/Discharge Unit (BCDU), and the Sequential Shunt Unit (SSU). These diagrams are high-level schematics/block diagrams depicting the overall functionality of each unit.
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....
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....
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....
Maunder's Butterfly Diagram in the 21st Century
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.
Maunder's Butterfly Diagram in the 21st Century
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.
The role of sample height in the stacking diagram of colloidal mixtures under gravity
Geigenfeind, Thomas; de las Heras, Daniel
2017-02-01
Bulk phase separation is responsible for the occurrence of stacks of different layers in sedimentation of colloidal mixtures. A recently proposed theory (de las Heras and Schmidt 2013 Soft Matter 9 8636) establishes a unique connection between the bulk phase behaviour and sedimentation-diffusion-equilibrium. The theory constructs a stacking diagram of all possible sequences of stacks under gravity in the limit of very high (infinite) sample heights. Here, we study the stacking diagrams of colloidal mixtures at finite sample height, h. We demonstrate that h plays a vital role in sedimentation-diffusion-equilibrium of colloidal mixtures. The region of the stacking diagram occupied by a given sequence of stacks depends on h. Hence, two samples with different heights but identical colloidal concentrations can develop different stacking sequences. In addition, the stacking diagrams for different heights can be qualitatively different since some stacking sequences occur only in a given interval of sample heights. We use the theory to investigate the stacking diagrams of both model bulk systems and mixtures of patchy particles that differ either by the number or by the types of patches.
Alexandrov, S.; Pioline, B.; Saueressig, F.; Vandoren, S.J.G.
2009-01-01
Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kähler metric on the hypermultiplet moduli space to the complex contact geome
Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo
Azadi, Sam; Cohen, R. E.
2016-08-01
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 P21/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 P21/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.
2-BODY AND 3-BODY PARQUET THEORY
LANDE, A; SMITH, RA
1992-01-01
One of the fundamental approaches to microscopic many-body theory is through the use of perturbation theory. This paper presents a clear derivation of the equations that sum the two-body and three body reducible diagrams that are generated from some input set of irreducible diagrams (typically the b
de Wit, Bernard
1990-01-01
After a brief and practical introduction to field theory and the use of Feynman diagram, we discuss the main concept in gauge theories and their application in elementary particle physics. We present all the ingredients necessary for the construction of the standard model.
Pathway collages: personalized multi-pathway diagrams.
Paley, Suzanne; O'Maille, Paul E; Weaver, Daniel; Karp, Peter D
2016-12-13
Metabolic pathway diagrams are a classical way of visualizing a linked cascade of biochemical reactions. However, to understand some biochemical situations, viewing a single pathway is insufficient, whereas viewing the entire metabolic network results in information overload. How do we enable scientists to rapidly construct personalized multi-pathway diagrams that depict a desired collection of interacting pathways that emphasize particular pathway interactions? We define software for constructing personalized multi-pathway diagrams called pathway-collages using a combination of manual and automatic layouts. The user specifies a set of pathways of interest for the collage from a Pathway/Genome Database. Layouts for the individual pathways are generated by the Pathway Tools software, and are sent to a Javascript Pathway Collage application implemented using Cytoscape.js. That application allows the user to re-position pathways; define connections between pathways; change visual style parameters; and paint metabolomics, gene expression, and reaction flux data onto the collage to obtain a desired multi-pathway diagram. We demonstrate the use of pathway collages in two application areas: a metabolomics study of pathogen drug response, and an Escherichia coli metabolic model. Pathway collages enable facile construction of personalized multi-pathway diagrams.
The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning
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,…
Stage line diagram: An age-conditional reference diagram for tracking development
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 disea
Stage line diagram: an age-conditional reference diagram for tracking development.
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 disea
Stage line diagram: an age-conditional reference diagram for tracking development.
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 disea
Fishbone Diagrams: Organize Reading Content with a "Bare Bones" Strategy
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…
Fishbone Diagrams: Organize Reading Content with a "Bare Bones" Strategy
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…
Visualizing Metrics on Areas of Interest in Software Architecture Diagrams
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 arc
First-order reversal curve (FORC) diagrams of natural and cultured biogenic magnetic particles
Chen, Amy P.; Egli, Ramon; Moskowitz, Bruce M.
2007-08-01
First-order reversal curve (FORC) diagrams are rapidly becoming a standard tool for characterizing magnetic particles because they simultaneously incorporate information regarding magnetostatic interaction and domain states. The simplest interpretation of FORC diagrams of single-domain (SD) particles is based on the Neel interpretation of Preisach theory, which predicts that the FORC function is the product of a coercivity and an interaction field distribution. Although the underlying assumptions of this interpretation are not correct, a strictly quantitative model of weakly interacting SD grains proves that the distributions of coercivities and interaction fields can be retrieved from a FORC diagram. To test this model, we present the possibility of a quantitative interpretation of FORC diagrams, and we present measurements of samples containing magnetosomes from cultures of magnetotactic bacteria and from a lake sediment. Two samples are investigated under the electron microscope to characterize the geometrical arrangement of the particles. We find that the clustering of otherwise similar particles has a strong influence on FORC diagrams. We also obtained a crude estimate of packing densities form the FORC diagrams, which were consistent with transmission electron microscopy observations and measurements of the anhysteretic remanent magnetization.
Phase diagram of a truncated tetrahedral model
Krcmar, Roman; Gendiar, Andrej; Nishino, Tomotoshi
2016-08-01
Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analog of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed.
Functionality Semantics of Predicate Data Flow Diagram
Institute of Scientific and Technical Information of China (English)
高晓雷; 缪淮扣; 刘玲
2004-01-01
SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is predicate data flow diagram (PDFD). In order to eliminate the ambiguity of predicate data flow diagrams and their associated textual specifications, a formalization of the syntax and semantics of predicate data flow diagrams is necessary. In this paper we use Z notation to define an abstract syntax and the related structural constraints for the PDFD notation, and provide it with an axiomatic semantics based on the concept of data availability and functionality of predicate operation. Finally, an example is given to establish functionality consistent decomposition on hierarchical PDFD (HPDFD).
MDM: A Mode Diagram Modeling Framework
DEFF Research Database (Denmark)
Wang, Zheng; Pu, Geguang; Li, Jianwen
2012-01-01
systems are widely used in the above-mentioned safety-critical embedded domains, there is lack of domain-specific formal modelling languages for such systems in the relevant industry. To address this problem, we propose a formal visual modeling framework called mode diagram as a concise and precise way...... checking technique can then be used to verify the mode diagram models against desired properties. To demonstrate the viability of our approach, we have applied our modelling framework to some real life case studies from industry and helped detect two design defects for some spacecraft control systems....
DEPENDENCE ANALYSIS FOR UML CLASS DIAGRAMS
Institute of Scientific and Technical Information of China (English)
Wu Fangjun; Yi Tong
2004-01-01
Though Unified Modeling Language (UML) has been widely used in software development, the major problems confronted lie in comprehension and testing. Dependence analysis is an important approach to analyze, understand, test and maintain programs. A new kind of dependence analysis method for UML class diagrams is developed. A set of dependence relations is definedcorresponding to the relations among classes. Thus, the dependence graph of UML class diagram can be constructed from these dependence relations. Based on this model, both slicing and measurement coupling are further given as its two applications.
Phase diagrams modified by interfacial penalties
Directory of Open Access Journals (Sweden)
Atanacković T.M.
2007-01-01
Full Text Available The conventional forms of phase diagrams are constructed without consideration of interfacial energies and they represent an important tool for chemical engineers and metallurgists. If interfacial energies are taken into consideration, it is intuitively obvious that the regions of phase equilibria must become smaller, because there is a penalty on the formation of interfaces. We investigate this phenomenon qualitatively for a one-dimensional model, in which the phases occur as layers rather than droplets or bubbles. The modified phase diagrams are shown in Chapters 3 and 4.
Partial chord diagrams and matrix models
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Fuji, Hiroyuki; Manabe, Masahide
spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations......In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length...... – obtained independently by cut-and-join arguments in an earlier work – for the corresponding generating functions....
The Voronoi diagram of circles made easy
DEFF Research Database (Denmark)
Anton, François; Mioc, Darka; Gold, Christopher
2007-01-01
Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delau......Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how...
Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals
Borja, Julio
2016-01-01
We propose a new set of Master Integrals which can be used as a basis for multiloop calculation in any gauge massless field theory. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The corresponding multiloop integrals may be decomposed in terms of this set of the Master Integrals. We construct a new reduction procedure which we apply to perform this decomposition.
Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals
Borja, Julio; Kondrashuk, Igor
2016-10-01
We propose a new set of Master Integrals which can be used as a basis for certain multiloop calculations in massless gauge field theories. In these theories we consider three-point Feynman diagrams with arbitrary number of loops. The corresponding multiloop integrals may be decomposed in terms of this set of the Master Integrals. We construct a new reduction procedure which we apply to perform this decomposition.
Linking the Budyko framework and the Dunne diagram
Trancoso, Ralph; Larsen, Joshua R.; McAlpine, Clive; McVicar, Tim R.; Phinn, Stuart
2016-04-01
The spatial and temporal heterogeneity of climate, soils, topography and vegetation control the water and energy balances among catchments. Two well-known hydrological theories underpinning these processes are the Budyko framework and the Dunne diagram. Relating the scaling of water-energy balances (Budyko) and runoff generation mechanisms (Dunne) raises some important catchment comparison questions, namely: (i) how do streamflow characteristics vary according to the annual water and energy balances?; (ii) to what extent do biophysical drivers of runoff explain the observed streamflow variability?; and (iii) are there quantifiable process overlaps between these two approaches, and can they offer insights into the mechanics of catchment co-evolution? This study addresses these questions by analysing daily streamflow and precipitation time series data to quantify hydrological similarity across 355 catchments located along a tropical-temperate climatic gradient in eastern Australia. We used eight hydrological metrics to describe the hydrological response over a 33-year period (1980-2013). Hierarchical cluster, ordination analysis, the Budyko framework, and generalized additive models were used to evaluate hydrological similarity, extract the dominant response, and examine how the landscape and climatic characteristics of catchments influence the dominant streamflow response. The catchments were classified into five clusters based on the analysis of their hydrological characteristics and similarity, which vary along the annual water and energy balances gradient in the Budyko framework. Furthermore, we show that the streamflow similarity is explained by six catchment-specific biophysical factors that overlap with those described by the Dunne diagram for runoff generation, which in this case have the following order of relative importance: (i) Dryness Index; (ii) Fraction of Photosynthetically Active Radiation; (iii) Saturated Hydraulic Conductivity; (iv) Soil Depth; (v
Modeling the phase diagram of carbon
Ghiringhelli, L.M.; Los, J.H.; Meijer, E.J.; Fasolino, A.; Frenkel, D.
2005-01-01
We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respect
Orphan-Free Anisotropic Voronoi Diagrams
Canas, Guillermo D
2011-01-01
We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.
The BFKL Pomeron calculus: Summing enhanced diagrams
Energy Technology Data Exchange (ETDEWEB)
Levin, E., E-mail: leving@post.tau.ac.il [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 (Israel); Departamento de Fisica, Universidad Tecnica Federico Santa Maria, and Centro Cientifico-Tecnologico de Valparaiso, Casilla 110-V, Valparaiso (Chile); Miller, J., E-mail: jeremy.miller@ist.utl.pt [Department of Particle Physics, School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 (Israel); CENTRA, Departamento de Fisica, Instituto Superior Tecnico (IST), Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
2012-07-01
The goal of this paper is to sum over a class of enhanced diagrams, and derive a new Pomeron Green function. It is found that this sum gives the Pomeron contribution to the scattering amplitude that decreases with energy. In other words, we found that the total cross section of two colourless dipoles of small but equal sizes, falls down at high energies.
Geometrical splitting and reduction of Feynman diagrams
Davydychev, Andrei I.
2016-10-01
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.
Influence Diagrams for Optimal Maintenance Planning
DEFF Research Database (Denmark)
Friis-Hansen, Andreas
2000-01-01
Over the last two decades Bayesian networks and influence diagrams have received notable attention within the field of artificial intelligence and expert systems. During the last few years the technology has been further developed for problem solving within other engineering fields. The objective...
Diagram of a LEP superconducting cavity
1991-01-01
This diagram gives a schematic representation of the superconducting radio-frequency cavities at LEP. Liquid helium is used to cool the cavity to 4.5 degrees above absolute zero so that very high electric fields can be produced, increasing the operating energy of the accelerator. Superconducting cavities were used only in the LEP-2 phase of the accelerator, from 1996 to 2000.
Influence Diagrams for Optimal Maintenance Planning
DEFF Research Database (Denmark)
Friis-Hansen, Andreas
2000-01-01
Over the last two decades Bayesian networks and influence diagrams have received notable attention within the field of artificial intelligence and expert systems. During the last few years the technology has been further developed for problem solving within other engineering fields. The objective...
Phase diagram distortion from traffic parameter averaging.
Stipdonk, H. Toorenburg, J. van & Postema, M.
2010-01-01
Motorway traffic congestion is a major bottleneck for economic growth. Therefore, research of traffic behaviour is carried out in many countries. Although well describing the undersaturated free flow phase as an almost straight line in a (k,q)-phase diagram, congested traffic observations and
Weight diagram construction of Lax operators
Energy Technology Data Exchange (ETDEWEB)
Carbon, S.L.; Piard, E.J.
1991-10-01
We review and expand methods introduced in our previous paper. It is proved that cyclic weight diagrams corresponding to representations of affine Lie algebras allow one to construct the associated Lax operator. The resultant Lax operator is in the Miura-like form and generates the modified KdV equations. The algorithm is extended to the super-symmetric case.
Solution space diagram in conflict detection scenarios
Rahman, S.M.A.; Borst, C.; Mulder, M.; Van Paassen, M.M.
2015-01-01
This research investigates the use of Solution Space Diagram (SSD) as a measure of sector complexity and also as a predictor of performance and workload, focusing on the scenarios regarding Air Traffic Controller (ATCO)’s ability to detect future conflicts. A human-in-the-loop experiment with varyin
Visualizing Multivariate Attributes on Software Diagrams
Byelas, Heorhiy; Telea, Alexandru; Winter, A; Knodel, J
2009-01-01
Software architecture diagrams and metrics are well-known and heavily used in many areas in software engineering. However they are rarely combined in one (visual) representation. Although there are some advances in this direction, there are also some limitations. In this research, we study how to ov
Phase Diagram of Vertically Shaken Granular Matter
Eshuis, P; Lohse, D; Van der Meer, D; Van der Weele, K; Bos, Robert; Eshuis, Peter; Lohse, Detlef; Meer, Devaraj van der; Weele, Ko van der
2006-01-01
A shallow, vertically shaken granular bed in a quasi 2-D container is studied experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions between them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.
Image Attributes: A Study of Scientific Diagrams.
Brunskill, Jeff; Jorgensen, Corinne
2002-01-01
Discusses advancements in imaging technology and increased user access to digital images, as well as efforts to develop adequate indexing and retrieval methods for image databases. Describes preliminary results of a study of undergraduates that explored the attributes naive subjects use to describe scientific diagrams. (Author/LRW)
On traces of tensor representations of diagrams
A. Schrijver
2015-01-01
Let T be an (abstract) set of types, and let (unknown symbol), o : T -> Z(+). A T-diagram is a locally ordered directed graph G equipped with a function tau : V (G) -> T such that each vertex v of G has indegree (unknown symbol)(tau(v)) and outdegree o(tau(v)). (A directed graph is locally ordered i
Complexities of One-Component Phase Diagrams
Ciccioli, Andrea; Glasser, Leslie
2011-01-01
For most materials, the solid at and near the triple-point temperature is denser than the liquid with which it is in equilibrium. However, for water and certain other materials, the densities of the phases are reversed, with the solid being less dense. The profound consequences for the appearance of the "pVT" diagram of one-component materials…
From ergodicity to extended phase diagrams.
Woodley, Scott M; Sokol, Alexey A
2012-04-16
Structure prediction of stable and metastable phases is put on equal footing for the first time, with a solid thermodynamical background. How to estimate the lifetime of metastable phases is demonstrated by recent groundbreaking work of Jansen, Pentin, and Schön. At the heart lies the exploration of the Gibbs free-energy landscapes and the extended phase diagrams for complex systems.
Fog Machines, Vapors, and Phase Diagrams
Vitz, Ed
2008-01-01
A series of demonstrations is described that elucidate the operation of commercial fog machines by using common laboratory equipment and supplies. The formation of fogs, or "mixing clouds", is discussed in terms of the phase diagram for water and other chemical principles. The demonstrations can be adapted for presentation suitable for elementary…
Lekkerkerker, H.N.W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc co
Lekkerkerker, H.N.W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc
({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.
The phase diagram of twisted mass lattice QCD
Sharpe, S R; Sharpe, Stephen R.; Wu, Jackson M. S.
2004-01-01
We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m_\\pi^2/(4\\pi f_\\pi)^2 ~ a \\Lambda (a being the lattice spacing, and \\Lambda = \\Lambda_{QCD}). We then focus on the region where m_\\pi^2/(4\\pi f_\\pi)^2 ~ (a \\Lambda)^2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is non-vanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transitio...
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...
Tarnopolski, Mariusz
2013-01-01
This paper presents bifurcation and generalized bifurcation diagrams for a rotational model of an oblate satellite. Special attention is paid to parameter values describing one of Saturn's moons, Hyperion. For various oblateness the largest Lyapunov Characteristic Exponent (LCE) is plotted. The largest LCE in the initial condition as well as in the mixed parameter-initial condition space exhibits a fractal structure, for which the fractal dimension was calculated. It results from the bifurcation diagrams of which most of the parameter values for preselected initial conditions lead to chaotic rotation. The First Recurrence Time (FRT) diagram provides an explanation of the birth of chaos and the existence of quasi-periodic windows occuring in the bifurcation diagrams.
A Simple Approach for Boundary Improvement of Euler Diagrams.
Simonetto, Paolo; Archambault, Daniel; Scheidegger, Carlos
2016-01-01
General methods for drawing Euler diagrams tend to generate irregular polygons. Yet, empirical evidence indicates that smoother contours make these diagrams easier to read. In this paper, we present a simple method to smooth the boundaries of any Euler diagram drawing. When refining the diagram, the method must ensure that set elements remain inside their appropriate boundaries and that no region is removed or created in the diagram. Our approach uses a force system that improves the diagram while at the same time ensuring its topological structure does not change. We demonstrate the effectiveness of the approach through case studies and quantitative evaluations.
STRUKTURISASI ENTITY RELATIONSHIP DIAGRAM DAN DATA FLOW DIAGRAM BERBASIS BUSINESS EVENT-DRIVEN
Suroto Adi; Desi Maya Kristin
2014-01-01
Entity relationship diagram (ERD) and data flow diagram (DFD) modeling are necessary parts in analysis and design of structured information systems in business. Definition of entities in the ERD, the process, and datastore in the DFD have well described in a lot of literatures. However, practically it is not easy to explain how to design ERD and DFD models so that the students well understand the modeling steps, especially in business applications. This study discussed step-by-step systematic...
Quarks and gluons in the phase diagram of quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Welzbacher, Christian Andreas
2016-07-14
In this dissertation we study the phase diagram of strongly interacting matter by approaching the theory of quantum chromodynamics in the functional approach of Dyson-Schwinger equations. With these quantum (field) equations of motions we calculate the non-perturbative quark propagator within the Matsubara formalism. We built up on previous works and extend the so-called truncation scheme, which is necessary to render the infinite tower of Dyson-Schwinger equations finite and study phase transitions of chiral symmetry and the confinement/deconfinement transition. In the first part of this thesis we discuss general aspects of quantum chromodynamics and introduce the Dyson-Schwinger equations in general and present the quark Dyson-Schwinger equation together with its counterpart for the gluon. The Bethe-Salpeter equation is introduced which is necessary to perform two-body bound state calculations. A view on the phase diagram of quantum chromodynamics is given, including the discussion of order parameter for chiral symmetry and confinement. Here we also discuss the dependence of the phase structure on the masses of the quarks. In the following we present the truncation and our results for an unquenched N{sub f} = 2+1 calculation and compare it to previous studies. We highlight some complementary details for the quark and gluon propagator and discus the resulting phase diagram, which is in agreement with previous work. Results for an equivalent of the Columbia plot and the critical surface are discussed. A systematically improved truncation, where the charm quark as a dynamical quark flavour is added, will be presented in Ch. 4. An important aspect in this investigation is the proper adjustment of the scales. This is done by matching vacuum properties of the relevant pseudoscalar mesons separately for N{sub f} = 2+1 and N f = 2+1+1 via a solution of the Bethe-Salpeter equation. A comparison of the resulting N{sub f} = 2+1 and N{sub f} = 2+1+1 phase diagram indicates
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.
Coherence Without Commutative Diagrams, Lie-Hedra and Other Curiosities
Markl, M; Markl, Martin; Shnider, Steve
1997-01-01
The paper is devoted to the coherence problem for algebraic structures on a category. We describe coherence constraints in terms of the cohomology of the corresponding operad. Our approach enables us to introduce the concept of coherence even for structures which are not given by commutative diagrams. In the second part of the paper we discuss `quantizations' of various algebraic structures. We prove that there always exists the `canonical quantization' and show that the two prominent examples -- Drinfel'd's quasi-Hopf algebras and Gurevich's generalized Lie algebras -- are canonical quantizations of their `classical limits.' The second part can be read independently, though the abstract theory of the first part is necessary for the full understanding of the results.
Using causal diagrams to guide analysis in missing data problems.
Daniel, Rhian M; Kenward, Michael G; Cousens, Simon N; De Stavola, Bianca L
2012-06-01
Estimating causal effects from incomplete data requires additional and inherently untestable assumptions regarding the mechanism giving rise to the missing data. We show that using causal diagrams to represent these additional assumptions both complements and clarifies some of the central issues in missing data theory, such as Rubin's classification of missingness mechanisms (as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR)) and the circumstances in which causal effects can be estimated without bias by analysing only the subjects with complete data. In doing so, we formally extend the back-door criterion of Pearl and others for use in incomplete data examples. These ideas are illustrated with an example drawn from an occupational cohort study of the effect of cosmic radiation on skin cancer incidence.
Phase diagrams and heterogeneous equilibria a practical introduction
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.
First-Principles Phase Diagram for Ce-Th System
Energy Technology Data Exchange (ETDEWEB)
Landa, A; Soderlind, P; Ruban, A; Vitos, L; Pourovskii, L
2004-05-11
Ab initio total energy calculations based on the exact muffin-tin orbitals (EMTO) theory are used to determine the high pressure and low temperature phase diagram of Ce and Th metals as well as the Ce{sub 43}Th{sub 57} disordered alloy. The compositional disorder for the alloy is treated in the framework of the coherent potential approximation (CPA). Equation of state for Ce, Th and Ce{sub 43}Th{sub 57} has been calculated up to 1 Mbar in good comparison with experimental data: upon compression the Ce-Th system undergoes crystallographic phase transformation from an fcc to a bct structure and the transition pressure increases with Th content in the alloy.
Phase diagram of hopping conduction mechanisms in polymer nanofiber network
Energy Technology Data Exchange (ETDEWEB)
Li, Jeng-Ting; Lu, Yu-Cheng; Jiang, Shiau-Bin; Zhong, Yuan-Liang, E-mail: ylzhong@cycu.edu.tw [Department of Physics and Center for Nanotechnology, Chung Yuan Christian University, Chung-Li 32023, Taiwan (China); Yeh, Jui-Ming [Department of Chemistry and Center for Nanotechnology, Chung Yuan Christian University, Chung-Li 32023, Taiwan (China)
2015-12-07
Network formation by nanofiber crosslinking is usually in polymer materials as application in organic semiconductor devices. Electron hopping transport mechanisms depend on polymer morphology in network. Conducting polymers morphology in a random network structure is modeled by a quasi-one-dimensional system coupled of chains or fibers. We observe the varying hopping conduction mechanisms in the polyaniline nanofibers of the random network structure. The average diameter d of the nanofibers is varied from approximately 10 to 100 nm. The different dominant hopping mechanisms including Efros-Shklovskii variable-range hopping (VRH), Mott VRH, and nearest-neighbor hopping are dependent on temperature range and d in crossover changes. The result of this study is first presented in a phase diagram of hopping conduction mechanisms based on the theories of the random network model. The hopping conduction mechanism is unlike in normal semiconductor materials.
Prediction of boron carbon nitrogen phase diagram
Yao, Sanxi; Zhang, Hantao; Widom, Michael
We studied the phase diagram of boron, carbon and nitrogen, including the boron-carbon and boron-nitrogen binaries and the boron-carbon-nitrogen ternary. Based on the idea of electron counting and using a technique of mixing similar primitive cells, we constructed many ''electron precise'' structures. First principles calculation is performed on these structures, with either zero or high pressures. For the BN binary, our calculation confirms that a rhmobohedral phase can be stablized at high pressure, consistent with some experimental results. For the BCN ternary, a new ground state structure is discovered and an Ising-like phase transition is suggested. Moreover, we modeled BCN ternary phase diagram and show continuous solubility from boron carbide to the boron subnitride phase.
Phase diagram of a single lane roundabout
Echab, H.; Lakouari, N.; Ez-Zahraouy, H.; Benyoussef, A.
2016-03-01
Using the cellular automata model, we numerically study the traffic dynamic in a single lane roundabout system of four entry/exit points. The boundaries are controlled by the injecting rates α1, α2 and the extracting rate β. Both the system with and without Splitter Islands of width Lsp are considered. The phase diagram in the (α1 , β) space and its variation with the roundabout size, Pagg (i.e. the probability of aggressive entry), and Pexit (i.e. the probability of preferential exit) are constructed. The results show that the phase diagram in both cases consists of three phases: free flow, congested and jammed. However, as Lsp increases the free flow phase enlarges while the congested and jammed ones shrink. On the other hand, the short sized roundabout shows better performance in the free flow phase while the large one is more optimal in the congested phase. The density profiles are also investigated.
Geometry Helps to Compare Persistence Diagrams
Energy Technology Data Exchange (ETDEWEB)
Kerber, Michael; Morozov, Dmitriy; Nigmetov, Arnur
2015-11-16
Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.), and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.
Flamelet Regime Diagram for Turbulent Combustion Simulations
Chan, Wai Lee; Ihme, Matthias; Kolla, Hemanth; Chen, Jacqueline
2016-11-01
The flamelet model has been widely used in numerical combustion investigations, particularly for the closure of large-eddy simulations (LES) of turbulent reacting flows. In most cases, the simulation results demonstrated good agreements with their experimental counterparts. However, a systematic analysis of the flamelet model's applicability, as well as its potential limitations, is seldom conducted, and the model performance is usually based only on a-posteriori comparisons. The objective of this work is to derive a metric that can formally quantify the suitability of the flamelet model in different flame configurations. For this purpose, a flamelet regime diagram has been developed and studied in the context of direct numerical simulations (DNS) of a turbulent lifted jet flame. The implementation of the regime diagram in LES has been investigated through explicit filtering of the DNS results.
The Mental Health Outcomes of Drought: A Systematic Review and Causal Process Diagram.
Vins, Holly; Bell, Jesse; Saha, Shubhayu; Hess, Jeremy J
2015-10-22
Little is understood about the long term, indirect health consequences of drought (a period of abnormally dry weather). In particular, the implications of drought for mental health via pathways such as loss of livelihood, diminished social support, and rupture of place bonds have not been extensively studied, leaving a knowledge gap for practitioners and researchers alike. A systematic review of literature was performed to examine the mental health effects of drought. The systematic review results were synthesized to create a causal process diagram that illustrates the pathways linking drought effects to mental health outcomes. Eighty-two articles using a variety of methods in different contexts were gathered from the systematic review. The pathways in the causal process diagram with greatest support in the literature are those focusing on the economic and migratory effects of drought. The diagram highlights the complexity of the relationships between drought and mental health, including the multiple ways that factors can interact and lead to various outcomes. The systematic review and resulting causal process diagram can be used in both practice and theory, including prevention planning, public health programming, vulnerability and risk assessment, and research question guidance. The use of a causal process diagram provides a much needed avenue for integrating the findings of diverse research to further the understanding of the mental health implications of drought.
Operational Modal Analysis Based on Subspace Algorithm with an Improved Stabilization Diagram Method
Directory of Open Access Journals (Sweden)
Shiqiang Qin
2016-01-01
Full Text Available Subspace-based algorithms for operational modal analysis have been extensively studied in the past decades. In the postprocessing of subspace-based algorithms, the stabilization diagram is often used to determine modal parameters. In this paper, an improved stabilization diagram is proposed for stochastic subspace identification. Specifically, first, a model order selection method based on singular entropy theory is proposed. The singular entropy increment is calculated from nonzero singular values of the output covariance matrix. The corresponding model order can be selected when the variation of singular entropy increment approaches to zero. Then, the stabilization diagram with confidence intervals which is established using the uncertainty of modal parameter is presented. Finally, a simulation example of a four-story structure and a full-scale cable-stayed footbridge application is employed to illustrate the improved stabilization diagram method. The study demonstrates that the model order can be reasonably determined by the proposed method. The stabilization diagram with confidence intervals can effectively remove the spurious modes.
Nanostructures and phase diagrams of ABC star triblock copolymers in pore geometries.
Li, Shiben; Qiu, Wenjuan; Zhang, Linxi; Liang, Haojun
2012-03-28
The nanostructures and phase diagrams of ABC star triblock copolymers in pore geometries are investigated using the real-space self-consistent field theory in two-dimensional space. Two types of pores with neutral surfaces, namely, pores with small and large diameters, are considered. A rich variety of nanostructures are exhibited by the ABC star triblock copolymers in these two types of pores, which differ from those observed in bulk and in other confinements. These structures include perpendicular undulating lamellae, concentric core-shell cylinders, polygonal tiling with cylindrical arrangements, and other complex structures. Triangular phase diagrams for the ABC star triblock copolymers are constructed. The small pores clearly affect the corner and central space of the phase diagrams by distorting the bulk structures into concentric arrangements. Meanwhile, the large pores induce the transformation of bulk structures into concentric structures in most of the phase space, but slightly affect the structures at the center of the phase diagrams. Furthermore, the order-order and order-disorder phase transitions, as well as the stable and metastable phases, in the triangular phase diagrams are examined by analyzing their free energies. These observations on the ABC star triblock copolymers in the pore geometries provide a deeper insight into the behavior of macromolecules in a confined system.
Disconnected diagrams with twisted-mass fermions
Abdel-Rehim, Abdou; Constantinou, Martha; Finkenrath, Jacob; Hadjiyiannakou, Kyriakos; Jansen, Karl; Kallidonis, Christos; Koutsou, Giannis; Avilés-Casco, Alejandro Vaquero
2016-01-01
The latest results from the Twisted-Mass collaboration on disconnected diagrams at the physical value of the pion mass are presented. In particular, we focus on the sigma terms, the axial charges and the momentum fraction, all of them for the nucleon. A detailed error analysis for each observable follows, showing the strengths and weaknesses of the one-end trick. Alternatives are discussed.
Hydrodynamics of bacterial colonies: Phase diagrams
Lega, J.; Passot, T.
2004-09-01
We present numerical simulations of a recent hydrodynamic model describing the growth of bacterial colonies on agar plates. We show that this model is able to qualitatively reproduce experimentally observed phase diagrams, which relate a colony shape to the initial quantity of nutrients on the plate and the initial wetness of the agar. We also discuss the principal features resulting from the interplay between hydrodynamic motions and colony growth, as described by our model.
Phase Diagram Modelling: Nickel - Aluminum - Chromium System
1998-04-01
conducted by Kaufman and co-workers and their lattice stabilities have formed the basis of phase diagram calculations to the present day.1 In...mol ( 0.74827 Ni + 0.73305E-01 Cr + 0.83609E-02 Al ( 1200.00 C, 1.0000 <—s -.Molten alloy <—s <—s) atm, L- NiCrAl , a=0.82994 ) 0.00000
Mixed wasted integrated program: Logic diagram
Energy Technology Data Exchange (ETDEWEB)
Mayberry, J.; Stelle, S. [Science Applications International Corp., Idaho Falls, ID (United States); O`Brien, M. [Univ. of Arizona, Tucson, AZ (United States); Rudin, M. [Univ. of Nevada, Las Vegas, NV (United States); Ferguson, J. [Lockheed Idaho Technologies Co., Idaho Falls, ID (United States); McFee, J. [I.T. Corp., Albuquerque, NM (United States)
1994-11-30
The Mixed Waste Integrated Program Logic Diagram was developed to provide technical alternative for mixed wastes projects for the Office of Technology Development`s Mixed Waste Integrated Program (MWIP). Technical solutions in the areas of characterization, treatment, and disposal were matched to a select number of US Department of Energy (DOE) treatability groups represented by waste streams found in the Mixed Waste Inventory Report (MWIR).
Fluctuations and the QCD Phase Diagram
Koch, Volker
2016-01-01
In this contribution we will discuss how the study of various fluctuation observables may be used to explore the phase diagram of the strong interaction. We will briefly summarize the present study of experimental and theoretical research in this area. We will then discuss various corrections and issues which need to be understood and applied for a meaningful comparison of experimental measurements with theoretical predictions. This contribution is dedicated to Andrzej Bialas on the occasion of his $80^{\\mathrm{th}}$ birthday.
Lectures on configuration space methods for sunrise-type diagrams
Groote, S
2003-01-01
In this lecture series I will give a fundamental insight into configuration space techniques which are of help to calculate a broad class of Feynman diagrams, the sunrise-type diagrams. Applications are shown along with basic concepts and techniques.
Efficient Analysis of Complex Diagrams using Constraint-Based Parsing
Futrelle, R P; Futrelle, Robert P.; Nikolakis, Nikos
1995-01-01
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of substantial complexity. The system is probably the first to demonstrate efficient diagram parsing using grammars that easily be retargeted to other domains. The work assumes that the diagrams are available as a flat collection of graphics primitives: lines, polygons, circles, Bezier curves and text. This is appropriate for future electronic documents or for vectorized diagrams converted from scanned images. The classes of diagrams that we have analyzed include x,y data graphs and genetic diagrams drawn from the biological literature, as well as finite state automata diagrams (states and arcs). As an example, parsing a four-part data graph composed of 133 primitives required 35 sec using Macintosh Common Lisp on a Macintosh Quadra 700.
75 FR 61512 - Outer Continental Shelf Official Protraction Diagrams
2010-10-05
... Bureau of Ocean Energy Management, Regulation and Enforcement Outer Continental Shelf Official... Outer Continental Shelf Official Protraction Diagrams (OPDs) located within Atlantic Ocean areas, with... informational purposes only. Outer Continental Shelf Official Protraction Diagrams in the North Atlantic,...
On diagram-chasing in double complexes
Bergman, George M
2011-01-01
Diagram-chasing arguments frequently lead to "magical" relations between distant points of diagrams: exactness implications, connecting morphisms, etc.. These long connections are usually composites of short "unmagical" connections, but the latter, and the objects they join, are not visible in the proofs. I try to remedy this situation. Given a double complex in an abelian category, we consider, for each object A of the complex, the familiar horizontal and vertical homology objects at A, and two other objects, which we name the "donor" A_{\\box} and and the "receptor" ^{\\box}A at A. For each arrow of the double complex, we prove the exactness of a 6-term sequence of these objects (the "Salamander Lemma"). Standard results such as the 3x3-Lemma, the Snake Lemma, and the long exact sequence of homology associated with a short exact sequence of complexes, are obtained as easy applications of this lemma. We then obtain some generalizations of the last of the above examples, getting various exact diagrams from doub...
Antiferromagnetic phase diagram of the cuprate superconductors
Nunes, L. H. C. M.; Teixeira, A. W.; Marino, E. C.
2017-02-01
Taking the spin-fermion model as the starting point for describing the cuprate superconductors, we obtain an effective nonlinear sigma-field hamiltonian, which takes into account the effect of doping in the system. We obtain an expression for the spin-wave velocity as a function of the chemical potential. For appropriate values of the parameters we determine the antiferromagnetic phase diagram for the YBa2Cu3O6+x compound as a function of the dopant concentration in good agreement with the experimental data. Furthermore, our approach provides a unified description for the phase diagrams of the hole-doped and the electron doped compounds, which is consistent with the remarkable similarity between the phase diagrams of these compounds, since we have obtained the suppression of the antiferromagnetic phase as the modulus of the chemical potential increases. The aforementioned result then follows by considering positive values of the chemical potential related to the addition of holes to the system, while negative values correspond to the addition of electrons.
MDM: A Mode Diagram Modeling Framework
Directory of Open Access Journals (Sweden)
Zheng Wang
2012-12-01
Full Text Available Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive computing in their modes. Despite the fact that such control systems are widely used in the above-mentioned safety-critical embedded domains, there is lack of domain-specific formal modelling languages for such systems in the relevant industry. To address this problem, we propose a formal visual modeling framework called mode diagram as a concise and precise way to specify and analyze such systems. To capture the temporal properties of periodic control systems, we provide, along with mode diagram, a property specification language based on interval logic for the description of concrete temporal requirements the engineers are concerned with. The statistical model checking technique can then be used to verify the mode diagram models against desired properties. To demonstrate the viability of our approach, we have applied our modelling framework to some real life case studies from industry and helped detect two design defects for some spacecraft control systems.
Application of Artificial Neural Network in Indicator Diagram
Institute of Scientific and Technical Information of China (English)
WuXiaodong; JiangHua; HanGuoqing
2004-01-01
Indicator diagram plays an important role in identifying the production state of oil wells. With an ability to reflect any non-linear mapping relationship, the artificial neural network (ANN) can be used in shape identification. This paper illuminates ANN realization in identifying fault kinds of indicator diagrams, including a back-propagation algorithm, characteristics of the indicator diagram and some examples. It is concluded that the buildup of a neural network and the abstract of indicator diagrams are important to successful application.
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...... the management and maintenance of these systems. Safety-barrier diagrams provide a useful framework for an electronic data structure that integrates information from risk analysis with operational safety management....
Geometry Algorisms of Dynkin Diagrams in Lie Group Machine Learning
Institute of Scientific and Technical Information of China (English)
Huan Xu; Fanzhang Li
2006-01-01
This paper uses the geometric method to describe Lie group machine learning (LML)based on the theoretical framework of LML, which gives the geometric algorithms of Dynkin diagrams in LML. It includes the basic conceptions of Dynkin diagrams in LML ,the classification theorems of Dynkin diagrams in LML, the classification algorithm of Dynkin diagrams in LML and the verification of the classification algorithm with experimental results.
The role of perceptual cues in matrix diagrams
van der Meij, Jan; van Amelsvoort, Marije; Anjewierden, A.
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 ce
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 ...
The role of perceptual cues in matrix diagrams
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
The role of perceptual cues in matrix diagrams
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
Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.
Willow, Soohaeng Yoo; Hirata, So
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 mEh after 10(6) Monte Carlo steps.
An automatic layout system for OMT-based object diagram
Energy Technology Data Exchange (ETDEWEB)
Nakashima, Satoshi; Ali, Jauhar; Tanaka, Jiro [Univ. of Tsukuba (Japan)
1996-12-31
In this paper, we propose an automatic layout method for the object diagram, the event trace diagram and the state diagram based on OMT (Object Modeling Technique) methodology. In our automatic layout system, when the elements of model (classes, associations etc.) are entered, an arrangement for them is computed, and the object model automatically appears in the editor`s window. We adopted Messinger`s algorithm using the rule of divide-and-conquer for the layout algorithm of the object diagram. Furthermore, diagrams can be maintained easily with the capabilities of automatic modification and direct manipulation interface.
Comprehending 3D Diagrams: Sketching to Support Spatial Reasoning.
Gagnier, Kristin M; Atit, Kinnari; Ormand, Carol J; Shipley, Thomas F
2016-11-25
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.
Design and Realization of Numerical Control Ladder Diagram Edition Software
Institute of Scientific and Technical Information of China (English)
ZHAO Haixin; MO Yimin; PAN Yunping
2006-01-01
The thesis is directed by the idea of oriented- object. Considering the basic functions that NC system Ladder Diagram editor should provide, and through theoretical research and practice, the thesis developed a set of NC system Ladder Diagram editor which can form a Ladder Diagram editor based on vector plotting, intelligently compiling, simulation. This system uses the ladder diagram symbol to express operational order and use the chart symbol series-parallel connection and the position order to express the logical relations between the operational orders, divide the ladder diagram into four parts: the stave, the line, the row and the part, uses the standard order vessel list vessel of the standard template stack (STL) to save the data which involved in the design process. This system can write PLC program by ladder diagram language and is easy to use. The compilation and simulation for PLC diagram have been achieved. It greatly improves the work-efficiency.
State-transition diagrams for biologists.
Bersini, Hugues; Klatzmann, David; Six, Adrien; Thomas-Vaslin, Véronique
2012-01-01
It is clearly in the tradition of biologists to conceptualize the dynamical evolution of biological systems in terms of state-transitions of biological objects. This paper is mainly concerned with (but obviously not limited too) the immunological branch of biology and shows how the adoption of UML (Unified Modeling Language) state-transition diagrams can ease the modeling, the understanding, the coding, the manipulation or the documentation of population-based immune software model generally defined as a set of ordinary differential equations (ODE), describing the evolution in time of populations of various biological objects. Moreover, that same UML adoption naturally entails a far from negligible representational economy since one graphical item of the diagram might have to be repeated in various places of the mathematical model. First, the main graphical elements of the UML state-transition diagram and how they can be mapped onto a corresponding ODE mathematical model are presented. Then, two already published immune models of thymocyte behavior and time evolution in the thymus, the first one originally conceived as an ODE population-based model whereas the second one as an agent-based one, are refactored and expressed in a state-transition form so as to make them much easier to understand and their respective code easier to access, to modify and run. As an illustrative proof, for any immunologist, it should be possible to understand faithfully enough what the two software models are supposed to reproduce and how they execute with no need to plunge into the Java or Fortran lines.
All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Bern, Z; Dixon, L J; Kosower, D A; Bern, Zvi; Duca, Vittorio Del; Dixon, Lance J.; Kosower, David A.
2004-01-01
We compute the non-MHV one-loop seven-gluon amplitudes in N=4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (- - - + + + +), (- - + - + + +), (- - + + -+ +) and (- + - + - + +). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n-3 positive-helicity gluons, and the color ordering (- - - + + ... + +); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.
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...
The Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Bern, Z.
2004-10-22
We compute the non-MHV one-loop seven-gluon amplitudes in N = 4 super-Yang-Mills theory, which contain three negative-helicity gluons and four positive-helicity gluons. There are four independent color-ordered amplitudes, (---++++), (--+-+++), (--++-++) and (-+-+-++). The MHV amplitudes containing two negative-helicity and five positive-helicity gluons were computed previously, so all independent one-loop seven-gluon helicity amplitudes are now known for this theory. We present partial information about an infinite sequence of next-to-MHV one-loop helicity amplitudes, with three negative-helicity and n - 3 positive-helicity gluons, and the color ordering (---+{center_dot}{center_dot}{center_dot}++); we give a new coefficient of one class of integral functions entering this amplitude. We discuss the twistor-space properties of the box-integral-function coefficients in the amplitudes, which are quite simple and suggestive.
Algorithms for Disconnected Diagrams in Lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Gambhir, Arjun Singh [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Stathopoulos, Andreas [College of William and Mary, Williamsburg, VA (United States); Orginos, Konstantinos [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Yoon, Boram [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gupta, Rajan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Syritsyn, Sergey [Stony Brook Univ., NY (United States)
2016-11-01
Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a quark loop as well as improvements to this method. Then, we motivate and introduce an algorithm based on the synergy between hierarchical probing and singular value deflation. We present results for the chiral condensate using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges with the basic algorithm.
On critical exponents without Feynman diagrams
Sen, Kallol; Sinha, Aninda
2016-11-01
In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov’s, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the O(n) model at the Wilson-Fisher fixed point in 4-ɛ dimensions up to O({ɛ }2). AS dedicates this work to the loving memory of his mother.
Magnetic phase diagram of Ho-Ag
Energy Technology Data Exchange (ETDEWEB)
Paul-Boncour, V [Chimie Metallurgique des Terres Rares, ICMPE, CNRS, 2 rue H Dunant, 94320 Thiais (France); Hoser, A; Stuesser, N [Hahn-Meitner Institut, Glienicker Strasse 100, 14109, Berlin (Germany); Hense, K; Gratz, E [Institute for Experimental Physics, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 (Austria); Rotter, M [Institut fuer Physikalische Chemie, Universitaet Wien, Waehringerstrasse 42, 1090 Wien (Austria)], E-mail: paulbon@glvt-cnrs.fr
2008-03-12
The magnetic phase diagram of Ho-Ag has been established using magnetoresistance, magnetostriction and neutron diffraction experiments versus applied field and temperature. Three different magnetic phases were observed: an incommensurate antiferromagnetic phase (IC) below T{sub N} = 33 K, a commensurate antiferromagnetic phase (C) above 5 T and below T{sub 1} (5-8 K) and a ferromagnetic component above 3 T. The IC phase undergoes spin reorientations around 5 T (IC') and 13 T (IC'')
On critical exponents without Feynman diagrams
Sen, Kallol
2015-01-01
In order to achieve a better analytic handle on the modern conformal bootstrap program, we re-examine and extend the pioneering 1974 work of Polyakov's, which was based on consistency between the operator product expansion and unitarity. As in the bootstrap approach, this method does not depend on evaluating Feynman diagrams. We show how this approach can be used to compute the anomalous dimensions of certain operators in the $O(n)$ model at the Wilson-Fisher fixed point in $4-\\epsilon$ dimensions up to $O(\\epsilon^2)$.
Applications of zero-suppressed decision diagrams
Sasao, Tsutomu
2014-01-01
A zero-suppressed decision diagram (ZDD) is a data structure to represent objects that typically contain many zeros. Applications include combinatorial problems, such as graphs, circuits, faults, and data mining. This book consists of four chapters on the applications of ZDDs. The first chapter by Alan Mishchenko introduces the ZDD. It compares ZDDs to BDDs, showing why a more compact representation is usually achieved in a ZDD. The focus is on sets of subsets and on sum-of-products (SOP) expressions. Methods to generate all the prime implicants (PIs), and to generate irredundant SOPs are show
Algorithms for Disconnected Diagrams in Lattice QCD
Gambhir, Arjun Singh; Orginos, Kostas; Yoon, Boram; Gupta, Rajan; Syritsyn, Sergey
2016-01-01
Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a quark loop as well as improvements to this method. Then, we motivate and introduce an algorithm based on the synergy between hierarchical probing and singular value deflation. We present results for the chiral condensate using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges with the basic algorithm.
Failure Assessment Diagram for Titanium Brazed Joints
Flom, Yury; Jones, Justin S.; Powell, Mollie M.; Puckett, David F.
2011-01-01
The interaction equation was used to predict failure in Ti-4V-6Al joints brazed with Al 1100 filler metal. The joints used in this study were geometrically similar to the joints in the brazed beryllium metering structure considered for the ATLAS telescope. This study confirmed that the interaction equation R(sub sigma) + R(sub Tau) = 1, where R(sub sigma) and R(sub Tau)are normal and shear stress ratios, can be used as conservative lower bound estimate of the failure criterion in ATLAS brazed joints as well as for construction of the Failure Assessment Diagram (FAD).
Spectral Transforms Calculation through Decision Diagrams
Directory of Open Access Journals (Sweden)
Radomir S. Stanković
2002-01-01
Full Text Available In this paper, calculation of spectral transforms through Decision diagrams (DDs and relationship of this method with FFT-like algorithms is discussed. It is shown that in DDs methods the basic operations in FFT-like algorithms are performed not on vectors but instead on parts of DDs as a data structure. Such a data structure represents the input signals, the intermediate results obtained during the calculation as well as the final output results. It should be noticed that, unlike FFT-like algorithms, DDs methods permit to take advantages from both, the properties of the transform matrices and the particular properties of the processed signals.
High temperature phase equilibria and phase diagrams
Kuo, Chu-Kun; Yan, Dong-Sheng
2013-01-01
High temperature phase equilibria studies play an increasingly important role in materials science and engineering. It is especially significant in the research into the properties of the material and the ways in which they can be improved. This is achieved by observing equilibrium and by examining the phase relationships at high temperature. The study of high temperature phase diagrams of nonmetallic systems began in the early 1900s when silica and mineral systems containing silica were focussed upon. Since then technical ceramics emerged and more emphasis has been placed on high temperature
BLOCK DIAGRAM MODELS FOR CORRELATED STRUCTURES
Directory of Open Access Journals (Sweden)
Adrian Stere PARIS
2016-05-01
Full Text Available The copula function offers new opportunities for advanced engineering design and can model correlated structures between random variables in reliability; in other words the dependence can describe time varying and nonlinear features of statistical links of marginal distributions. The paper proposes the study of reliability block diagrams by the analysis of the bridge model with links like serial-parallel, parallel-serial, based on total probability formula. The proposed reliability model built by copula functions is a new possible variant for statistical approach in the quality practice.
Combinatorics of Link Diagrams and Volume
Giambrone, Adam
2013-01-01
We show that the volumes of certain hyperbolic A-adequate links can be bounded (above and) below in terms of two diagrammatic quantities: the twist number and the number of certain alternating tangles in an A-adequate diagram. We then restrict our attention to plat closures of certain braids, a rich family of links whose volumes can be bounded in terms of the twist number alone. Furthermore, in the absence of special tangles, our volume bounds can be expressed in terms of a single stable coef...
Hysteresis Loops and Phase Diagrams of the Spin-1 Ising Model in a Transverse Crystal Field
Institute of Scientific and Technical Information of China (English)
S. Bouhou; I. Essaoudi; A. Ainane; M. Saber; J. J. de Miguel; M. Kerouad1
2012-01-01
Within the framework of the effective-Geld theory with a probability distribution technique, which accounts for the self-spin correlation functions, the ferromagnetic spin-l Ising model with a transverse crystal field on honeycomb, square and simple cubic lattices is studied. We have investigated the effect of the transverse crystal field on the phase diagrams, magnetization, hysteresis loops and χz,h of the system. A number of interesting phenomena of the system are discussed.%Within the framework of the effective-field theory with a probability distribution technique,which accounts for the self-spin correlation functions,the ferromagnetic spin-1 Ising model with a transverse crystal field on honeycomb,square and simple cubic lattices is studied.We have investigated the effect of the transverse crystal field on the phase diagrams,magnetization,hysteresis loops and xz,h of the system.A number of interesting phenomena of the system are discussed.
A comparative study of linear and region based diagrams
Directory of Open Access Journals (Sweden)
Björn Gottfried
2015-06-01
Full Text Available There are two categories of objects spatial information science investigates: actual objects and their spatial properties, such as in geography, and abstract objects which are employed metaphorically, as for visual languages. A prominent example of the latter are diagrams that model knowledge of some domain. Different aspects of diagrams are of interest, including their formal properties or how human users work with them, for example, with diagrams representing sets. The literature about diagrammatic systems for the representation of sets shows a dominance of region-based diagrams like Euler circles and Venn diagrams. The effectiveness of these diagrams, however, is limited because region-based diagrams become quite complex for more then three sets. By contrast, linear diagrams are not equally prevalent but enable the representation of a greater number of sets without getting cluttered. Cluttered diagrams exhibit inherent complexity due to overlapping objects, irrelevant details, or other reasons that impinge upon their legibility. This study contrasts both types of diagrammatic systems and investigates whether the performance of users differs for both kinds of diagrams. A significant difference can be shown regarding the number of diagrams that can be drawn within a fixed period of time and regarding the number of errors made. The results indicate that linear diagrams are more effective by being more restrictive and because region based diagrams show much clutter due to overlapping, coincident, and tangentially touching contours, as well as an overwhelming number of empty zones. Linear diagrams are less prone to errors and do not suffer from clutter.
Effects of pion-fold-pion diagrams in the energy-independent nucleon-nucleon potential
de Guzman, G.; Kuo, T. T. S.; Holinde, K.; Machleidt, R.; Faessler, A.; Müther, H.
1985-10-01
Based on a T-matrix equivalence theory, an energy-independent or locally energy-dependent nucléon-nucléon potential VNN derived from meson exchanges is studied. The potential, given as a series expansion of folded diagrams, is independent of the asymptotic energy of the scattering nucleons. It is, however, locally energy dependent in the sense that its matrix elements depend on the energies associated with its bra and ket states a and b. Our formulation makes use of right-hand-side on-shell T-matrix equivalence of the field-theoretical and potential descriptions when limited to the space of neutrons and protons only. This preserves not only scattering (e.g. phase shifts, projections of wave functions) but also bound-state properties. The matrix elements of V were calculated for two potential models, one based on one-pion exchange (OPEP) and the other on one-boson exchange (OBEP) using {π, ρ, σ, ω, δ, η }. Three types of phase-shift calculations have been carried out to study the viability of constructing an energy-independent potential using the folded-diagram expansion: (A) NN phase shifts for an energy-dependent OPEP and OBEP. For the OBEP we used parameters adjusted to fit experimental data. (B) The same phase shifts for the energy-independent case for both OPEP and OBEP. (C) Repetition of (B) with effects of the two-pion folded diagrams included. Our results show two important points: (i) folded diagrams are of essential importance, and (ii) the first-order folded diagrams contain the dominant effect and the neglect of terms with more than two folds can be regarded as a good approximation. The effects of folded diagrams are large especially for low partial waves and high energies. For high partial waves ( J greater than 2) the folded terms are negligible, and the phase shifts given by (A), (B) and (C) practically coincide.
Phase diagram and entanglement of two interacting topological Kitaev chains
Herviou, Loïc; Mora, Christophe; Le Hur, Karyn
2016-04-01
A superconducting wire described by a p -wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb-type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising-type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultracold atoms and Josephson junctions.
From 4d ambitwistor strings to on shell diagrams and back
Farrow, Joseph A.; Lipstein, Arthur E.
2017-07-01
We investigate the relation between 4d ambitwistor string theory and on-shell diagrams for planar N=4 super-Yang-Mills and N=8 supergravity, and deduce several new results about their scattering amplitudes at tree-level and 1-loop. In particular, we derive new Grassmannian integral formulae for tree-level amplitudes and obtain new world-sheet formulae for 1-loop amplitudes which are manifestly supersymmetric and supported on scattering equations refined by MHV degree.
Ab initio study of the composite phase diagram of Ni-Mn-Ga shape memory alloys
Sokolovskaya, Yu. A.; Sokolovskiy, V. V.; Zagrebin, M. A.; Buchelnikov, V. D.; Zayak, A. T.
2017-07-01
The magnetic and structural properties of a series of nonstoichiometric Ni-Mn-Ga Heusler alloys are theoretically investigated in terms of the density functional theory. Nonstoichiometry is formed in the coherent potential approximation. Concentration dependences of the equilibrium lattice parameter, the bulk modulus, and the total magnetic moment are obtained and projected onto the ternary phase diagram of the alloys. The stable crystalline structures and the magnetic configurations of the austenitic phase are determined.
Kinematical Diagrams for Conical Relativistic Jets
Indian Academy of Sciences (India)
Gopal-Krishna; Pronoy Sircar; Samir Dhurde
2007-03-01
We present diagrams depicting the expected inter-dependences of two key kinematical parameters of radio knots in the parsec-scale jets of blazars, deduced from VLBI observations. The two parameters are the apparent speed (app = capp) and the effective Doppler boosting factor (eff) of the relativistically moving radio knot. A novel aspect of these analytical computations of – diagrams is that they are made for parsecscale jets having a conical shape, with modest opening angles ( up to 10°), in accord with the VLBI observations of the nuclei of the nearest radio galaxies. Another motivating factor is the recent finding that consideration of a conical geometry can have important implications for the interpretation of a variety of radio observations of blazar jets. In addition to uniform jet flows (i.e., those having a uniform bulk Lorentz factor, ), computational results are also presented for stratified jets where an ultra-relativistic central spine along the jet axis is surrounded by a slower moving sheath, possibly arising from a velocity shear.
The Critical Importance of Russell's Diagram
Gingerich, Owen
2013-01-01
The idea of dwarf and giants stars, but not the nomenclature, was first established by Eijnar Hertzsprung in 1905; his first diagrams in support appeared in 1911. In 1913 Henry Norris Russell could demonstrate the effect far more strikingly because he measured the parallaxes of many stars at Cambridge, and could plot absolute magnitude against spectral type for many points. The general concept of dwarf and giant stars was essential in the galactic structure work of Harlow Shapley, Russell's first graduate student. In order to calibrate the period-luminosity relation of Cepheid variables, he was obliged to fall back on statistical parallax using only 11 Cepheids, a very sparse sample. Here the insight provided by the Russell diagram became critical. The presence of yellow K giant stars in globular clusters credentialed his calibration of the period-luminosity relation by showing that the calibrated luminosity of the Cepheids was comparable to the luminosity of the K giants. It is well known that in 1920 Shaple...
Ab initio phase diagram of iridium
Burakovsky, L.; Burakovsky, N.; Cawkwell, M. J.; Preston, D. L.; Errandonea, D.; Simak, S. I.
2016-09-01
The phase diagram of iridium is investigated using the Z methodology. The Z methodology is a technique for phase diagram studies that combines the direct Z method for the computation of melting curves and the inverse Z method for the calculation of solid-solid phase boundaries. In the direct Z method, the solid phases along the melting curve are determined by comparing the solid-liquid equilibrium boundaries of candidate crystal structures. The inverse Z method involves quenching the liquid into the most stable solid phase at various temperatures and pressures to locate a solid-solid boundary. Although excellent agreement with the available experimental data (to ≲65 GPa) is found for the equation of state (EOS) of Ir, it is the third-order Birch-Murnaghan EOS with B0'=5 rather than the more widely accepted B0'=4 that describes our ab initio data to higher pressure (P ) . Our results suggest the existence of a random-stacking hexagonal close-packed structure of iridium at high P . We offer an explanation for the 14-layer hexagonal structure observed in experiments by Cerenius and Dubrovinsky.
The magnetized effective QCD phase diagram
Ayala, Alejandro; Hernandez, L A; Loewe, M; Zamora, R
2015-01-01
The QCD phase diagram in the temperature versus quark chemical potential plane is studied in the presence of a magnetic field, using the linear sigma model coupled to quarks. It is shown that the decrease of the couplings with increasing field strength obtained in this model leads to the critical temperature for the phase transition to decrease with increasing field intensity (inverse magnetic catalysis). This happens provided that plasma screening is properly accounted for. It is also found that with increasing field strength the location of the critical end point (CEP) in the phase diagram moves toward lower values of the critical quark chemical potential and larger values of the critical temperature. In addition, the CEP approaches the temperature axis for large values of the magnetic field. We argue that a similar behavior is to be expected in QCD, since the physical impact of the magnetic field, regardless of strength, is to produce a spatial dimension reduction, whereby virtual quark-antiquark pairs are...
Reliability block diagrams to model disease management.
Sonnenberg, A; Inadomi, J M; Bauerfeind, P
1999-01-01
Studies of diagnostic or therapeutic procedures in the management of any given disease tend to focus on one particular aspect of the disease and ignore the interaction between the multitude of factors that determine its final outcome. The present article introduces a mathematical model that accounts for the joint contribution of various medical and non-medical components to the overall disease outcome. A reliability block diagram is used to model patient compliance, endoscopic screening, and surgical therapy for dysplasia in Barrett's esophagus. The overall probability of a patient with a Barrett's esophagus to comply with a screening program, be correctly diagnosed with dysplasia, and undergo successful therapy is 37%. The reduction in the overall success rate, despite the fact that the majority of components are assumed to function with reliability rates of 80% or more, is a reflection of the multitude of serial subsystems involved in disease management. Each serial component influences the overall success rate in a linear fashion. Building multiple parallel pathways into the screening program raises its overall success rate to 91%. Parallel arrangements render systems less sensitive to diagnostic or therapeutic failures. A reliability block diagram provides the means to model the contributions of many heterogeneous factors to disease outcome. Since no medical system functions perfectly, redundancy provided by parallel subsystems assures a greater overall reliability.
Phase Diagram of Spiking Neural Networks
Directory of Open Access Journals (Sweden)
Hamed eSeyed-Allaei
2015-03-01
Full Text Available In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probablilty of 2%, 20% of neurons are inhibitory and 80% are excitatory. These common values are based on experiments, observations. but here, I take a different perspective, inspired by evolution. I simulate many networks, each with a different set of parameters, and then I try to figure out what makes the common values desirable by nature. Networks which are configured according to the common values, have the best dynamic range in response to an impulse and their dynamic range is more robust in respect to synaptic weights. In fact, evolution has favored networks of best dynamic range. I present a phase diagram that shows the dynamic ranges of different networks of different parameteres. This phase diagram gives an insight into the space of parameters -- excitatory to inhibitory ratio, sparseness of connections and synaptic weights. It may serve as a guideline to decide about the values of parameters in a simulation of spiking neural network.
Chen, Jing-Yuan; Son, Dam Thanh
2017-02-01
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.
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
Phase diagram of aggregation of oppositely charged colloids in salty water.
Zhang, R; Shklovskii, B I
2004-02-01
Aggregation of two oppositely charged colloids in salty water is studied. We focus on the role of Coulomb interaction in strongly asymmetric systems in which the charge and size of one colloid is much larger than the other one. In the solution, each large colloid (macroion) attracts a certain number of oppositely charged small colloids (Z-ion) to form a complex. If the concentration ratio of the two colloids is such that complexes are not strongly charged, they condense in a macroscopic aggregate. As a result, the phase diagram in a plane of concentrations of two colloids consists of an aggregation domain sandwiched between two domains of stable solutions of complexes. The aggregation domain has a central part of total aggregation and two wings corresponding to partial aggregation. A quantitative theory of the phase diagram in the presence of monovalent salt is developed. It is shown that as the Debye-Hückel screening radius r(s) decreases, the aggregation domain grows, but the relative size of the partial aggregation domains becomes much smaller. As an important application of the theory, we consider solutions of long double-helix DNA with strongly charged positive spheres (artificial chromatin). We also consider implications of our theory for in vitro experiments with the natural chromatin. Finally, the effect of different shapes of macroions on the phase diagram is discussed.
Anisimov, M. P.
2016-12-01
One can find in scientific literature a pretty fresh idea of the nucleation rate surfaces design over the diagrams of phase equilibria. That idea looks like profitable for the nucleation theory development and for various practical applications where predictions of theory have no high enough accuracy for today. The common thermodynamics has no real ability to predict parameters of the first order phase transition. Nucleation experiment can be provided in very local nucleation conditions even the nucleation takes place from the critical line (in two-component case) down to the absolute zero temperature limit and from zero nucleation rates at phase equilibria up to the spinodal conditions. Theory predictions have low reliability as a rule. The computational chemistry has chance to make solution of that problem easier when a set of the used axiomatic statements will adapt enough progressive assumptions [1]. Semiempirical design of the nucleation rate surfaces over diagrams of phase equilibria have a potential ability to provide a reasonable quality information on nucleation rate for each channel of nucleation. Consideration and using of the nucleation rate surface topologies to optimize synthesis of a given phase of the target material can be available when data base on nucleation rates over diagrams of phase equilibria will be created.
Rapid and Accurate Estimates of Alloy Phase Diagrams for Design and Assessment
Tan, Teck; Johnson, Duane
2009-03-01
Based on first-principles cluster expansion (CE), we obtain rapid but accurate assessments of alloy T vs c phase diagrams from a mean-field theory that conserves sum rules over pair correlations. Such conserving mean-field theories are less complicated than the popular cluster variation method, and better reproduce the Monte Carlo (MC) phase boundaries and Tc for the nearest-neighbor Ising model [1]. The free-energy f(T,c) is a simple analytic expression and its value at fixed T or c is obtained by solving a set of n non-linear coupled equations, where n is determined by the number of sublattices in the groundstate structure and the range of pair correlations included. While MC is ``exact,'' conserving mean-field theories are 10 to 10^3 faster, allowing for rapid phase diagram construction, dramatically saving computation time. We have generalized the method to account for multibody interactions to enable phase diagram calculations via first-principles CE, and its accuracy is showed vis-à-vis exact MC for several alloy systems. The method is included in our Thermodynamic ToolKit (TTK), available for general use in 2009. [1] V. I. Tokar, Comput. Mater. Sci. 8 (1997), p.8
Heydarinasab, F.; Abouie, J.
2017-09-01
We introduce an inhomogeneous bosonic mixture composed of two kinds of hard-core and semi-hard-core bosons with different nilpotency conditions and demonstrate that in contrast with the standard hard-core Bose-Hubbard model, our bosonic mixture with nearest- and next-nearest-neighbor interactions on a square lattice develops the checkerboard supersolid phase characterized by the simultaneous superfluid and checkerboard solid orders. Our bosonic mixture is created from a two-orbital Bose-Hubbard model including two kinds of bosons: a single-orbital boson and a two-orbital boson. By mapping the bosonic mixture to an anisotropic inhomogeneous spin model in the presence of a magnetic field, we study the ground-state phase diagram of the model by means of cluster mean field theory and linear spin-wave theory and show that various phases such as solid, superfluid, supersolid, and Mott insulator appear in the phase diagram of the mixture. Competition between the interactions and magnetic field causes the mixture to undergo different kinds of first- and second-order phase transitions. By studying the behavior of the spin-wave excitations, we find the reasons of all first- and second-order phase transitions. We also obtain the temperature phase diagram of the system using cluster mean field theory. We show that the checkerboard supersolid phase persists at finite temperature comparable with the interaction energies of bosons.
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 ...
The Diagram as Story: Unfolding the Event-Structure of the Mathematical Diagram
de Freitas, Elizabeth
2012-01-01
This paper explores the role of narrative in decoding diagrams. I focus on two fundamental facets of narrative: (1) the recounting of causally related sequences of events, and (2) the positioning of the narrator through point-of-view and voice. In the first two sections of the paper I discuss philosophical and semiotic frameworks for making sense…
Superstring Theory 2 Volume Hardback Set
Green, Michael B.; Schwarz, John H.; Witten, Edward
2012-07-01
Volume 1: Preface; 1. Introduction; 2. Free bosonic strings; 3. Modern covariant quantization; 4. World-sheet supersymmetry in string theory; 5. Space-time supersymmetry in string theory; 6. Nonabelian gauge symmetry; 7. Tree amplitudes; Bibliography; Index; Volume 2: Preface; 8. One-loop diagrams in the bosonic string theory; 9. One-loop diagrams in superstring theory; 10. The gauge anomaly in type I superstring theory; 11. Functional methods in the light-cone gauge; 12. Some differential geometry; 13. Low-energy effective action; 14. Compactification of higher dimensions; 15. Some algebraic geometry; 16. Models of low-energy supersymmetry; Bibliography; Index.
Directory of Open Access Journals (Sweden)
F Keshavarz
2017-02-01
Full Text Available In this study, the effect of four-spin exchanges between the nearest and next nearest neighbor spins of honeycomb lattice on the phase diagram of S=3/2 antiferomagnetic Heisenberg model is considered with two-spin exchanges between the nearest and next nearest neighbor spins. Firstly, the method is investigated with classical phase diagram. In classical phase diagram, in addition to Neel order, classical degeneracy is also seen. The existance of this phase in diagram phase is important because of the probability of the existence of quantum spin liquid in this region for such amount of interaction. To investigate the effect of quantum fluctuation on the stability of the obtained classical phase diagram, linear spin wave theory has been used. Obtained results show that in classical degeneracy regime, the quantum fluctuations cause the order by disorder in the spin system and the ground state is ordered
How to See a Diagram: A Visual Anthropology of Chemical Affinity.
Eddy, Matthew Daniel
2014-01-01
In 1766, Thomas Cochrane entered the Edinburgh classroom of Joseph Black (1728-99) to learn chemistry for the first time. Cochrane was studying medicine, and, like so many of Black's students, he dutifully recorded several diagrams in his notebooks. These visualizations were not complex. They were, in fact, simple. One of them, reproduced in this essay, was a single "X" a chiasm. Black used it to illustrate ratios of chemical attraction. This diagram is particularly important for the history of chemistry because it is often held to be the first chemical formula, and, as such, historians have endeavored to explain why it was unique and how Black invented it. In this essay, I wish to turn the foregoing premise on its head by arguing that Black's chiasm was neither visually unique nor invented by him. I do this by approaching a number of his diagrams via a visual anthropology that allows me to examine how students learned to attach meaning to patterns that were already familiar to them. In the end, we will see that Black's diagrams were successful because their visual simplicity and familiarity made them ideally suited to represent the chemical theories that he so skillfully attached to them.
Generalized Ellingham diagrams for utilization in solid oxide fuel cells
Directory of Open Access Journals (Sweden)
Kishimoto H.
2008-01-01
Full Text Available Generalized Ellingham diagram for the P-O-H and the Ni-P-OH systems have been constructed to investigate thermodynamically the chemical stability of nickel anode against the gaseous impurities containing phosphorous compounds. In the same way as the original Ellingham diagram, the oxygen potential is used as the vertical axis, while the temperature is adopted as horizontal axis. For the P-O-H system which contains many gaseous species, the dominant areas of gaseous species are displayed with a parameter of their partial pressure in an analogous way to the aqueous species in the Pourbaix diagram. The multicomponent Ellingham diagram for the Ni-P-O-H system was constructed in a similar manner to the multicomponent Pourbaix diagram. The obtained diagrams have been discussed to examine the reactivity of nickel anodes with phosphorus compounds in SOFCs in terms of operational variables such as temperature, oxygen potential, overpotential under the anode polarization and so on.
Database design using entity-relationship diagrams
Bagui, Sikha
2011-01-01
Data, Databases, and the Software Engineering ProcessDataBuilding a DatabaseWhat is the Software Engineering Process?Entity Relationship Diagrams and the Software Engineering Life Cycle Phase 1: Get the Requirements for the Database Phase 2: Specify the Database Phase 3: Design the DatabaseData and Data ModelsFiles, Records, and Data ItemsMoving from 3 × 5 Cards to ComputersDatabase Models The Hierarchical ModelThe Network ModelThe Relational ModelThe Relational Model and Functional DependenciesFundamental Relational DatabaseRelational Database and SetsFunctional
Phase diagram of a Schelling segregation model
Gauvin, L.; Vannimenus, J.; Nadal, J.-P.
2009-07-01
The collective behavior in a variant of Schelling’s segregation model is characterized with methods borrowed from statistical physics, in a context where their relevance was not conspicuous. A measure of segregation based on cluster geometry is defined and several quantities analogous to those used to describe physical lattice models at equilibrium are introduced. This physical approach allows to distinguish quantitatively several regimes and to characterize the transitions between them, leading to the building of a phase diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We also establish links with ‘spin-1’ models in physics. Our approach provides generic tools to analyze the dynamics of other socio-economic systems.
Phase Diagram of the Frustrated Hubbard Model
Zitzler, R.; Tong, N.-H.; Pruschke, Th.; Bulla, R.
2004-07-01
The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the one-band Hubbard model has long been used to describe similar features in real materials like V2O3. In this Letter we investigate the antiferromagnetic phase of this model with frustration. At T=0 we find a first-order transition from a paramagnetic metal to an antiferromagnetic insulator. We show that even in the presence of strong magnetic frustration, the paramagnetic metal-insulator transition is hidden inside an extended antiferromagnetic region. This raises the question of whether the one-band Hubbard model with frustration is sufficient to describe the phase diagram of V2O3 or similar transition metal oxides even qualitatively.
Revised state diagram of Laponite dispersions.
Mongondry, Philippe; Tassin, Jean François; Nicolai, Taco
2005-03-15
We propose a state diagram of charged disk-like mineral particle (Laponite) dispersions as a function of the Laponite concentration (C) and the concentration of added salt (C(s)), based on simple observation and light-scattering measurements. At low C or high C(s) the dispersions separate into two domains due to sedimentation of Laponite aggregates, while at high C and low C(s) they form homogeneous gels that do not flow upon tube reversal. The aggregation rate and the structure factor of the Laponite dispersions is determined with light scattering as a function of C and C(s). We discuss in detail the controversy on the origin of gelation of Laponite dispersions in the absence of added salt. We argue that aggregation rather than glass formation causes gelation.
Cuts and coproducts of massive triangle diagrams
Energy Technology Data Exchange (ETDEWEB)
Abreu, Samuel [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Mayfield Road, Edinburgh EH9 3JZ, Scotland (United Kingdom); Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France); Britto, Ruth [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France); School of Mathematics, Trinity College,College Green, Dublin 2 (Ireland); Hamilton Mathematical Institute, Trinity College,College Green, Dublin 2 (Ireland); Grönqvist, Hanna [Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS,Orme des Merisiers, F-91191 Gif-sur-Yvette (France)
2015-07-21
Relations between multiple unitarity cuts and coproducts of Feynman integrals are extended to allow for internal masses. These masses introduce new branch cuts, whose discontinuities can be derived by placing single propagators on shell and identified as particular entries of the coproduct. First entries of the coproduct are then seen to include mass invariants alone, as well as threshold corrections for external momentum channels. As in the massless case, the original integral can possibly be recovered from its cuts by starting with the known part of the coproduct and imposing integrability contraints. We formulate precise rules for cuts of diagrams, and we gather evidence for the relations to coproducts through a detailed study of one-loop triangle integrals with various combinations of external and internal masses.
The Gamma Ray Bursts Hubble diagram
Capozziello, S; Dainotti, M G; De Laurentis, M; Izzo, L; Perillo, M
2011-01-01
Thanks to their enormous energy release, Gamma Rays Bursts (GRBs) have recently attracted a lot of interest to probe the Hubble diagram (HD) deep into the matter dominated era and hence complement Type Ia Supernovae (SNeIa). We consider here three different calibration methods based on the use of a fiducial LCDM model, on cosmographic parameters and on the local regression on SNeIa to calibrate the scaling relations proposed as an equivalent to the Phillips law to standardize GRBs finding any significant dependence. We then investigate the evolution of these parameters with the redshift to obtain any statistical improvement. Under this assumption, we then consider possible systematics effects on the HDs introduced by the calibration method, the averaging procedure and the homogeneity of the sample arguing against any significant bias.
Specification of Learning Content Using Feature Diagrams
Damaševičius, Robertas
The main idea of a learning object (LO) is to break educational content down into small chunks that can be reused in various learning environments. When reused, such small chunks of educational content are combined in various ways leading to a great variability of the learning content. We propose using feature diagrams (FDs) for the specification of learning content at different layers of abstraction starting from the organization of teaching material in a lecture down to the specification and demonstration of particular software/hardware components. FDs can be used by (1) designers, teachers, and learners for graphical representation of domain knowledge in LOs; (2) programmers to specify and express variability-commonality relationships of LOs at a higher abstraction level to allow the development and implementation of generative LOs; and (3) researchers as a vehicle for analysis and better understanding of the e-Learning domain itself.
Bianchi I meets the Hubble diagram
Schucker, Thomas; Valent, Galliano
2014-01-01
We improve existing fits of the Bianchi I metric to the Hubble diagram of supernovae and find an intriguing yet non-significant signal for anisotropy that should be verified or falsified in the near future by the Large Synoptic Survey Telescope. Since the literature contains two different formulas for the apparent luminosity as a function of time of flight in Bianchi I metrics, we present an independent derivation confirming the result by Saunders (1969). The present fit differs from earlier ones by Koivisto & Mota and by Campanelli et al. in that we use Saunders' formula, a larger sample of supernovae, Union 2 and JLA, and we use the general Bianchi I metric with three distinct eigenvalues.
Bayesian Image Reconstruction Based on Voronoi Diagrams
Cabrera, G F; Hitschfeld, N
2007-01-01
We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric images. We use a variable Voronoi diagram as our model in place of the usual fixed pixel grid. A quantization of the intensity field allows us to calculate the likelihood function and a-priori probabilities. The Voronoi image is optimized including the number of polygons as free parameters. We apply our algorithm to deconvolve simulated interferometric data. Residuals, restored images and chi^2 values are used to compare our reconstructions with fixed grid models. VIR has the advantage of modeling the image with few parameters, obtaining a better image from a Bayesian point of view.
Understanding starch gelatinization: The phase diagram approach.
Carlstedt, Jonas; Wojtasz, Joanna; Fyhr, Peter; Kocherbitov, Vitaly
2015-09-20
By constructing a detailed phase diagram for the potato starch-water system based on data from optical microscopy, synchrotron X-ray scattering and differential scanning calorimetry, we show that gelatinization can be interpreted in analogy with a eutectic transition. The phase rule explains why the temperature of the gelatinization transition (G) is independent on water content. Furthermore, the melting (M1) endotherm observed in DSC represents a liquidus line; the temperature for this event increases with increasing starch concentration. Both the lamellar spacing and the inter-helix distance were observed to decrease with increasing starch content for starch concentrations between approximately 65 wt% and 75 wt%, while the inter-helix distance continued decreasing upon further dehydration. Understanding starch gelatinization has been a longstanding challenge. The novel approach presented here shows interpretation of this phenomenon from a phase equilibria perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.
The Phase Diagram of Superionic Ice
Sun, Jiming; Clark, Bryan; Car, Roberto
2014-03-01
Using the variable cell Car-Parrinello molecular dynamics method, we study the phase diagram of superionic ice from 200GPa to 2.5TPa. We present evidence that at very high pressure the FCC structure of the oxygen sublattice may become unstable allowing for a new superionic ice phase, in which the oxygen sublattice takes the P21 structure found in zero-temperature total energy calculations. We also report on how the melting temperature of the hydrogen sublattice is affected by this new crystalline structure of the oxygen sublattice. This work was supported by the NSF under grant DMS-1065894(J.S. and R.C.) and PHY11-25915(B.C.).
The Eh-pH Diagram and Its Advances
Hsin-Hsiung Huang
2016-01-01
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,...
Duals of Orphan-Free Anisotropic Voronoi Diagrams are Triangulations
Canas, Guillermo D
2011-01-01
We show that, under mild conditions on the underlying metric, duals of appropriately defined anisotropic Voronoi diagrams are embedded triangulations. Furthermore, they always triangulate the convex hull of the vertices, and have other properties that parallel those of ordinary Delaunay triangulations. These results apply to the duals of anisotropic Voronoi diagrams of any set of vertices, so long as the diagram is orphan-free.
Zone diagrams in compact subsets of uniformly convex normed spaces
Kopecká, E. (Eva); Reem, D.; Reich, S.
2012-01-01
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the exist...
Zone diagrams in compact subsets of uniformly convex normed spaces
2010-01-01
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matousek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and proved the existence and uniqueness of zone diagrams there. In the present paper we prove the exist...
Thermodynamic Equilibrium Diagrams of Sulphur-Chromium System
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The chemical and electrochemical equilibria in the presence of gaseous phase were investigated. Many substances, which consisted of sulphur and chromium, were considered. Various thermodynamic equilibria were calculated in different pressures. Calculation results were shown as log p―1/T and E―T diagrams. These diagrams may be used to study the corrosion of chromium in sulphur-containing circumstances. The diagrams are also used to thermodynami-cally determine the existence area of various substances and so on.
Solid-liquid phase diagram of disubstituted benzene systems
Institute of Scientific and Technical Information of China (English)
黑恩成; 刘国杰
1995-01-01
The cooling curves of different compositions of the systems of ortho-chlorotoluene/para-chlorotoluene and ortho-nitrochlorobenzene/para-nitrochlorobenzene are carefully determined by the thermal analysis method. The crystals obtained are also tested. The conclusion that both systems are of simple eutectic diagram but not the solid solution diagram with a minimum melting point is confirmed. The characteristics of the diagram are explained according to the physical and thermodynarmc properties of the components.
Group theory for chemists fundamental theory and applications
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
Binary decision diagrams by shared rewriting
Pol, J. van de; Zantema, H.
2000-01-01
BDDs provide an established technique for propositional formula manipulation. In this paper we re-develope the basic BDD theory using standard rewriting techniques. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develope appropriate theory. A rewriting system is
Computer recognition of slag property diagrams in ternary systems
Institute of Scientific and Technical Information of China (English)
Jinxiong Lu; Li Wang; Jiongming Zhang; Xinhua Wang
2004-01-01
In order to take data information from the slag property diagram in a ternary system automatically and actually, a picture recognition and drawing software has been developed by Visual Basic 6.0 based on the image coding principle of computer system and the graphics programming method of VB. This software can transform the ternary system isopleth diagram from bitmap format to data file and establish a corresponding database which can be applied to rapidly retrieve a mass of data and make correlative thermodynamics or kinetics calculation. Besides, it still has the function of drawing the ternary system diagram which can draw different kinds of property parameters in the same diagram.
Wellformedness properties in Euler diagrams: which should be used?
Rodgers, Peter; Zhang, Leishi; Purchase, Helen
2012-07-01
Euler diagrams are often used to visualize intersecting data sets in applications such as criminology; genetics, medicine, and computer file systems. One interesting aspect of these diagrams is that some data sets cannot be drawn without breaking one or more "wellformedness properties," which are considered to reduce the user comprehension of the diagrams. However, it is possible to draw the same data with different diagrams, each of which breaks different wellformedness properties. Hence, some properties are "swappable," so motivating the study of which of the alternatives would be best to use. This paper reports on the two empirical studies to determine how wellformedness properties affect comprehension. One study was with abstract data, the other was with concrete data that visualized students' enrollment on university modules. We have results from both studies that imply that diagrams with concurrency or disconnected zones perform less well than other some other properties. Further, we have no results that imply that diagrams with brushing points adversely affect performance. Our data also indicate that nonsimple curves are preferred less than diagrams with other properties. These results will inform both human diagram designers and the developers of automated drawing systems on the best way to visualize data using Euler diagrams.
Visualization design and verification of Ada tasking using timing diagrams
Vidale, R. F.; Szulewski, P. A.; Weiss, J. B.
1986-01-01
The use of timing diagrams is recommended in the design and testing of multi-task Ada programs. By displaying the task states vs. time, timing diagrams can portray the simultaneous threads of data flow and control which characterize tasking programs. This description of the system's dynamic behavior from conception to testing is a necessary adjunct to other graphical techniques, such as structure charts, which essentially give a static view of the system. A series of steps is recommended which incorporates timing diagrams into the design process. Finally, a description is provided of a prototype Ada Execution Analyzer (AEA) which automates the production of timing diagrams from VAX/Ada debugger output.
Maries, Alexandru
2016-01-01
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a give problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing a diagram facilitates problem solution. We conducted an investigation in which 111 students in an algebra-based introductory physics course were subjected to two different interventions during recitation quizzes throughout the semester. They were either (1) asked to solve problems in which the diagrams were drawn for them or (2) explicitly told to draw a diagram. A comparison group was not given any instruction regarding diagrams. We developed a rubric to score the problem-solving performance of students in different intervention groups. We investigated two problems involving electric field and electric force and found that students who draw expert-like diagrams are more successful problem solvers and that a higher level of detai...
Lekkerkerker, H. N. W.; Oversteegen, S.M.
2004-01-01
Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas–liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and ...
Putting Consistent Theories Together in Institutions
Institute of Scientific and Technical Information of China (English)
应明生
1995-01-01
The problem of putting consistent theories together in institutions is discussed.A general necessary condition for consistency of the resulting theory is carried out,and some sufficient conditions are given for diagrams of theories in which shapes are tree bundles or directed graphs.Moreover,some transformations from complicated cases to simple ones are established.
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.
OntoDiagram: Automatic Diagram Generation for Congenital Heart Defects in Pediatric Cardiology
Vishwanath, Kartik; Viswanath, Venkatesh; Drake, William; Lee, Yugyung
2005-01-01
In pediatric cardiology as well as many other medical specialties, the accurate portrayal of a large volume of patient information is crucial to providing good patient care. Our research aims at utilizing clinical and spatial ontologies representing the human heart, to automatically generate a Mullins-like diagram [6] based on a patient's information in the cardiology databases. Our ontology allows an intuitive way of modeling congenital defects with the structure of the hum...
ALLOYS, YTTERBIUM, TERBIUM, MANGANESE ALLOYS, MERCURY ALLOYS, X RAY DIFFRACTION, X RAY SPECTROSCOPY, DIFFERENTIAL THERMAL ANALYSIS, PHASE DIAGRAMS , MAGNETIC PROPERTIES, CRYSTAL STRUCTURE, METALLOGRAPHY, AUSTRIA
Le Minh, Tam; von Langermann, Jan; Lorenz, Heike; Seidel-Morgenstern, Andreas
2010-09-01
A systematic study of binary melting point and ternary solubility phase diagrams of the enantiomeric 3-chloromandelic acid (3-ClMA) system was performed under consideration of polymorphism. The melting point phase diagram was measured by means of thermal analysis, that is, using heat-flux differential scanning calorimetry (DSC). The results reveal that 3-ClMA belongs to the racemic compound-forming systems. Polymorphism was found for both the enantiomer and the racemate as confirmed by X-ray powder diffraction analysis. The ternary solubility phase diagram of 3-ClMA in water was determined between 5 and 50 degrees C by the classical isothermal technique. The solubilities of the pure enantiomers are extremely temperature-dependent. The solid-liquid equilibria of racemic 3-ClMA are not trivial due to the existence of polymorphism. The eutectic composition in the chiral system changes as a function of temperature. Further, solubility data in the alternative solvent toluene are also presented.
Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo
Azadi, Sam
2016-01-01
We study the low-pressure (0 to 10 GPa) phase diagram of crystalline benzene using quantum Monte Carlo (QMC) and density functional theory (DFT) methods. We consider the $Pbca$, $P4_32_12$, and $P2_1/c$ structures as the best candidates for phase I and phase II. We perform diffusion quantum Monte Carlo (DMC) calculations to obtain accurate static phase diagrams as benchmarks for modern van der Waals density functionals. We use density functional perturbation theory to compute phonon contribution in the free-energy calculations. Our DFT enthalpy-pressure phase diagram indicates that the $Pbca$ and $P2_1/c$ structures are the most stable phases within the studied pressure range. The DMC Gibbs free-energy calculations predict that the room temperature $Pbca$ to $P2_1/c$ phase transition occurs at 2.1(1) GPa. This prediction is consistent with available experimental results at room temperature. Our DMC calculations show an estimate of 50.6$\\pm$0.5 kJ/mol for crystalline benzene lattice energy.
Aoyama, T; Kinoshita, T; Nio, M
2014-01-01
This paper presents a detailed account of evaluation of the electron anomalous magnetic moment a_e which arises from the gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte-Carlo integration routine VEGAS is 8.726(336)(\\alpha/\\pi)^5, which replaces the very preliminary value reported in 2012. Combining it with other 6318 tenth-order diagrams published previously we obtain 7.795(336)(\\alpha/\\pi)^5 as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to a_e(theory)=1 159 652 181.643 (25)(23)(16)(763) \\times 10^{-12}, where first three uncertainties are from the eighth-order term, tenth-order term, and hadronic and elecroweak terms. The fourth and largest uncertainty is from \\alpha^{-1}=137.035 999 049(90), the fine-structure constant derived from the rubidium recoil measurement. a_e(theory) and a_e(experiment) agree wi...
Atomic density functional and diagram of structures in the phase field crystal model
Ankudinov, V. E.; Galenko, P. K.; Kropotin, N. V.; Krivilyov, M. D.
2016-02-01
The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindrical tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.
Phase diagram for ortho-para-hydrogen monolayers
Sullivan, N S
2003-01-01
The phase diagram for orientational ordering of hydrogen monolayers on graphite and boron nitride is revised in view of current theory and experimental observations from nuclear magnetic resonance (NMR) studies recently reported for ortho-H sub 2 concentrations 0.35 <= c <= 0.92 and temperatures 0.14 <= T <= 1.80 K. The characteristic interaction coupling GAMMA sub 0 = 0.50 +- 0.03 K and the crystalline field amplitude V sub 0 = 0.70 +- 0.10 K are derived from experimental data, and distinct types of the local orientationally ordered structures are analysed using a proposed model for site-diluted uniaxial quadrupoles on a triangular plane lattice of hexagonal symmetry. The long-range periodic pinwheel structure and the short-range quadrupolar glass (QG) phase are stable above the 2D site-percolation limit, c sub p = 0.72, and for 0.48 < c < c sub p , respectively, where quadrupolar-order effects dominate. At very low T, the QG phase shows instability with respect to local dipole-like polariz...
Application of causality diagram in system safety analysis
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Causality Diagram (CD) is a new graphical knowledge representation based on probability theory. The application of this methodology in the safety analysis of the gas explosion in collieries was discussed in this paper, and the Minimal Cut Set, the Minimal Path Set and the Importance were introduced to develop the methodology. These concepts are employed to analyze the influence each event has on the top event ( the gas explosion, so as to find out about the defects of the system and accordingly help to work out the emphasis of the precautionary work and some preventive measures as well. The results of the safety analysis are in accordance with the practical requirements; therefore the preventive measures are certain to work effectively. In brief, according to the research CD is so effective in the safety analysis and the safety assessment that it can be a qualitative and quantitative method to predict the accident as well as offer some effective measures for the investigation, the prevention and the control of the accident.
Vertex operator algebras, extended E_8 diagram, and McKay's observation on the Monster simple group
2004-01-01
We study McKay's observation on the Monster simple group, which relates the 2A-involutions of the Monster simple group to the extended E_8 diagram, using the theory of vertex operator algebras (VOAs). We first consider the sublattices L of the E_8 lattice obtained by removing one node from the extended E_8 diagram at each time. We then construct a certain coset (or commutant) subalgebra U associated with L in the lattice VOA V_{\\sqrt{2}E_8}. There are two natural conformal vectors of central ...
Towards Complete Phase Diagrams of a Holographic P-wave Superconductor Model
Cai, Rong-Gen; Li, Li-Fang; Yang, Run-Qiu
2014-01-01
We study in detail the phase structure of a holographic p-wave superconductor model in a five dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. To construct complete phase diagrams of the model, we consider both the soliton and black hole backgrounds. In both two cases, there exist second order, first order and zeroth order phase transitions, and the so-called "retrograde condensation" also happens. In particular, in the soliton case with the mass of the vector field being beyond a certain critical value, we find a series of phase transitions happen such as "insulator/superconductor/insulator/superconductor", as the chemical potential continuously increases. We construct complete phase diagrams in terms of temperature and chemical potential and find some new phase boundaries.
Kantar, Ersin
2016-08-01
In this paper, within the framework of the effective-field theory with correlation, mixed spin-1/2 and spin-3/2 bilayer system on a square lattice is studied. The characteristic behaviors for the magnetic hysteresis, compensation types and phase diagrams depending on effect of the surface and interface exchange parameters as well as crystal field are investigated. From the behavior of total magnetization as a function of the magnetic field and temperature, we obtain the single, double and triple hysteresis loops and the L-, Q-, P-, S-, and N-type compensation behaviors in the system. Moreover, we detect the more effective the J1 and crystal field parameters on the bilayer Ising model according to the behaviors of the phase diagrams.
Magnetic hysteresis, compensation behaviors, and phase diagrams of bilayer honeycomb lattices
Institute of Scientific and Technical Information of China (English)
Ersin Kantar
2015-01-01
Magnetic behaviors of the Ising system with bilayer honeycomb lattice (BHL) structure are studied by using the effective-field theory (EFT) with correlations. The effects of the interaction parameters on the magnetic properties of the system such as the hysteresis and compensation behaviors as well as phase diagrams are investigated. Moreover, when the hysteresis behaviors of the system are examined, single and double hysteresis loops are observed for various values of the interaction parameters. We obtain the L-, Q-, P-, and S-type compensation behaviors in the system. We also observe that the phase diagrams only exhibit the second-order phase transition. Hence, the system does not show the tricritical point (TCP).
Cognitive Networks Autonomic Decision-making Approach Based on Influence Diagram
Directory of Open Access Journals (Sweden)
Jin Qi
2012-05-01
Full Text Available The current research focus on the areas such as definition and system structure of cognitive networks (CNs, with the lack of autonomic decision-making theory and approach. In this paper, we proposed an autonomic decision-making approach based on influence diagram for CNs. Utilizing influence diagram to choose and execute the action which maximized the network overall performance can effectively predict the trend in network performance, archive autonomic decision-making and avoid network performance deterioration. The simulation results show that the CNs autonomic decision-making approach given network the abilities of learning, reasoning and autonomic decision-making without any human intervention. As a result, the network cognition has been archived while the network Quality of Service (QoS has been guaranteed.
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.
Academic Training Lecture | Beyond Feynman Diagrams (1/3) | 24 April
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 ...
Ranking using the Copeland score: a comparison with the Hasse diagram.
Al-Sharrah, Ghanima
2010-05-24
This study concerns the problem of ranking objects (chemicals, projects, databases, etc.) when a number of indicators are available for these objects that convey different comparative information. There is no unique way to rank these objects while taking all indicators into account. Using the concept of partially ordered sets and the social choice theory, the Copeland score ranking methodology was applied outside of its usual political environment (voting) to rank objects in the sciences. This method avoids the disadvantages of the Hasse diagram and the linear extension usually used to resolve this issue. The ranking methodology was assessed using eight data sets, each with different numbers of objects and indicators. The results showed that the Copeland method appears to be an effective and stable tool for ranking objects, yielding results comparable to those of an evaluation by a Hasse diagram. Also, it has the advantage of facilitating the analysis of large partially ordered sets, which were practically impossible to handle using existing methods.