Diagrammatic Structure Research Articles

Probing Double Beta-Decay by Heavy Ion Charge Exchange Reactions

A special class of nuclear double charge exchange (DCE) reactions proceeding as a one-step reaction through a two-body process are shown to involve nuclear matrix elements of the same diagrammatic structure as in 0ν2β decay. These hadronic Majorana-type DCE reactions (MDCE) have to be distinguished from second order DCE reactions, given by double single charge exchange (DSCE) processes resembling 2ν2β decay. The theoretical concepts of MDCE are discussed. First results show that ion-ion DCE reactions are the ideal testing grounds for investigations of second order nuclear matrix elements.

Fermi-edge singularity and the functional renormalization group

We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.

A Structural and Nominal Syntax for Diagrams

The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical perspective, diagrams can be specified using (name-free) combinators which enjoy elegant equational properties. However, conventional notations for diagrammatic structures, such as hardware description languages (VHDL, Verilog) or graph languages (Dot), use a different style, which is flat, relational, and reliant on extensive use of names (labels). Such languages are not known to enjoy nice syntactic equational properties. However, since they make it relatively easy to specify (and modify) arbitrary diagrammatic structures they are more popular than the combinator style. In this paper we show how the two approaches to diagram syntax can be reconciled and unified in a way that does not change the semantics and the existing equational theory. Additionally, we give sound and complete equational theories for the combined syntax.

Nestajanje Jugoslavije na tržištu globalnog kapitala

The process of the disintegration of Yugoslavia is a direct result of modern capitalism and its unfettered market expansion in economic terms and neoliberalism in the ideological sense. The fragmentation of Yugoslavia became a precondition for the globalization of its markets and the seizure of its wealth. Global financial forces are directly related to the weakening and disappearance of the state on the basis of the neoliberal model and the universalization of neoliberal discourse, which require changes in the ruling forms of the state, redefining its sovereignty through structural changes. Through the dominance of the global financial system, the Western powers, in search of national and collective strategic interests, helped the Yugoslav economy to collapse and instigated its citizens to ethnic and social conflicts. Global media have been advocating the 'free market' as the basis for rebuilding a war shattered economy. Through the social and political influence of economic restructuring in Yugoslavia, collective understanding, social cohesion and the common Yugoslav identity gradually eroded. The intellectual and political elite dogmatically represented cultural, ethnic and religious divisions as the only cause of war and destruction. The aim of this paper is to prove that Yugoslavia has disappeared by the power of capital, through a corporate system that, through its diagrammatic structures of dispersed power based on manipulation and neoliberal ideology, managed to realize its goal of total privatization of all that belonged to the area of public goods.

Role of vertex corrections in the matrix formulation of the random phase approximation for the multiorbital Hubbard model

In the framework of a multiorbital Hubbard model description of superconductivity, a matrix formulation of the superconducting pairing interaction that has been widely used is designed to treat spin, charge and orbital fluctuations within a random phase approximation (RPA). In terms of Feynman diagrams, this takes into account particle-hole ladder and bubble contributions as expected. It turns out, however, that this matrix formulation also generates additional terms which have the diagrammatic structure of vertex corrections. Here we examine these terms and discuss the relationship between the matrix-RPA superconducting pairing interaction and the Feynman diagrams that it sums.

Mathematical Working Spaces in schooling: an introduction

The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10 years, the model has been the object of collaborative research among various researchers, generally coming from French and Spanish speaking countries. Articulating epistemological and cognitive aspects, the MWS model is aimed at providing a tool for the specific study of mathematical work in which students and teachers are effectively engaged during mathematics sessions. The abstract space thus conceived refers to a structure organized in a way that allows the analysis of the mathematical activity of individuals dealing with mathematical problems. Thus, analyzing mathematical work through the lens of MWS enables tracking down how meaning is progressively constructed, as a process of bridging the epistemological and the cognitive perspectives—these being modelled as two planes at different levels in the diagrammatic structure—in accordance with different specific yet intertwined genetic developments. Each is identified as a genesis related to a specific dimension in the model: semiotic, instrumental and discursive geneses. A general overview of the different papers included in this issue is given, and shows how the model can be used to study different tasks, teaching situations and activities set in specific mathematical fields or domains. Some perspectives are finally drawn, while reflecting on the possibility of ‘networking’ different theoretical frames with the MWS framework. Indeed, the latter is not proposed as a holistic theory, but rather should function as a tool interacting strongly with other approaches.

From sociality of media to the social as a medium: Diagrams and models of media theory

Abstract This article takes mediating processes, rather than media objects, as its focus. It examines three different formulations of knowledge mediation, each of which can be modelled as a diagrammatic structure that takes historical as well as contemporary form. These three formulations are declarative/instrumental, contemplative/generative, and stochastic/constitutive, and each is positioned differently with respect to the idea that media “operationalize” knowledge. The goal is to suggest that we might “think media” beyond instrumental activity, by paying attention to mediating processes, rather than media objects, and that this might shift focus in media theory from attending to the social character of media, towards understanding the mediating aspects of “the social”.

Narrated Life — On the Imagery and the Diagrammatics of the Motif of Way

This article examines diagrammatic options in the metaphor of the ›path of life‹. Logical methods to determine a metaphor, a narration, and felicity, as defined by Aristotle, all coincide in the diagrammatic structure of the ›path of life‹ in order to master the problem of temporality by means of geometrical constructions, and in order to make intangible ideas visible through the aid of different models of space. This article focusses on the plurality of models made possible by this diagrammatically shaped metaphor. However, this diagrammatic metaphor of the ›path of life‹ also includes the fact that the seeds of disintegration are always already inscribed in this metaphor as soon as the particular formulates claims against the universal and the diagrammatic model becomes a playing field of rhetorical and poetic practices.

Recent developments in classical density functional theory: Internal energy functional and diagrammatic structure of fundamental measure theory

An overview of several recent developments in density functional theory for classical inhomogeneous liquids is given. We show how Levy's constrained search method can be used to derive the variational principle that underlies density functional theory. An advantage of the method is that the Helmholtz free energy as a functional of a trial one-body density is given as an explicit expression, without reference to an external potential as is the case in the standard Mermin-Evans proof by reductio ad absurdum. We show how to generalize the approach in order to express the internal energy as a functional of the one-body density distribution and of the local entropy distribution. Here the local chemical potential and the bulk temperature play the role of Lagrange multipliers in the Euler-Lagrange equations for minimiziation of the functional. As an explicit approximation for the free-energy functional for hard sphere mixtures, the diagrammatic structure of Rosenfeld's fundamental measure density unctional is laid out. Recent extensions, based on the Kierlik-Rosinberg scalar weight functions, to binary and ternary non-additive hard sphere mixtures are described.

Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

A higher-derivative classical nonrelativistic U(1)×U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2+1 dimensions is proposed. The model contains a Chern-Simons U(1) field and the electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. The model is obtained by adding suitable higher-derivative terms to the Lagrangian of a model previously proposed. One of them for the electromagnetic field and the other for the Chern-Simons field. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev-Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. In this context, only a mixed bosonic propagator can be defined. The use of the higher-derivative terms eliminates the ultraviolet divergence of the primitively divergent Feynman diagrams where the bosonic propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the Becchi-Rouet-Stora-Tyutin algorithm is applied to the model. We will focus our attention on the issue from the point of view of the field theory.

Density functional for ternary non-additive hard sphere mixtures

Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein–Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data.

Analogy-making in the Semai Sensory World

ABSTRACTIn the interplay between language, culture, and perception, iconicity structures our representations of what we experience. By examining secondary iconicity in sensory vocabulary, this study draws attention to diagrammatic qualities in human interaction with, and representation of, the sensory world. In semai (Mon-Khmer, Aslian), spoken on Peninsular Malaysia, sensory experiences are encoded by expressives. Expressives display a diagrammatic iconic structure whereby related sensory experiences receive related linguistic forms. Through this type of form-meaning mapping, gradient relationships in the perceptual world receive gradient linguistic representations. Form-meaning mapping such as this enables speakers to categorize sensory events into types and subtypes of perceptions, and provide sensory specifics of various kinds. This study illustrates how a diagrammatic iconic structure within sensory vocabulary creates networks of relational sensory knowledge. Through analogy, speakers draw on this knowledge to comprehend sensory referents and create new unconventional forms, which are easily understood by other members of the community. Analogy-making such as this allows speakers to capture fine-grained differences between sensory events, and effectively guide each other through the semai sensory landscape.

Charge-transfer separability and size-extensivity in the equation-of-motion coupled cluster method: EOM-CCx

We study the charge-transfer separability (CTS) property of the Fock space (FS) and equation-of-motion (EOM) coupled cluster (CC) methods by analysing the charge-transfer (CT) excitation energy versus the donor-acceptor (D-A) distance. All FS-CC approaches fulfill the CT separability condition which is not the case for the standard EOM-CC approaches. This defect of the EOM-CC scheme can be fixed by slight modification of the H matrix's diagrammatic structure, namely by adding some "dressing" composed of disconnected terms. The latter guarantee CTS of the respective EOM-CC scheme and marginally improve local excitations. The newly proposed variant of the EOM-CCSD approach is termed EOM-CCSDx (size-extensive EOM-CCSD).

Regularization of Diagrammatic Series with Zero Convergence Radius

The divergence of perturbative expansions which occurs for the vast majority of macroscopic systems and follows from Dyson's collapse argument prevents the direct use of Feynman's diagrammatic technique for controllable studies of strongly interacting systems. We show how the problem of divergence can be solved by replacing the original model with a convergent sequence of successive approximations which have a convergent perturbative series while maintaining the diagrammatic structure. As an instructive model, we consider the zero-dimensional |ψ|⁴ theory.

TOPOLOGICALLY MASSIVE ELECTROMAGNETIC INTERACTION OF COMPOSITE PARTICLES IN A HIGHER-DERIVATIVE NONRELATIVISTIC GAUGE FIELD MODEL

A higher-derivative classical nonrelativistic U (1) × U (1) gauge field model that describes the topologically massive electromagnetic interaction of composite particles in 2+1 dimensions is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of a model previously proposed. The model contains a Chern–Simons U(1) field and the topologically massive electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev–Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams where the electromagnetic field propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the Becchi–Rouet-Stora–Tyutin algorithm is applied to the model.

Diagramas semióticos em textos comunicacionais

O presente artigo discorre sobre a leitura dos textos de comunicação como processo de aprimoramento cognitivo. Para isso, parte da hipótese da necessidade de alfabetização semiótica nas estruturas relacionais e diagramáticas que as linguagens dos meios introduziram na cultura. Propõe, assim, exercícios de leitura estrutural de textos jornalísticos em seu processo de representação. Pretende com isso examinar como os acontecimentos significam, como se tornam textos e de que instrumentos as linguagens se servem para construir argumentos que possam ser lidos na estruturalidade de sua composição.

Water-like structure with repulsive double-core interactions

The soft-core repulsive interaction together with a Gaussian repulsive interaction are used to reproduce major features of the structure of liquid water, both in direct and reciprocal space, by Monte Carlo and integral equation theories. The study reveals that the structure of liquid water is determined, within the model studied here, by the competition of the two repulsive cores, which results in a two-fold spatial distribution, very reminiscent of the two-state water model proposed by many authors. The fact is that many of the structural features of water could be reproduced without any recourse to direct attractive interactions, such as directional hydrogen bonds, and appear to be the result of long-range competing packing correlations, as witnessed by the particular features of the structure factor. The Hypernetted-Chain integral equation is able to reproduce very accurately the most important features of the experimental structure of room temperature water, whereas the Percus–Yevick approximation fails to reach this state point. A high-temperature study shows that this failure is related to the insufficient diagrammatic structure of this closure.

Quantum Field Formalism for the Electromagnetic Interaction of Composite Particles in a Nonrelativistic Gauge Model III

A classical nonrelativistic U(1)×U(1) gauge field model that describes the topologically massive electromagnetic interaction of composite particles in (2+1) dimensions is proposed. The model, generalization of a previously postulated one, contains a Chern-Simons U(1) field and the topologically massive electromagnetic U(1) field, and it uses both a composite boson system or a composite fermion one. The second case is considered explicitly. By using the Dirac Hamiltonian method for constrained systems, the canonical quantization is carried out. By means of the Faddeev-Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is treated. The application of the Becchi-Rouet-Stora-Tyutin algorithm is discussed. The present and previous models are compared.

L-MOVES AND MARKOV THEOREMS

Given a knot theory (virtual, singular, knots in a 3-manifold etc.), there are deep relations between the diagrammatic knot equivalence in this theory, the braid structures and a corresponding braid equivalence. The L-moves between braids, due to their fundamental nature, may be adapted to any diagrammatic situation in order to formulate a corresponding braid equivalence. In this short paper, we discuss and compare various diagrammatic set-ups and results therein, in order to draw the underlying logic relating diagrammatic isotopy, braid structures, Markov theorems and L-move analogues. Finally, we apply our conclusions to singular braids.

Correlates of the cognitive dimensions for tangible user interface

We describe an application of the cognitive dimensions (CDs) of notations framework to tangible user interfaces (TUIs)—interaction with computers using physical devices other than mice and keyboards. We are particularly interested in situations where the TUI is used to construct some information structure (a manipulable solid diagram) and where that structure is intended to specify computer behaviour other than by direct manipulation (a tangible programming language). We analyse several tangible programming languages that have been described in previous research, considering the ways in which their physical properties influence the manipulability of the diagrammatic structure. This is the contribution that a CDs analysis would provide for any notation, but we find consistent ways in which particular dimensions can be predicted to apply to any solid diagram. We describe these as the tangible correlates of those dimensions. We then demonstrate that the tangible correlates can be used for both generative and analytic purposes in early stages of TUI design, much as CDs are applicable to the design of visual notations, but more immediately recognisable in their physical implications.