Bubble Diagrams Research Articles

Diagramming development for a base camp and staging area in a humanitarian logistics base airport

PurposeThe purpose of this paper is to develop a method for diagramming a base camp or space for emergency workers and a staging area to be used during sorting, storing, loading, and unloading of relief goods in a humanitarian logistics base airport.Design/methodology/approachA method is developed based on a synthesis of the relevant literature and current practices of airports. This provides a means for estimating the area required for each facility and visualizes the layout of the base through an adjacency diagram and a bubble diagram. The method is applied to the Shizuoka Airport in Japan as a case study.FindingsThe proposed method can be used to determine the approximate size and layout of a humanitarian logistics base in an airport based on the affected population and the number of emergency workers.Research limitations/implicationsAirport operation regulations and mathematical models from architectural planning need to be reflected further.Practical implicationsThe method provides potential operational improvements for policies and standards for airport operations and enables government officials and humanitarian logistics organizations to identify concerns in facilitating and managing constraints in existing airports.Originality/valueThis study addresses the detailed phases in a diagramming for a humanitarian logistics base airport by integrating an architectural approach and airport disaster management. The results highlight the importance of managing the flexible use of space to improve effective humanitarian logistics.

Three-loop massive tadpoles and polylogarithms through weight six

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments ekiπ/3.

Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

Embodying networks: bubble diagrams and the image of modern organicism

Embodying networks: bubble diagrams and the image of modern organicism

Loops in AdS from conformal field theory

We propose and demonstrate a new use for conformal field theory (CFT) crossing equations in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. Loops in AdS are largely unexplored, mostly due to technical difficulties in direct calculations. We revisit this problem, and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. Our second approach involves Mellin space. We show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of ϕ4 theory in AdS, our crossing solution reproduces a previous computation of the one-loop bubble diagram. We can go further, deriving the four-point scalar triangle diagram in AdS, which had never been computed. In the process, we show how to analytically derive anomalous dimensions from Mellin amplitudes with an infinite series of poles, and discuss applications to more complicated cases such as the mathcal{N} = 4 super-Yang-Mills theory.

A new formulation of Lee-Wick quantum field theory

The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well-defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinchings of the Lee-Wick poles, with no need of external ad hoc prescriptions. We describe these features in detail by calculating the one-loop bubble diagram and explaining how the key properties generalize to more complicated diagrams. The physical results of our formulation are different from those of the previous ones. The unusual behaviors of the physical amplitudes lead to interesting phenomenological predictions.

Massive Fluctuations in Deconfining SU(2) Yang-Mills Thermodynamics

We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasiparticles in bubble diagrams constituting corrections to the free thermal quasiparticle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase.

Core polarization and modern realistic shell-model Hamiltonians

The understanding of the convergence properties of the shell-model effective Hamiltonian, within the framework of the many-body perturbation theory, is a long-standing problem. The infinite summation of a certain class of diagrams, the so-called “bubble diagrams,” may be provided calculating the Kirson–Babu–Brown induced interaction, and provides a valid instrument to study whether or not the finite summation of the perturbative series is well-grounded. Here, we perform an application of the calculation of the Kirson–Babu–Brown induced interaction to derive the shell-model effective Hamiltonian for [Formula: see text]-shell nuclei starting from a modern nucleon–nucleon potential, obtained by way of the chiral perturbation theory. The outcome of our calculation is compared with a standard calculation of the shell-model Hamiltonian, where the core-polarization effects are calculated only up to third-order in perturbation theory. The results of the two calculations are very close to each other, evidencing that the perturbative approach to the derivation of the shell-model Hamiltonian is still a valid tool for nuclear structure studies.

On quantum corrections in higher-spin theory in flat space

We consider an interacting theory of an infinite tower of massless higher-spin fields in flat space with cubic vertices and their coupling constants found previously by Metsaev. We compute the one-loop bubble diagram part of the self-energy of the spin 0 member of the tower by summing up all higher-spin loop contributions. We find that the result contains an exponentially UV divergent part and we discuss how it could be cancelled by a tadpole contribution depending on yet to be determined quartic interaction vertex. We also compute the tree-level four-scalar scattering amplitude due to all higher-spin exchanges and discuss its inconsistency with the BCFW constructibility condition. We comment on possible relation to similar computations in AdS background in connection with AdS/CFT.

Configraphics: Graph Theoretical Methods for Design and Analysis of Spatial Configurations

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications.

Configraphics

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: • arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and • analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications.

Developing clinical decision tools to implement chronic disease prevention and screening in primary care: the BETTER 2 program (building on existing tools to improve chronic disease prevention and screening in primary care).

BackgroundThe Building on Existing Tools to Improve Chronic Disease Prevention and Screening in Family Practice (BETTER) trial demonstrated the effectiveness of an approach to chronic disease prevention and screening (CDPS) through a new skilled role of a ‘prevention practitioner’(PP). The PP has appointments with patients 40–65 years of age that focus on primary prevention activities and screening of cancer (breast, colorectal, cervical), diabetes and cardiovascular disease and associated lifestyle factors. There are numerous and occasionally conflicting evidence-based guidelines for CDPS, and the majority of these guidelines are focused on specific diseases or conditions; however, primary care providers often attend to patients with multiple conditions. To ensure that high-level evidence guidelines were used, existing clinical practice guidelines and tools were reviewed and integrated into blended BETTER tool kits. Building on the results of the BETTER trial, the BETTER tools were updated for implementation of the BETTER 2 program into participating urban, rural and remote communities across Canada.MethodsA clinical working group consisting of PPs, clinicians and researchers with support from the Centre for Effective Practice reviewed the literature to update, revise and adapt the integrated evidence algorithms and tool kits used in the BETTER trial. These resources are nuanced, based on individual patient risk, values and preferences and are designed to facilitate decision-making between providers across the target diseases and lifestyle factors included in the BETTER 2 program. Using the updated BETTER 2 toolkit, clinicians 1) determine which CDPS actions patients are eligible to receive and 2) develop individualized ‘prevention prescriptions’ with patients through shared decision-making and motivational interviewing.ResultsThe tools identify the patients’ risks and eligible primary CDPS activities: the patient survey captures the patient’s health history; the prevention visit form and integrated CDPS care map identify eligible CDPS activities and facilitate decisions when certain conditions are met; and the ‘bubble diagram’ and ‘prevention prescription’ promote shared decision-making.ConclusionThe integrated clinical decision-making tools of BETTER 2 provide resources for clinicians and policymakers that address patients’ complex care needs beyond single disease approaches and can be adapted to facilitate CDPS in the urban, rural and remote clinical setting.Trial registrationThe registration number of the original RCT BETTER trial was ISRCTN07170460.Electronic supplementary materialThe online version of this article (doi:10.1186/s13012-015-0299-9) contains supplementary material, which is available to authorized users.

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW+DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second order diagram. FLEX+DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

Practical Modeling: Making the Invisible Visible

EDITOR'S SUMMARYA fundamental part of information architecture is translating rough ideas through language to a set of organized relationships, understandable to all stakeholders. Modeling information helps visualize the problem to be addressed en route to finding a solution. The process may be complex, iterative and time consuming but necessary to transition from a vague idea to a final implementation. Modeling takes place throughout a project to facilitate analysis of the problem being addressed. It helps clarify relationships and ideas without moving too quickly to specifics, like bubble diagrams of spatial relationships that evolve in phases into detailed architectural drawings. Modeling captures assumptions, even if unstated and invisible, and it can take multiple forms as it progresses to support clear navigation, logical filters and effective discovery.

(d¯)-(u¯) asymmetry in the proton in chiral effective theory.

We compute the d[over ¯]-u[over ¯] asymmetry in the proton in chiral effective theory, including both nucleon and Δ degrees of freedom, within the relativistic and heavy baryon frameworks. In addition to the distribution at x>0, we compute the corrections to the asymmetry from zero momentum contributions from pion rainbow and bubble diagrams at x=0, which have not been accounted for in previous analyses. We find that the empirical x dependence of d[over ¯]-u[over ¯] as well as the integrated asymmetry can be well reproduced in terms of a transverse momentum cutoff parameter.

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We write the generic diagram for the density-response spectrum as the sum of partitions. In a partition the original diagram is evaluated using time-ordered Green's functions (GF) on the left-half of the diagram, antitime-ordered GF on the right-half of the diagram and lesser or greater GF gluing the two halves. As there exist more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare GF and subsequently extend it to dressed GF. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zero-th order bubble diagram, the first-order vertex diagram and a partition of the second-order ladder diagram. We evaluate this approximation in the 3D homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.

Signatures of electron-magnon interaction in charge and spin currents through magnetic tunnel junctions: A nonequilibrium many-body perturbation theory approach

We develop a numerically exact scheme for resumming certain classes of Feynman diagrams in the self-consistent perturbative expansion for the electron and magnon self-energies in the nonequilibrium Green function formalism applied to a coupled electron-magnon (e-m) system driven out of equilibrium by the applied finite bias voltage. Our scheme operates with the electronic and magnonic GFs and the corresponding self-energies viewed as matrices in the Keldysh space, rather than conventionally extracting their retarded and lesser components, which greatly simplifies translation of diagrams into compact mathematical expressions and their computational implementation. This is employed to understand the effect of inelastic e-m scattering on charge and spin current vs bias voltage ${V}_{b}$ in F/I/F (F-ferromagnet; I-insulating barrier) magnetic tunnel junctions (MTJs), which are modeled on a quasi-one-dimensional (quasi-1D) tight-binding lattice for the electronic subsystem and quasi-1D Heisenberg model for the magnonic subsystem. For this purpose, we evaluate the Fock diagram for the electronic self-energy and the electron-hole polarization bubble diagram for the magnonic self-energy. The respective electronic and magnonic GF lines within these diagrams are the fully interacting ones, thereby requiring to solve the ensuing coupled system of nonlinear integral equations self-consistently. Despite using the quasi-1D model and treating e-m interaction in many-body fashion only within a small active region consisting of few lattice sites around the F/I interface, our analysis captures essential features of the so-called zero-bias anomaly observed [V. Drewello, J. Schmalhorst, A. Thomas, and G. Reiss, Phys. Rev. B 77, 014440 (2008)] in both MgO- and ${\mathrm{AlO}}_{x}\ensuremath{-}$based realistic 3D MTJs where the second derivative ${d}^{2}I/d{V}_{b}^{2}$ (i.e., inelastic electron tunneling spectrum) of charge current exhibits sharp peaks of opposite sign on either side ${V}_{b}=0$. We show that this is closely related to a substantially modified magnonic density of states (DOS) after the e-m interaction is turned on---the magnonic bandwidth over which DOS is nonzero becomes broadened, thereby making e-m scattering at arbitrary small bias voltage possible, while DOS also acquires peaks (on the top of a continuous background) signifying the formation of quasibound states of magnons dressed by the cloud of electron-hole pair excitations. We also demonstrate that the sum of electronic spin currents in all of the semi-infinite leads attached to the active region quantifies the loss of spin angular momentum carried away from the active region by the magnonic spin current.

One-loop photon–photon scattering in a thermal, deconfining SU(2) Yang–Mills plasma

For a deconfining thermal SU(2) Yang–Mills plasma we discuss the role of (anti)calorons in introducing non-thermal behavior effectively described in terms of Planck’s quantum of action ħ. This non-thermality cancels exactly between the ground-state estimate and its free quasiparticle excitations. Kinematic constraints in 4-vertex scattering and the counting of radial loop variables versus the number of independent constraints on them are re-visited. Next, we consider thermal 2→2 one-loop scattering of the modes remaining massless upon the (anti)caloron induced adjoint Higgs mechanism (thermal ground state after spatial coarse graining). Starting with stringent analytical arguments, we are able to exclude the contribution to photon–photon scattering from diagrams containing at least one three-vertex and, in a next step, a vast majority of all possible configurations involving two four-vertices. By numerical analysis we show that the remaining contribution of the overall S channel is severely suppressed compared those of the T and U channels, meaning that the creation of a pair of massive vector modes by a pair of photons and vice versa practically does not occur in the Yang–Mills plasma. For the T and U channels the domain of loop integration represents less than 10−7 times the volume of the unconstrained integration region. The thus introduced photon–photon correlation should affect the Cosmic Microwave Background’s polarization at low redshift. An adaption of the here-developed methods to the analysis of irreducible bubble diagrams could prove the conjecture of hep-th/0609033 on the termination of the loop expansion of thermodynamical quantities at a finite irreducible order.

Superconducting pairing in the spin-density-wave phase of iron pnictides

Some of the iron pnictides show coexisting superconductivity and spin-density-wave order. We study the superconducting pairing instability in the spin-density-wave phase. Assuming that the pairing interaction is due to spin fluctuations, we calculate the effective pairing interactions in the singlet and triplet channels by summing the bubble and ladder diagrams taking the reconstructed band structure into account. The leading pairing instabilities and the corresponding superconducting gap structures are then obtained from the superconducting gap equation. We illustrate this approach for a minimal two-band model of the pnictides. Analytical and numerical results show that the existence of propagating magnons in the spin-density-wave phase strongly enhances the pairing in both the singlet and the spin s_z=0 triplet channel. Over a limited parameter range, a spin s_z=0 triplet p_x-wave state is the dominant instability. It competes with various singlet states, which have mostly s^\pm-type structures. We analyze the effect of various symmetry-allowed interactions on the pairing in some detail.

Safety oriented bubble diagrams vs. risk plots based on prediction intervals and strength-of-knowledge assessments. Which one to use as an alternative to risk matrices?

The use of risk matrices for visualising risks has been discussed in the literature. It is argued that risk matrices are not appropriate as the uncertainty is not properly taken into account. As an alternative to risk matrices, the use of bubble diagrams has been suggested. Risk plots based on prediction (uncertainty) intervals and strength-of-knowledge assessments have also been recommended. In this paper, we discuss which of these two alternatives to traditional risk matrices is considered most appropriate for visualising risks. We show that risk plots are more precise in reflecting important aspects of risks than bubble diagrams, while bubble diagrams are considered to give a better basis for ranking between risks. In this paper, a new visualisation tool closely related to the risk plots and the bubble diagrams is suggested.