Field In Space Research Articles

Collective coordinate fix in the path integral

Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parametrize a manifold of zero modes and more broadly provide judicious coordinates on the space of fields. However, changing from local coordinates around a saddle point to more global collective coordinates is remarkably subtle. The main complication is that the mapping from local coordinates to collective coordinates is generically multivalued. Consequently one is forced to either restrict the domain of path integral in a delicate way, or otherwise correct for the multivaluedness by dividing the path integral by certain intersection numbers. We provide a careful treatment of how to fix collective coordinates while accounting for these intersection numbers, and then demonstrate the importance of the fix for free theories. We also provide a detailed study of the fix for interacting theories and show that the contributions of higher intersections to the path integral can be nonperturbatively suppressed. Using a variety of examples ranging from single-particle quantum mechanics to quantum field theory, we explain and resolve various pitfalls in the implementation of collective coordinates. Published by the American Physical Society 2024

Kinetic Theory with Casimir Invariants-Toward Understanding of Self-Organization by Topological Constraints.

A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characterize a self-organized structure as a thermal equilibrium on a leaf of foliated phase space. By introducing a model of a grand canonical ensemble, the Casimir invariant is interpreted as the number of topological particles.

Non-supersymmetric heterotic strings on a circle

Motivated by a recent construction of non-supersymmetric AdS3, we revisit the O(16) × O(16) heterotic string compactified on a torus. The string one-loop potential energy has interesting dependence on the classical moduli; extrema of this potential include loci where the gauge symmetry is maximally enhanced. Focusing on the case of a circle, we use lattice embeddings to find the maximal enhancement points together with their spectra of massless and tachyonic modes. We find an extended Dynkin diagram that encodes the global structure of the moduli space, as well as all symmetry enhancements and the loci where they occur. We find 107 points of maximal enhancement with 8 that are free of tachyons. The tachyon-free points each have positive cosmological constant. We determine the profile of the potential energy near each of these points and find that one is a maximum while three are saddle points. The remaining four live at the boundary of a tachyonic region in field space. In this way, we show that every point of maximal symmetry enhancement is unstable. We further find that the curvature of this stringy potential satisfies the de Sitter swampland conjecture. Finally, we discuss the implications for constructions of AdS3.

Characterization of Wind Turbine Blade Deformation and Wake Flow Field with Different Numbers of Lay-Up Layers

The change in the composite lay-up method affects the blade stiffness, which in turn affects the structural dynamic and aerodynamic characteristics, but the influence law is not yet clear. In this paper, two-way fluid–structure coupling is used to study wind turbine blades with different numbers of lay-up layers. The analysis results show the following: (1) With the increase in the number of pavement layers, the maximum deformation of the blade tip decreases, the magnitude of the decrease also decreases gradually, and the growth trend of deformation along the blade spreading direction is gradually flattened. (2) The maximum stress–strain of the root of the blade gradually decreases, the tip of the blade is the opposite of the blade, the unevenness of the distribution of the stress–strain of the surface of the blade is gradually slowed down, and the concentration area is shifted back. (3) The different numbers of pavement layers affect the turbulence intensity of the blade in the flow field space. Herein, the spatial distribution trend of turbulence intensity in the flow field of wind turbine blades with different numbers of layers is basically the same, and the trend of turbulence intensity changes is gentle when the number of layers is increased. (4) The amount of the tip vortex in the wake stream of the wind turbine decreases, and the decay rate of the center vortex increases. A reasonable lay-up scheme can improve the deformation and stress of the blade, extend the service life of the blade, promote airflow mixing, and enhance the energy conversion efficiency.

A survey on deep 3D human pose estimation

3D Human Pose Estimation (3D-HPE) is a highly active and evolving research area in computer vision with numerous applications such as extended reality, action recognition, and video surveillance. The field has significantly advanced with deep learning, public datasets, and enhanced computational power, addressing challenges like depth ambiguity, occlusion, and data scarcity. Researchers confront scenario-specific issues such as ill-posed problems in monocular setups, cross-view aggregation with camera synchronizations in multi-view systems, and inter-person occlusion in multi-person scenarios. This survey comprehensively reviews contemporary strategies covering a technological spectrum including Convolutional Neural Networks, Graph Convolutional Networks, Transformers, and their combinations employed to address these challenges. It includes scenarios such as monocular and multi-view setups, single and multi-person cases, as well as image and video inputs. The survey explores various solution paradigms, including single-stage vs 2D-to-3D lifting, absolute vs relative keypoints, pixel vs voxel vs Neural Radiance Field spaces, and deterministic, probabilistic, or diffusion-based strategies, along with top-down vs bottom-up approaches. It examines advanced learning techniques beyond supervised methods and data augmentation for diverse pose datasets. It analyzes the performance of recent methods on benchmark datasets for different scenarios. Challenges are categorized into common and scenario-specific issues, and future research directions are proposed to foster further advancements in the field. Additionally, key sections are summarized in tables or visual formats for quick understanding. This survey is a valuable resource and a solid reference for researchers in the dynamic landscape of 3D human pose estimation.

Dirac algebra formalism for Two Higgs Doublet Models: The one-loop effective potential

We present a novel covariant bilinear formalism for the Two Higgs Doublet Model (2HDM) which utilises the Dirac algebra associated with the SL(2,C) group that acts on the scalar doublet field space. This Dirac-algebra approach enables us to obtain a fully O(1,3)-covariant and IR-safe expression for the one-loop effective potential. We illustrate how the formalism can be used to evaluate the breaking of global symmetries of the 2HDM potential by loop effects, in a field-reparameterisation invariant manner.

Swampland conjectures constraints on dark energy from a highly curved field space

We study the interplay of the trans-Planckian censorship conjecture (TCC) and the swampland distance conjecture (SDC) in the context of multifield dark energy in a curved field space. In this scenario, the phase of accelerated expansion is realized as nongeodesic motion in a highly curved field space, reminiscent of models developed in the context of inflation. The model features a stable attractor solution with near constant equation of state w≃−1, and predicts that the current era of accelerated expansion is eternal. The latter implies an eventual conflict with the TCC, which holds that the duration of any epoch of cosmic acceleration is bounded by the requirement that the large-scale observable universe is blind to Planck-scale early universe physics. This tension can be resolved by an interplay with the distance conjecture: for suitable parameter values, the apparent violation of the TCC occurs well after the fields have traversed a Planckian distance. The SDC then predicts a breakdown of the effective field theory before the TCC can be violated. We derive the constraints on the model arising from the SDC+TCC and the de Sitter conjecture. We demonstrate that the model can be consistent with both swampland conjectures and observational data from Planck 2018 and the Dark Energy Spectroscopic Instrument. Published by the American Physical Society 2024

Color-kinematics duality for nonlinear sigma models with nonsymmetric cosets

We propose an extension of the color-kinematics duality for nonlinear sigma models with nonymmetric cosets. The role of color is replaced with curvatures in field space. The duality between curvature and kinematics allows for a new double copy: the double copy of the nonlinear sigma model for nonsymmetric cosets is the general Galileon theory. We provide evidence for this new double copy of geometry. Published by the American Physical Society 2024

Quotient quiver subtraction

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the SU(n) hyper-Kähler quotient (HKQ) of the Coulomb branch of a 3dN=4 unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as “good” or “ugly”, which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are “bad”, differing thereby from quiver subtractions based on Kraft-Procesi transitions. The simple diagrammatic procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.

Constraining dark matter from strong phase transitions in a U1Lμ−Lτ model: implications for neutrino masses and muon g − 2

In this paper, we study a non-minimal gauged U1Lμ−Lτ model, where we add two complex singlet scalars, three right-handed Majorana neutrinos (RHN), and a vector-like dark fermion to the Standard Model (SM), all non-trivially charged under the extra gauge symmetry. The model offers an easy resolution to the muon (g – 2) anomaly, which fixes the scale of spontaneous symmetry breaking. Furthermore, the two-zero minor structure in the RHN mass matrix provides successful predictions for neutrino oscillation parameters, including the Dirac phase. The extended scalar sector can easily induce first-order phase transitions. We identify all possible phase transition patterns in the three-dimensional field space. We quantify the associated gravitational waves from the sound wave source and demonstrate that the signatures can be observed in future space-based experiments. We find that strong first-order phase transitions require large values of scalar quartic couplings which constrain the scalar dark matter (DM) relic density to a maximum of 10−2 and 10−5 when we consider the DM direct detection bound. Nonetheless, the model successfully explains the DM relic density via contribution from the vector-like dark fermion. We show the allowed range of the model parameters that can address all the beyond SM issues targeted in this study.

Free Reflection Multiarrangements and Quasi-Invariants

Abstract To a complex reflection arrangement with an invariant multiplicity function one can relate the space of logarithmic vector fields and the space of quasi-invariants, which are both modules over invariant polynomials. We establish a close relation between these modules. Berest–Chalykh freeness results for the module of quasi-invariants lead to new free complex reflection multiarrangements. Saito’s primitive derivative gives a linear map between certain spaces of quasi-invariants. We also establish a close relation between non-homogeneous quasi-invariants for root systems and logarithmic vector fields for the extended Catalan arrangements. As an application, we prove the freeness of Catalan arrangements corresponding to the non-reduced root system $BC_{N}$.

Explicit A Posteriori Error Representation for Variational Problems and Application to TV-Minimization

AbstractIn this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discrete orthogonality relations in the space of element-wise constant vector fields as well as a discrete integration-by-parts formula between the Crouzeix–Raviart and the Raviart–Thomas element, all convex duality relations are transferred to a discrete level, making the explicit a posteriori error representation –initially based on continuous arguments only– practicable from a numerical point of view. In addition, we provide a generalized Marini formula that determines a discrete primal solution in terms of a given discrete dual solution. We benchmark all these concepts via the Rudin–Osher–Fatemi model. This leads to an adaptive algorithm that yields a (quasi-optimal) linear convergence rate.

Asymptotic Behavior of Saxion–Axion System in Stringy Quintessence Model

AbstractThe late time behavior of the slow‐roll parameter in the stringy quintessence model is studied when axion as well as saxion are allowed to move. Even though the potential is independent of the axion at tree level, the axion can move through its coupling to the saxion and the background geometry. Then the contributions of the axion kinetic energy to the slow‐roll parameter and the vacuum energy density are not negligible when the slow‐roll approximation does not hold. As the dimension of the field space is doubled, the fixed point at which the time variation of the slow‐roll parameter vanishes is not always stable. It is found that the fixed point in the saxion–axion system is at most partially stable, in particular when the volume modulus and the axio‐dilaton, the essential ingredients of the string compactification, are taken into account. It seems that as more saxion–axion pairs are considered, achieving the stability of the fixed point becomes difficult.

Enhancing soil carbon and rice dry biomass with microbial fuel cells, optimal spacing, and fertilizer in rice fields

Abstract. Nurhutami SR, Sudadi, Komariah, Dewi WS, Fauzan AA. 2024. Enhancing soil carbon and rice dry biomass with microbial fuel cells, optimal spacing, and fertilizer in rice fields. Biodiversitas 25: 3331-3338. Microbial fuel cell (MFC) uses electroactive anode bacteria to compete in rice fields without disrupting cultivation or altering diversity. Therefore, this research aimed to explore the combination of MFC, different spacing methods (Jajarlegowo and conventional), and NPK (Nitrogen, Phosphorus, and Potassium) fertilizer affecting soil carbon dynamics and rice dry biomass. The key parameters included bacterial community, soil respiration, microbial biomass carbon, Soil Organic Carbon (SOC), Carbon to Nitrogen (CN) Ratio, and rice dry biomass. The results showed that there were no significant differences across the parameters when combined. However, MFC increased soil respiration (0.618 CO2.day-1) and microbial biomass carbon (0.121 ?g. g-1) but decreased SOC and rice dry biomass (0.039% and 3.978 g. clump-1). Jajarlegowo plant spacing enhanced soil respiration (0.583 CO2.day-1), microbial biomass carbon (0.122 ?g. g-1), and rice dry biomass (10.635 g. clump-1). Meanwhile, NPK fertilizer enhanced microbial biomass carbon (0.170 ?g. g-1), soil respiration (0.615 CO2.day-1), and rice dry biomass (5.993 g.clump-1) but lowered CN Ratio by 3.471. A positive correlation was also observed between soil carbon and rice dry biomass. These emphasized the need for a holistic method to develop MFC technology in rice paddy soils. Further research was suggested on the role of Electroactive Anodes Bacteria (EAB) in organic matter decomposition over multiple rice growing seasons.

Remarks on 2D quantum cosmology

We consider two-dimensional quantum gravity endowed with a positive cosmological constant and coupled to a conformal field theory of large and positive central charge. We study cosmological properties at the classical and quantum level. We provide a complete ADM analysis of the classical phase space, revealing a family of either bouncing or big bang/crunch type cosmologies. At the quantum level, we solve the Wheeler-DeWitt equation exactly. In the semiclassical limit, we link the Wheeler-DeWitt state space to the classical phase space. Wavefunctionals of the Hartle-Hawking and Vilenkin type are identified, and we uncover a quantum version of the bouncing spacetime. We retrieve the Hartle-Hawking wavefunction from the disk path integral of timelike Liouville theory. To do so, we must select a particular contour in the space of complexified fields. The quantum information content of the big bang cosmology is discussed, and contrasted with the de Sitter horizon entropy as computed by a gravitational path integral over the two-sphere.

Influence of Campus Outdoor Spaces on Students Behavior: Enhancing Social Interaction and Learning at An-Najah University

This study examines how the physical features of university campus outdoor spaces affect student behavior, aiming to promote social interaction and improve learning outcomes. Two central questions guide the research: how student movements relate to open space features, and how campus layout influences student circulation and interaction. By employing a mixed-method approach, including field observations and space syntax analysis, five areas at An-Najah University Campus are studied. The findings highlight the importance of these insights in urban design and planning, especially for teaching staff, students, and visitors. Results indicate that spatial layout and physical features significantly affect space usage, with students favoring areas with seating, shade, and social opportunities, adapting to informal setups when formal options are limited. Visibility is key, with students favoring spaces offering maximum visibility for seating. This understanding informs architects and planners in creating engaging campus environments for social interaction and learning.

Analytic bounds on late-time axion-scalar cosmologies

The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration, without solving for the on-shell solution. In this work, we present bounds on late-time FLRW-cosmologies in classes of theories that involve arbitrary numbers of scalar and pseudoscalar fields coupled both kinetically (leading to a curved field space metric) and through scalar potentials. Such bounds are proven analytically, independently of initial conditions, with no approximation in the field equations and without referring to explicit solutions. Besides their broad applications to cosmological model building, our bounds can be applied to studying asymptotic cosmologies of certain classes of string compactifications.

STRUCTURAL AND SEMANTIC ORIGINALITY OF THE SEMANTIC FIELD ‟POWER” IN VLADIMIR MAKSIMOV’S NOVEL ‟TO LOOK INTO THE ABYSS”

The article characterises the semantic field ‟Power” in the novel by the famous Russian prose writer of the 2nd half of the 20th century, Vladimir Maksimov (1930–1995). The purpose of the study is a comprehensive analysis of the structural and semantic features of the field, determination of the originality of the textual functioning of its core components, which are the semantic dominants of the work, actively involved in the organisation of the narrative, in the artistic depiction of historical events and the creation of images of literary characters. The theoretical concepts of the semantic field and semantic space of the text, which unites its conceptual, denotative and emotive meanings, are defined. Linguistic modelling of the field structure is based on the principles of discourse analysis of the text and is determined by the specific linguistic personality of the writer, genre-stylistic and plot-compositional features of the work. Characteristic of component composition of the field, its core, centre and periphery, microfields is given. Semantic connections and intersections of field components are determined with contextual synonymy and antonymy revealed. The core of the field includes the key lexemes “power”, “strength”, “leader”, “will”. The semantic field unites five microfields: the central part of the field structure includes the microfields ‟White-Guard Power of Alexander Kolchak” and ‟Soviet Power of Vladimir Lenin”; the peripheral zone includes the microfields ‟Power of Social Elements”, ‟Military Force of Foreign Intervention” and ‟Power of Selfless and unselfish Love”. The semantic dominants of the text, being the key components of the field, contribute to the dynamics of the narrative, create an artistic chronotope, reflect the author’s position, and convey the bright features of the writer’s linguistic personality.

Capacity of entanglement and volume law

We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.

Moduli dynamics in effective nested warped geometry in four dimensions and some cosmological implications

We analyze the effective four-dimensional dynamics of the extra-dimensional moduli fields in curved braneworlds having nested warping, with particular emphasis on the doubly warped model which is interesting in the light of current collider constraints on the mass of the Kaluza-Klein graviton. The presence of a non-zero brane cosmological constant (Ω) naturally induces an effective moduli potential in the four-dimensional action, which shows distinct features in dS (Ω > 0) and AdS (Ω < 0) branches. For the observationally interesting case of dS 4-branes, a metastable minimum in the potential arises along the first modulus, with no minima along the higher moduli. The underlying nested geometry also leads to interesting separable forms of the non-canonical kinetic terms in the Einstein frame, where the brane curvature directly impacts the kinetic properties of only the first modulus. The non-canonicity of the scenario has been illustrated via an explicit computation of the field space curvature. We subsequently explore the ability of curved multiply warped geometries to drive inflation with an in-built exit mechanism, by considering predominant slow roll along each modular direction on a case-by-case basis. We find slow roll on top of the metastable plateau along the first modular direction to be the most viable scenario, with the higher-dimensional moduli parametrically tuning the height of the potential without significant impact on the inflationary observables. On the other hand, while slow roll along the higher moduli can successfully inflate the background and eventually lead to an exit, consistency with observations seemingly requires unphysical hierarchies among the extra-dimensional radii, thus disfavouring such scenarios.