Suitable Gauge Research Articles

Robust Recovery of Robinson Property in $L^p$-Graphons: A Cut-Norm Approach

This paper investigates the Robinson graphon completion/recovery problem within the class of $L^p$-graphons, focusing on the range $5<p\leq \infty$. A graphon $w$ is Robinson if it satisfies the Robinson property: if $x\leq y\leq z$, then $w(x,z)\leq \min\{w(x,y),w(y,z)\}$. We demonstrate that if a graphon possesses localized near-Robinson characteristics, it can be effectively approximated by a Robinson graphon in terms of cut-norm. To achieve this recovery result, we introduce a function $\Lambda$, defined on the space of $L^p$-graphons, which quantifies the degree to which a graphon $w$ adheres to the Robinson property. We prove that $\Lambda$ is a suitable gauge for measuring the Robinson property when proximity of graphons is understood in terms of cut-norm. Namely, we show that (1) $\Lambda(w)=0$ precisely when $w$ is Robinson; (2) $\Lambda$ is cut-norm continuous, in the sense that if two graphons are close in the cut-norm, then their $\Lambda$ values are close; and (3) for $p > 5$, any $L^p$-graphon $w$ can be approximated by a Robinson graphon, with error of the approximation bounded in terms of $\Lambda(w)$. When viewing $w$ as a noisy version of a Robinson graphon, our method provides a concrete recipe for recovering a cut-norm approximation of a noiseless $w$. Given that any symmetric matrix is a special type of graphon, our results can be applicable to symmetric matrices of any size. Our work extends and improves previous results, where a similar question for the special case of $L^\infty$-graphons was answered.

A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces

This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.

Path integral and conformal instability in nonlocal quantum gravity

We introduce the Lorentzian path integral of nonlocal quantum gravity. After introducing the functional measure, the Faddeev-Popov sector and the field correlators, we move to perturbation theory and describe Efimov analytic continuation of scattering amplitudes to Euclidean momenta and back to Lorentzian. We show that the conformal instability problem in the Euclidean path integral is solved by suitable gauge choices at the perturbative level. The three examples of Einstein gravity, Stelle gravity and nonlocal quantum gravity are given.

Jacobi–Lie Models and Supergravity Equations

Abstract Poisson–Lie T-duality/plurality was recently generalized to Jacobi–Lie T-plurality formulated in terms of double field theory and based on Leibniz algebras given by the structure coefficients fabc, fcab, and Za, Za. We investigate three- and four-dimensional sigma models corresponding to six-dimensional Leibniz algebras with fbba ≠ 0, Za = 0. We show that these algebras are plural one to another and, moreover, to an algebra with fbba = 0, Za = 0. These pluralities are used for construction of Jacobi–Lie models. It was conjectured that plural models should satisfy generalized supergravity equations. We have found examples of models satisfying “true” generalized supergravity equations where no trivialization to usual supergravity equations is possible. On the other hand, we show that there are also models corresponding to algebras with fbba ≠ 0, Za = 0 where the Killing vector appearing in generalized supergravity equations either vanishes or can be removed by suitable gauge transformation. Such models then satisfy usual supergravity equations, i.e. vanishing beta-function equations.

On the canonical equivalence between Jordan and Einstein frames

A longstanding issue is the classical equivalence between the Jordan and the Einstein frames, which is considered just a field redefinition of the metric tensor and the scalar field. In this work, based on the previous result that the Hamiltonian transformations from the Jordan to the Einstein frame are not canonical on the extended phase space, we study the possibility of the existence of canonical transformations. We show that on the reduced phase space – defined by suitable gauge fixing of the lapse and shifts functions – these transformations are Hamiltonian canonical. Poisson brackets are replaced by Dirac’s brackets following the Bergman-Dirac’s procedure. The Hamiltonian canonical transformations map solutions of the equations of motion in the Jordan frame into solutions of the equations of motion in the Einstein frame.

Improving flood forecasting in Narmada river basin using hierarchical clustering and hydrological modelling

The purpose of the study was to use hierarchical clustering and Thiessen polygon algorithms to identify the significant rain gauge stations for flood forecasting at Sardar Sarovar Dam. Rainfall data from 2010 to 2018 was utilized to analyze the catchment region between Omkareshwar Dam and Sardar Sarovar Dam. The study identified two clusters of rain gauge stations with similar rainfall patterns and divided the study area into seventeen regions using Thiessen polygons. The land use map showed that the study area was mostly covered by crop lands, and the soil map divided the area into three types of sedimentary claystone soil. A hydrological model, Hydrologic Engineering Center – Hydrologic Modelling System (HEC-HMS), was used for rainfall-runoff modeling, and the computed runoff was compared with observed gauge discharge and inflow of Sardar Sarovar Dam. Regression analysis was performed to assess the performance of the model, and the results showed a good correlation between observed rainfall and estimated runoff values for 2012 and 2016. The study concludes that the existing rain gauge network is sufficient for flood forecasting, and the developed model along with the Thiessen polygon method can provide more accurate predictions of flow. The study highlights the importance of selecting suitable rain gauge stations for reliable flood forecasting in flood-prone basins. The study findings can be useful for future runoff prediction and flood forecasting in the study area.

Revisiting the transorbital approach for emergency external ventricular drainage: an anatomical study of relevant parameters and their effect on the effectiveness of using Tubbs' point.

The transorbital approach (TOA) can provide immediate access to the lateral ventricles by piercing the roof of the orbit (ROO) with a spinal needle and without the need of a drill. Reliable external landmarks for the TOA ventriculostomy have been described, however, the necessary spinal needle gauge and other relevant parameters such as the thickness of the ROO have not been evaluated. Nineteen formalin-fixed adult cadaveric heads underwent the TOA. Spinal needles of different gauges were consecutively used in each specimen beginning with the smallest gauge until the ROO was successfully pierced. The thickness of the ROO at the puncture site and around its margins was measured. Other parameters were also measured. The TOA was successfully performed in 14 cases (73.68%), where the most suitable needle gauge was 13 (47.37%), followed by a 10-gauge needle (36.84%). The mean thickness of the ROO at the puncture site, and the mean length of the needle to the puncture site were 1.7mm (range 0.2-3.4mm) and 15.5mm (range 9.2-23.4mm), respectively. A ROO thickness of greater than 2.0mm required a 10-gauge needle in seven cases, and in five cases, a 10-gauge needle was not sufficient for piercing the ROO. The presence of hyperostosis frontalis interna (HFI) (21.05%) was related to the failure of this procedure (80%; p < 0.00). Using a 13/10-gauge spinal needle at Tubbs' point for TOA ventriculostomy allowed for external ventricular access in most adult specimens. The presence of HFI can hinder this procedure. These findings are important when TOA ventriculostomy is considered.

Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional

AbstractGiven a hermitian line bundle on a closed Riemannian manifold , the self‐dual Yang–Mills–Higgs energies are a natural family of functionals defined for couples consisting of a section and a hermitian connection ∇ with curvature . While the critical points of these functionals have been well‐studied in dimension two by the gauge theory community, it was shown in [52] that critical points in higher dimension converge as (in an appropriate sense) to minimal submanifolds of codimension two, with strong parallels to the correspondence between the Allen–Cahn equations and minimal hypersurfaces. In this paper, we complement this idea by showing the Γ‐convergence of to (2π times) the codimension two area: more precisely, given a family of couples with , we prove that a suitable gauge invariant Jacobian converges to an integral ‐cycle Γ, in the homology class dual to the Euler class , with mass . We also obtain a recovery sequence, for any integral cycle in this homology class. Finally, we apply these techniques to compare min‐max values for the ‐area from the Almgren–Pitts theory with those obtained from the Yang–Mills–Higgs framework, showing that the former values always provide a lower bound for the latter. As an ingredient, we also establish a Huisken‐type monotonicity result along the gradient flow of .

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

An exact, time-dependent analytical solution for the magnetic field in the inner heliosheath

We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic divergence constraint. To this end, we assume that the magnetic field is frozen into a plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. Furthermore, we make use of the ideal Ohm’s law for the magnetic vector potential and the electric scalar potential. By employing a suitable gauge condition that relates the potentials and working with a characteristic coordinate representation, we thus obtain an inhomogeneous first-order system of ordinary differential equations for the magnetic vector potential. Then, using the general solution of this system, we compute the magnetic field via the magnetic curl relation. Finally, we analyze the well-posedness of the corresponding Dirichlet-type initial-boundary value problem, specify compatibility conditions for the initial-boundary values, and outline the implementation of initial-boundary conditions.

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether’s theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor ταη becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy–momentum complex in fR gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor ταη to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle Ω emitted by a localized source carried by a gravitational wave in a direction x^ for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann–Lemaître–Robertson–Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy–momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving □−k terms.

Energy–momentum tensor and duality symmetry of linearized gravity in the Fierz formalism

A formulation of linearized gravity in flat background, based on the Fierz tensor as a counterpart of the electromagnetic field strength, is discussed in detail and used to study fundamental properties of the linearized gravitational field. In particular, the linearized Einstein equations are written as first order partial differential equations in terms of the Fierz tensor, in analogy with the first order Maxwell equations. An energy–momentum tensor with favourable properties and exhibiting remarkable similarity to the standard energy–momentum tensor of the electromagnetic field is found for the linearized gravitational field. is quadratic in the Fierz tensor (which is constructed from the first derivatives of the linearized metric), traceless, and satisfies the dominant energy condition in a gauge that contains the transverse traceless (TT) gauge. It is further shown that in suitable gauges, including the TT gauge, linearized gravity in the absence of matter has a duality symmetry that maps the Fierz tensor, which is antisymmetric in its first two indices, into its dual. Conserved currents associated with the gauge and duality symmetries of linearized gravity are also determined. These currents show good analogy with the corresponding currents in electrodynamics.

Blázquez-Salcedo–Knoll–Radu wormholes are not solutions to the Einstein-Dirac-Maxwell equations

Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric, traversable wormhole spacetimes with Dirac and Maxwell fields. The BSKR wormholes are obtained by joining a classical solution to the Einstein-Dirac-Maxwell (EDM) equations on the "up" side of the wormhole ($r \geq 0$) to a corresponding solution on the "down" side of the wormhole ($r \leq 0$). However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. We prove that if the matching were done in such a way that the resulting spacetime metric, Dirac field, and Maxwell field composed a solution to the EDM equations in a neighborhood of $r=0$, then all of the fields would be smooth at $r=0$ in a suitable gauge. Thus, the BSKR wormholes cannot be solutions to the EDM equations. The failure of the BSKR wormholes to solve the EDM equations arises both from the failure of the Maxwell field to satisfy the required matching conditions (which implies the presence of an additional shell of charged matter at $r=0$) and, more significantly, from the failure of the Dirac field to satisfy required matching conditions (which implies the presence of a spurious source term for the Dirac field at $r=0$.

Inflation from inhomogeneous polarized Gowdy model

We study polarized Gowdy cosmologies on the three torus coupled to a massive scalar field. The phase space of the model admits a simple splitting between homogeneous and inhomogeneous sectors after a suitable gauge fixing. The presence of the mass term of the scalar field breaks the linearity of the equations of motion of the inhomogeneous fields. We discuss regimes of physical interest in which we recover a linear dynamics of these nonperturbative inhomogeneities, despite the metric is fully inhomogeneous at early times. We expand the inhomogeneous fields in Fourier modes and express them at all times as linear combinations of a basis of orthonormal complex solutions to the equations of motion, with coefficients that turn out to be an infinite collection of constants of motion. We argue that the resulting model can describe a nonperturbative inhomogeneous early Universe dominated by the kinetic energy of an inflaton at early times that can eventually reach a slow-roll regime with a nearly exponential expansion at late times that isotropices and homogenizes the geometry.

Obtaining Solutions of a Vakhnenko Lattice System by N-Fold Darboux Transformation

Using a suitable gauge transformation matrix, we present a N -fold Darboux transformation for a Vakhnenko lattice system. This transformation preserves the form of Lax pair of the Vakhnenko lattice system. Applying the obtained Darboux transformation, we arrive at an exact solution of the Vakhnenko lattice system.

Improving Hourly Precipitation Estimates for Flash Flood Modeling in Data-Scarce Andean-Amazon Basins: An Integrative Framework Based on Machine Learning and Multiple Remotely Sensed Data

Accurate estimation of spatiotemporal precipitation dynamics is crucial for flash flood forecasting; however, it is still a challenge in Andean-Amazon sub-basins due to the lack of suitable rain gauge networks. This study proposes a framework to improve hourly precipitation estimates by integrating multiple satellite-based precipitation and soil-moisture products using random forest modeling and bias correction techniques. The proposed framework is also used to force the GR4H model in three Andean-Amazon sub-basins that suffer frequent flash flood events: upper Napo River Basin (NRB), Jatunyacu River Basin (JRB), and Tena River Basin (TRB). Overall, precipitation estimates derived from the framework (BC-RFP) showed a high ability to reproduce the intensity, distribution, and occurrence of hourly events. In fact, the BC-RFP model improved the detection ability between 43% and 88%, reducing the estimation error between 72% and 93%, compared to the original satellite-based precipitation products (i.e., IMERG-E/L, GSMAP, and PERSIANN). Likewise, simulations of flash flood events by coupling the GR4H model with BC-RFP presented satisfactory performances (KGE* between 0.56 and 0.94). The BC-RFP model not only contributes to the implementation of future flood forecast systems but also provides relevant insights to several water-related research fields and hence to integrated water resources management of the Andean-Amazon region.

Reduced phase space approach to the U(1)3 model for Euclidean quantum gravity

If one replaces the constraints of the Ashtekar–Barbero SU(2) gauge theory formulation of Euclidean gravity by their U(1)3 version, one arrives at a consistent model which captures significant structure of its SU(2) version. In particular, it displays a non trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. In this paper we consider a reduced phase space approach to this model. This is especially attractive because, after a canonical transformation, the constraints are at most linear in the momenta. In suitable gauges, it is therefore possible to find a closed and explicit formula for the physical Hamiltonian which depends only on the physical observables. The corresponding reduced phase space quantisation can be confronted with the constraint quantisation due to Varadarajan et al to gain further insights into the quantum realisation of the hypersurface deformation algebra.

Gravitational multipole moments for asymptotically de Sitter spacetimes

We provide a prescription to compute the gravitational multipole moments of compact objects for asymptotically de Sitter spacetimes. Our prescription builds upon a recent definition of the gravitational multipole moments in terms of Noether charges associated to specific vector fields, within the residual harmonic gauge, dubbed multipole symmetries. We first derive the multipole symmetries for spacetimes which are asymptotically de Sitter; we also show that these symmetry vector fields eliminate the non-propagating degrees of freedom from the linearized gravitational wave equation in a suitable gauge. We then apply our prescription to the Kerr-de Sitter black hole and compute its multipole structure. Our result recovers the Geroch-Hansen moments of the Kerr black hole in the limit of vanishing cosmological constant.

Actions, equations of motion and boundary conditions for Chern-Simons branes

Actions for extended objects based on Transgression and Chern-Simons forms for space-time groups and supergroups provide a gauge theoretic framework in which to embed previously studied String and Brane actions, extending them in interesting ways that may be useful in a future non perturbative formulation of String Theory. In this Letter I investigate aspects of the actions of these theories, including equations of motion and boundary conditions, gauge and space-time symmetries, and Dirac quantization of tensions. This theoretical framework is shown to include in certain limit and for a suitable gauge group the standard Bosonic String Theory.

Stochastic Quantization of an Abelian Gauge Theory

We study the Langevin dynamics of a U(1) lattice gauge theory on the two-dimensional torus, and prove that they converge for short time in a suitable gauge to a system of stochastic PDEs driven by space-time white noises. We fix gauge via a DeTurck trick. This also yields convergence of some gauge invariant observables on a short time interval. The proof relies on a discrete version of the theory of regularity structures.