Order In Expansion Research Articles

Entropy current and fluid-gravity duality in Gauss-Bonnet theory

Working within the approximation of small amplitude expansion, recently an entropy current has been constructed on the horizons of dynamical black hole solution in any higher derivative theory of gravity. In this note, we have dualized this horizon entropy current to a boundary entropy current in an asymptotically AdS black hole metric with a dual description in terms of dynamical fluids living on the AdS boundary. This boundary entropy current is constructed using a set of mapping functions relating each point on the horizon to a point on the boundary. We have applied our construction to black holes in Einstein-Gauss-Bonnet theory. We have seen that up to the first order in derivative expansion, Gauss-Bonnet terms do not add any extra corrections to fluid entropy as expected. However, at the second order in derivative expansion, the boundary current will non-trivially depend on how we choose our horizon to boundary map, which need not be expressible entirely in terms of fluid variables. So generically, the boundary entropy current generated by dualizing the horizon current will not admit a fluid dynamical description.

Static homotopy response analysis of structure with random variables of arbitrary distributions by minimizing stochastic residual error

The modelling of realistic engineering structures with uncertainties often involves various probabilistic distribution types, which bring forward higher requirements for the generality of stochastic analysis methods. This paper proposes a novel stochastic homotopy method to evaluate the static response of the structure with random variables of arbitrary distributions. In this method, a homotopy series expansion is used to approximate the stochastic static response, and the optimal form of the expansion can be determined by minimizing the residual error about the stochastic static equilibrium equation regardless of distribution types of random variables. The numerical results of a logarithmic function and a thin plate show that the new method exhibits excellent accuracy and stability compared to the homotopy stochastic finite element method depending on the sample selection. Compared with the arbitrary polynomial chaos method (aPC), the proposed method is more efficient under equivalent accuracy. On the other hand, as the expansion order increases, this new method shows better convergence than the aPC method and the perturbation stochastic finite element method in the case of non-Gaussian distributed random variables of large fluctuation. In addition, a cable-stayed bridge example illustrates the application of the proposed method on the large-scale structure.

Component Analysis and Accuracy Improvement of Linear Power Flow Equation Based on Legendre Polynomial Expansion

The linearization of the power flow equation is widely used in power industry. Existing linearization approaches are generally regarded as nonlinear state variable space transformation, where the original power flow equation can be approximately reformulated as the linear forms in transformed state variable spaces. However, the optimality of linear power flow equations cannot be theoretically compared in different spaces and is only verified based on case studies. In this paper, based on Legendre polynomial expansion, power flow equations are uniformly transformed into a single state variable space, where dimensions correspond to certain orders of Legendre expansion. Through component analysis of power flow equations on each dimension, we find that the accuracy of the linear power flow equation can be improved by formulating an appropriate state variable space transformation to reduce Legendre component loss. Based on this, a linearization method minimizing Legendre component loss is formulated. Compared with the regular case-based linearization, the proposed method does not depend on empirical data, and can theoretically guide the selection of the linear power flow equation within the specified operating bound. The accuracy performance is verified in OPF calculation based on numerous IEEE and Polish test systems.

The modified CUF-EFG method for the dynamic analysis of GPLs-CNTs-reinforced FG multilayer thick cylindrical shells under shock loadings: A modified meshless implementation

The main scope of this paper is to develop the Carrera unified formulation in cylindrical coordinates for two-dimensional meshless modelling of graphene platelet and carbon nanotube reinforced functionally graded multilayer thick cylindrical shells with the same accuracy of three-dimensional modelling. The cylindrical shell is composed of several homogeneous layers with uniform distribution of both GPL and CNT contents in each layer. The effective macroscopic mechanical properties of each GPLs and CNTs reinforced layer are estimated using the modified Halpin-Tsai (H-T) micromechanical model and rule of mixture. The volume fraction of nanofillers gradually changes layer to layer by nonlinear continuous function which leads to functionally graded (FG) distribution of nanofillers. Five grading patterns of layer distribution along the thickness direction of cylindrical shell are considered to investigate the effect of layer arrangement on dynamic behavior of cylindrical shells. The FG multilayer hybrid nanocomposite cylindrical shell is assumed to be under mechanical shock loading. The numerical method for dynamic analysis of multilayer cylindrical shell is based on element free Galerkin (EFG) method with radial basis shape functions in the framework of displacement-based Carrera unified formulation (CUF). The present EFG-CUF method is compared with analytical method for isotropic homogeneous shells and results available in the literature for FG multilayer cylindrical shells. Considering the results related to various expansion orders, proved accuracy and efficiency of proposed method for dynamic analysis of thin to thick FG multilayer cylindrical shells at high expansion orders ‘n > 2’. After verifying the analytical method, the effects of several key factors such as layer distribution patterns, volume fraction index, number of layers, nanofiller weight fraction, aspect ratios of cylinder, and damping ratio on static, free vibration, time history and wave propagation of cylinder are studied in detail.

HPOSS: A hierarchical portfolio optimization stacking strategy to reduce the generalization error of ensembles of models.

Surrogate models are frequently used to replace costly engineering simulations. A single surrogate is frequently chosen based on previous experience or by fitting multiple surrogates and selecting one based on mean cross-validation errors. A novel stacking strategy will be presented in this paper. This new strategy results from reinterpreting the model selection process based on the generalization error. For the first time, this problem is proposed to be translated into a well-studied financial problem: portfolio management and optimization. In short, it is demonstrated that the individual residues calculated by leave-one-out procedures are samples from a given random variable ϵi, whose second non-central moment is the i-th model's generalization error. Thus, a stacking methodology based solely on evaluating the behavior of the linear combination of the random variables ϵi is proposed. At first, several surrogate models are calibrated. The Directed Bubble Hierarchical Tree (DBHT) clustering algorithm is then used to determine which models are worth stacking. The stacking weights can be calculated using any financial approach to the portfolio optimization problem. This alternative understanding of the problem enables practitioners to use established financial methodologies to calculate the models' weights, significantly improving the ensemble of models' out-of-sample performance. A study case is carried out to demonstrate the applicability of the new methodology. Overall, a total of 124 models were trained using a specific dataset: 40 Machine Learning models and 84 Polynomial Chaos Expansion models (which considered 3 types of base random variables, 7 least square algorithms for fitting the up to fourth order expansion's coefficients). Among those, 99 models could be fitted without convergence and other numerical issues. The DBHT algorithm with Pearson correlation distance and generalization error similarity was able to select a subgroup of 23 models from the 99 fitted ones, implying a reduction of about 77% in the total number of models, representing a good filtering scheme which still preserves diversity. Finally, it has been demonstrated that the weights obtained by building a Hierarchical Risk Parity (HPR) portfolio perform better for various input random variables, indicating better out-of-sample performance. In this way, an economic stacking strategy has demonstrated its worth in improving the out-of-sample capabilities of stacked models, which illustrates how the new understanding of model stacking methodologies may be useful.

Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen

The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in alpha , which is O(alpha ^5) in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (Bchi PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (mu H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the Bchi PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius R_textrm{Z}, if one uses the well-known experimental 1S hfs in H or the 2S hfs in mu H. We, respectively, obtain R_textrm{Z}(textrm{H}) = 1.010(9) fm, R_textrm{Z}(mu textrm{H}) = 1.040(33) fm. The total proton-structure effect to the hfs at O(alpha ^5) is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the 1S hfs in mu text {H} is 182.640(18),textrm{meV}.

Bpi excited-state contamination in lattice calculations of B-meson correlation functions

Multi-particle states with additional pions are expected to result in a difficult-to-control excited-state contamination in lattice simulations. We show that heavy meson chiral perturbation theory can be employed to estimate the contamination due to two-particle Bpi states in various B-meson observables, like the B-meson decay constant and the B^*Bpi coupling. We work in the static limit and to next-to-leading order in the chiral expansion, i.e. including textrm{O}(p). The Bpi states are found to typically lead to an overestimation of the observables at the few percent level. We determine two of the LECs from Brightarrow pi form factor computations of the KEK group (Colquhoun et al. in Phys. Rev. D 106:054502, 2022) and discuss ways to determine the others. In particular, one LEC which is associated with smeared interpolating fields seems to be easily accessible and thus opens up a way to systematically study the effect of smearing on excited-state effects.

A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections

By exploiting the Kerr-Schild gauge, we study the scattering of a massive (charged) scalar off a Kerr-Newman black hole. In this gauge, the interactions between the probe and the target involve only tri-linear vertices. We manage to write down the tree-level scattering amplitudes in analytic form, from which we can construct an expression for the eikonal phase which is exact in the spin of the black hole at arbitrary order in the Post-Minkowskian expansion. We compute the classical contribution to the cross-section and deflection angle at leading order for a Kerr black hole for arbitrary orientation of the spin. Finally, we test our method by reproducing the classical amplitude for a Schwarzschild black hole at second Post-Minkowskian order and outline how to extend the analysis to the Kerr-Newman case.

Повноваження Конституційного Суду України:шляхи вдосконалення.

Annotation. The article examines the problems of regulatory regulation of the powers of the Constitutional Court of Ukraine at the level of the Constitution of Ukraine and the Law of Ukraine "On the Constitutional Court of Ukraine", the question of the adequacy of the scope of the powers of the Constitutional Court of Ukraine and the possibility of their improvement through a significant expansion in order to qualitatively ensure the performance of the function of protecting the Constitution of Ukraine. The foreign experience regarding the peculiarities of the powers of the constitutional counter bodies, in particular those of the states where the American, French, or Austrian models are used, is analyzed. Since the Constitutional Court of Ukraine must be an effective protection of the norms of the Constitution of Ukraine, it is proposed to: expand the scope of powers of the Constitutional Court of Ukraine, in particular, to grant the Constitutional Court of Ukraine the authority, if necessary, to independently initiate questions about the conformity of the Constitution of Ukraine (constitutionality) of laws and other legal acts of the Verkhovna Rada of Ukraine, acts of the President of Ukraine, acts of the Cabinet of Ministers of Ukraine, legal acts of the Verkhovna Rada of the Autonomous Republic of Crimea, and not only at the request of the relevant authorized subjects; to return the authority regarding the official interpretation of the laws of Ukraine; to provide a clear mechanism for the implementation of decisions and conclusions of the Constitutional Court of Ukraine and responsibility for their non-implementation; at the level of the Constitution of Ukraine, determine an exhaustive list of acts accepted by the Constitutional Court of Ukraine.

Renormalization group analysis of a self-organized critical system: intrinsic anisotropy vs random environment

Abstract We study a self-organized critical system coupled to an isotropic random fluid environment. The former is described by a strongly anisotropic continuous (coarse-grained) model introduced by Hwa and Kardar (1989 Phys. Rev. Lett. 62 1813; 1992 Phys. Rev. A 45 7002); the latter is described by the stirred Navier–Stokes equation due to Forster et al (1977 Phys. Rev. A 16 732). The full problem of two coupled stochastic equations is represented as a field-theoretic model, which is shown to be multiplicatively renormalizable. The corresponding renormalization group (RG) equations possess a semi-infinite curve of fixed points in the four-dimensional space of the model parameters. The whole curve is infrared attractive for realistic values of parameters; its endpoint corresponds to the purely isotropic regime where the original Hwa–Kardar nonlinearity becomes irrelevant. There, one is left with a simple advection of a passive scalar field by the external environment. The main critical dimensions are calculated to leading (one-loop) order (first terms in the ϵ = 4 − d expansion); some of them are exact in all orders. These dimensions remain the same along that curve, which makes it reasonable to interpret it as a single universality class. However, the correction exponents do vary along the curve. It is therefore not clear whether the curve survives in all orders of the RG expansion or shrinks to a single point when the higher-order corrections are taken into account.

Gaussian and Faddeeva broadening of the Franz-Keldysh oscillations at three-dimensional critical-points

Faddeeva broadening (FB) couples the physical characteristics of Gaussian and Lorentzian broadening into a single profile shaping the spectral response of dielectric functions. The electric field induces Franz-Keldysh oscillations (FKOs) as deviations in the dielectric function of semiconductors. We investigated the impact of Gaussian and FB on FKOs at the isotropic M0 of three-dimensional critical points. The twenty-pole Martin–Donoso–Zamudio quadrature was applied to compute the FB of FKOs in differential reflectivity based on the electro-optic function, H(z), with the complex Airy function, Ai(z). H(z) was simplified into a compact product of to reduce the truncation error and determine its asymptotics. We derived a general asymptotic expansion of order N, accounting for Stokes’ phenomenon as the arg(z) crosses The computation of H(z) is detailed for twelve digits of accuracy. The effects of higher Gaussian and FB widths on the damping of FKOs are assessed using FKO peak-to-peak attenuations. For the low-field regime, this work H(z) smoothly evolves into Aspnes’ third derivative functional form (TDFF). Between low- to intermediate-field regimes, we investigated the boundaries for the relevant use of the TDFF by assessing parameters extracted from simulated lineshapes, and the average root mean-squared error. We fitted of the Faddeeva broadened single Airy model to published experimental photoreflectance (PR) lineshapes of InGaAsP. To model degenerate light-and heavy-holes transitions, we fitted of the Faddeeva broadened double Airy model to published experimental contactless electroreflectance (CER) lineshapes of GaAs. In addition to legacy mean-squared error () and coefficient of determination (), the goodness of fit was evaluated using the unbiased Akaike information criteria. The effectiveness of Faddeeva versus Lorentzian broadening in sample PR and CER spectra analysis was assessed using Airy function FKO models. Concludingly, the FB of the differential reflectivity model outperformed the Lorentzian broadening even with the empirical energy-dependent width.

System reliability of corroded pipelines considering spatial and stochastic dependency in irregular zones

This paper presents a probabilistic methodology for assessing the system reliability of corroded pipelines subjected to spatial and stochastic dependency, taking into account irregular zones (elbows, weld joints, and flanges). The space-variant corrosion and residual stress are considered by the mean of Karhunen-Loève expansion in order to take into account spatial variability of residual stress and soil aggressiveness over the pipe's entire length. The failure probability is evaluated by a series system combination using Monte Carlo simulations. Finally, the proposed model is applied to gas pipeline crossing several soil types in order to show the effects of the main parameters of the system, where the irregular zones have a significant influence on the pipeline system reliability and that the developed model can provide valuable information for decision-makers to improve system reliability performance.

Reflected wave energy by two collinear submerged wavy breakwaters

Under the assumption of a potential flow, we obtain an asymptotic solution up to the second order in a regular expansion, for the problem of the interaction between linear long waves and two submerged floating breakwaters of wavy surfaces, placed in a collinear manner. The hydrodynamics that results from the interaction between the waves and the structures is modeled with the aid of the well-known shallow water wave equations together with the Laplace equation. For this purpose, the domain perturbation method is used to obtain the solution of the governing equations and assume, as is common, small amplitudes of the breakwater's wavy surfaces. This solution is compared with classical analytical solutions reported in the specialized literature, and they adjust properly. Several geometrical configurations of the breakwaters are analyzed. As the breakwaters are near the free surface elevation, just at one-third of the total water depth, larger values of the reflection coefficients are obtained. The maximum wave reflection occurs for four undulations of the breakwater surfaces. In addition, the wave reflection increases as the amplitude of the surfaces of the breakwaters increases. The results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged breakwaters with wavy surfaces.

Form factors in HQEFT and model independent analysis of relevant semileptonic decays with NP effects* *Supported in part by the National Natural Science Foundation of China (12147214)

The form factors of decays into P-wave excited charmed mesons (including , , , and their strange counterparts, denoted generically as ) are systematically calculated via QCD sum rules in the framework of heavy quark effective field theory (HQEFT). We consider contributions up to the next leading order of heavy quark expansion and give all the relevant form factors, including the scalar and tensor ones only relevant for possible new physics effects. The expressions for the form factors in terms of several universal wave functions are derived via heavy quark expansion. These universal functions can be evaluated through QCD sum rules. Then, the numerical results of the form factors are presented. With the form factors given here, a model independent analysis of relevant semileptonic decays is performed, including the contributions from possible new physics effects. Our predictions for the differential decay widths, branching fractions, and ratios of branching fractions may be tested in more precise experiments in the future.

Momentum dependence of mixing in the pion vector form factor and its effect on * *Supported in part by the Fundamental Research Funds for the Central Universities (FRF-BR-19-001A), and the National Natural Science Foundation of China (11975028, 11974043)

The inclusion of the mixing effect is essential for a precise description of the pion electromagnetic form factor in the process, which quantifies the two-pion contribution to the anomalous magnetic moment of muon . In this study, we analyze the momentum dependence of mixing by considering loop contributions at the next-to-leading order in expansion within the framework of resonance chiral theory. We revisit a previous study [Y. H. Chen, D. L. Yao, and H. Q. Zheng, Commun. Theor. Phys. 69, 1 (2018)] and consider the contribution arising from the kaon mass splitting in the kaon loops and latest experimental data. We perform two types of fits (with momentum-independent or momentum-dependent mixing amplitude) to describe and data within the energy region of 600900 MeV and decay width of . Furthermore, we compare their results. Our findings indicate that the momentum-independent and momentum-dependent mixing schemes provide appropriate descriptions of the data. However, the momentum-dependent scheme exhibits greater self-consistency, considering the reasonable imaginary part of the mixing matrix element obtained. Regarding the contribution to the anomalous magnetic moment of the muon, , the results obtained from the fits considering the momentum-dependent mixing amplitude are in good agreement with those obtained without incorporating the momentum dependence of mixing, within the margin of errors. Furthermore, based on the fitted values of the relevant parameters, we observe that the decay width of is predominantly influenced by the mixing effect.

The hunt for the Kármán ‘constant’ revisited

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on the value of the prefactor, the inverse of the Kármán ‘constant’ $\kappa$ , or on its universality. The choice diagnostic tool to locate logarithmic parts of the MVP is to look for regions where the indicator function $\varXi$ (equal to the wall-normal coordinate $y^+$ times the mean velocity derivative $\mathrm {d} U^+/\mathrm {d} y^+$ ) is constant. In pressure-driven flows, however, such as channel and pipe flows, $\varXi$ is significantly affected by a term proportional to the wall-normal coordinate, of order $O({Re}_{\tau }^{-1})$ in the inner expansion, but moving up across the overlap to the leading $O(1)$ in the outer expansion. Here we show that, due to this linear overlap term, ${Re}_{\tau }$ values well beyond $10^5$ are required to produce one decade of near constant $\varXi$ in channels and pipes. The problem is resolved by considering the common part of the inner asymptotic expansion carried to $O({Re}_{\tau }^{-1})$ , and the leading order of the outer expansion. This common part contains a superposition of the log law and a linear term $S_0 \,y^+{Re}_{\tau }^{-1}$ , and corresponds to the linear part of $\varXi$ , which, in channel and pipe, is concealed up to $y^+ \approx 500\unicode{x2013}1000$ by terms of the inner expansion. A new and robust method is devised to simultaneously determine $\kappa$ and $S_0$ in pressure-driven flows at currently accessible ${Re}_{\tau }$ values, yielding $\kappa$ values which are consistent with the $\kappa$ values deduced from the Reynolds number dependence of centreline velocities. A comparison with the zero-pressure-gradient turbulent boundary layer, further clarifies the issues and improves our understanding.

On the boundary conformal field theory approach to symmetry-resolved entanglement

We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as Kac-Moody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetry-resolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with U(1)U(1), \mathbb{R}ℝ and \mathbb{Z}_2ℤ2 symmetry.

A travelling wave-based fault locator for radial distribution systems using decision trees to mitigate multiple estimations

Electrical systems have been facing transformations, such as distributed generation insertion, system expansion and regulatory standards in order to increase reliability and quality of the power supply. Thus, fault location methods must be updated to ensure accuracy in estimating the location of electrical faults. The delay in restoring the system causes damage to utilities and consumers. Considering this, the current work presents an approach capable of locating faults accurately in radial distribution systems. At first, the distance is estimated using the travelling wave theory with data acquired from two terminals. Next, due to the radial characteristic of the system, the proposal aims to mitigate the problem of multiple estimation of faults. Thus, features are extracted from the voltage and current signals, which are used as inputs of decision trees to identify the fault region. The proposed approach was validated in a medium voltage distribution system, in which the results presented an average error of 0.79% (with a standard deviation of 0.4%) in estimating the fault distances and an average accuracy above 88.7% in identifying the region under fault. Thus, it was demonstrated that the proposed methodology is efficient to locate faults, mitigating the problem of multiple estimation.

Purification as a tactic of marginalisation in business-community relations: Epistemic dimensions in the exclusion of Indigeneity in Arctic development strategy

This study reveals the tactic of purification as a form of neo-colonial marginalisation present in contemporary development strategies on Indigenous lands. The research is based on my fieldwork study of exclusive tactics in a contemporary development conflict on Indigenous lands: the Arctic Railway project in Sápmi, in Northern Europe. The tactic of purification works through the selective use of opposites in excluding Indigeneity. On the one hand, ‘pure’ Indigeneity is an excuse for proponents of extractive development projects to exclude Indigenous knowledge and identities as ‘too Indigenous’ according to modern standards, denouncing them as ‘backward’, ‘only culture’, ‘not profitable’, or ‘without knowledge’. Yet, simultaneously, a resemblance to profitable livelihood practices, beyond culture, the use of several knowledge systems, and multi-ethnicity in communities, is deemed ‘too modern’, therefore ‘not pure enough’, thus invalidating Indigeneity. Building on classification systems introduced during colonialism, settler societies employ purification as a tactic to deny Indigenous peoples their right to decolonisation projects, and strengthen their control of Indigenous lands. The purification tactic thereby enables the expansion of the modern-colonial capitalist world order.

A Riemann–Hilbert Approach to the Perturbation Theory for Orthogonal Polynomials: Applications to Numerical Linear Algebra and Random Matrix Theory

Abstract We establish a new perturbation theory for orthogonal polynomials using a Riemann–Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with respect to two measures can be effectively compared using the difference of their Stieltjes transforms on a suitably chosen contour. Moreover, when two measures are close and satisfy some regularity conditions, we use the theta functions of a hyperelliptic Riemann surface to derive explicit and accurate expansion formulae for the perturbed orthogonal polynomials. In contrast to other approaches, a key strength of the methodology is that estimates can remain valid as the degree of the polynomial grows. The results are applied to analyze several numerical algorithms from linear algebra, including the Lanczos tridiagonalization procedure, the Cholesky factorization, and the conjugate gradient algorithm. As a case study, we investigate these algorithms applied to a general spiked sample covariance matrix model by considering the eigenvector empirical spectral distribution and its limits. For the first time, we give precise estimates on the output of the algorithms, applied to this wide class of random matrices, as the number of iterations diverges. In this setting, beyond the first order expansion, we also derive a new mesoscopic central limit theorem for the associated orthogonal polynomials and other quantities relevant to numerical algorithms.