Order In Expansion Research Articles

Radiation fluxes of gravitational, electromagnetic, and scalar perturbations in type-D black holes: an exact approach

We present a novel method that solves Teukolsky equations with the source to calculate radiation fluxes at infinity and event horizon for any perturbation fields of type-D black holes. For the first time, we use the confluent Heun function to obtain the exact solutions of ingoing and outgoing waves for the Teukolsky equation. This benefits from our derivation of the asymptotic analytic expression of the confluent Heun function at infinity. It is interesting to note that these exact solutions are not subject to any constraints, such as low-frequency and weak-field. To illustrate the correctness, we apply these exact solutions to calculate the gravitational, electromagnetic, and scalar radiations emitted by a particle in circular orbits around a Schwarzschild black hole. Numerical results show that the proposed exact solution appreciably improves the computational accuracy and efficiency compared with the 23rd post-Newtonian order expansion and the Mano-Suzuki-Takasugi method.

Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

SummaryA multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called “dynamical” or “second‐order” term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the “dynamical” component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions.

Development of Wordwall-Based Assessment Instruments to Measure Higher Order Thinking Skills Science Material Temperature, Heat, and Expansion

The application of higher order thinking skills (HOTS) in evaluation aims to improve the quality of students' thinking, especially about the process of solving a problem. This study aims to develop a wordwall-based assessment instrument to measure HOTS. This study methods used the Borg and Gall development model with 8 stages covering, looking for potential and formulating problems, information gathering, product design, product design validation, design revision, small group trials, product revisions, field trials. Respondents who took the test were divided into 2, namely 25 students for small group trials and all of class VII SMPN 2 Maesan, Bondowoso for field trials. The questionnaires used in this study were interview questionnaires, validation questionnaires and tests to find out students' HOTS. The results showed that the validity of the assessment instrument was 80.99% with a valid category along with the items, and the reliability of the assessment instrument was 0.770. The analysis of the discriminating power of the items produced 3 items in the very good category, 10 items in the good category, 4 items in the sufficient category, and 3 items in the poor category. Then the difficulty level analysis produces 5 questions in the too easy category, 12 questions in the medium category, and 3 questions in the too difficult category. Based on the results of the research, the assessment instrument developed was stated to be valid and suitable for use for subsequent learning evaluations even though there were minor revisions

Toeplitz operators and the full asymptotic torsion forms

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles {Fp}p∈N⁎. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang have studied the first order expansion and expressed the leading term as the integral of a locally computable differential form.

Wrong Way Risk corrections to CVA in CIR reduced-form models

In this paper we provide an efficient methodology to compute the credit value adjustment of a European contingent claim subject to some default event concerning the issuer solvability, when the underlying and the default event are correlated. In particular, in a Black and Scholes market/CIR intensity-default model, we consider a second order expansion around the origin of a vulnerable call option with respect to a correlation parameter rho, which may be used to describe the wrong way risk of the contract, measuring the dependence between the underlying asset price and the option’s issuer default intensity. Numerical implementations of this approach are compared with the benchmark Monte Carlo simulations.

An arbitrary order numerical framework for transient heat conduction problems

This paper presents an arbitrary order numerical approach for achieving highly accurate solutions in transient heat conduction problems. In this framework, the arbitrary order Krylov deferred correction method (KDC) is first utilized to discretize the temporal direction of the problems, ensuring high-accuracy results by selecting an adequate number of Gaussian nodes. During each time iteration, a boundary value problem in terms of the inhomogeneous modified Helmholtz equation is generated by utilizing the KDC methodology. Subsequently, the arbitrary order GFDM is introduced to solve the boundary value problem, allowing for flexible selection of the Taylor series expansion order to improve spatial accuracy. Consequently, the present numerical framework is of arbitrary order of accuracy and very stable through integrating advantages of the arbitrary order KDC and the arbitrary order GFDM. The developed numerical framework is ultimately verified for its characteristic of high accuracy and stability through two numerical examples in two-dimensions and three numerical examples in three-dimensions. The results highlight the significant improvement in numerical accuracy achieved by the present arbitrary-order numerical approach for long-time simulations.

Method of acoustic separation on the surface of cylindrical baffle

This paper suggests a statistically optimal near-field acoustic holography method based on the combination of plane waves and cylindrical waves, which is used for underwater cylindrical baffles. The method addresses the issue that the extraction of scattered acoustic waves from the surface of underwater cylindrical baffles requires too many measurement points in practical applications: separation of incident and dispersed sound fields and near-field measurements of sound fields at baffle surfaces.The underwater detection sound source is situated in the scatterer's far-field region, so in the actual application scenario for the surface acoustic scattering separation of the cylindrical baffle, the plane wave expansion is used to represent the surface incident acoustic wave and the cylindrical wave expansion is used to describe the scattered acoustic wave on the baffle surface. As a result, fewer expansion orders are required to describe the entire sound field on the baffle's surface. It is verified by simulation that the method is valid and efficient for near-field total sound field measurement and dispersed sound field separation of roughly cylindrical targets under underwater far-field incidence situations because the measurement holographic surface of the surface permits unlimited geometries.

Classical observables from the exponential representation of the gravitational S-matrix

By combining the KMOC-formalism with the exponential representation of the scattering matrix we show that the two-body scattering angle is given by the corresponding matrix element of the exponential representation. This holds to all orders in the Post-Minkowskian expansion of gravity when restricted to the conservative sector. Once gravitational radiation is taken into account new terms correcting this relationship appear starting at fourth Post-Minkowskian order. A systematic expansion of the momentum kick is provided to any order, thus illustrating the iterative structure that partly recycles terms from lower orders in the Post-Minkowskian expansion. We provide explicit results for this computation to fourth Post-Minkowskian order, the first complete calculation at this order based on scattering amplitudes.

Closed-form solutions for clamped FGM plates via the unified formulation and boundary discontinuous method

There are very few precise and reliable solutions available in the existing literature for functionally graded plates with fully clamped ends under mechanical loads, indicating a significant research gap in this area. In this article, an analytical solution for clamped functionally graded plates subjected to mechanical load is introduced. The shear deformation theory, governing equations, and boundary conditions are derived based on the Carrera Unified Formulation (CUF) strategy, and the solution is obtained by using the boundary-discontinuous Fourier method. The mechanical properties of the plates are assumed to vary according to an exponential law and a power-law distribution along the thickness direction in terms of the volume fractions of the constituents. The results presented in this article cover a large spectrum of plate thicknesses, ranging from thick to thin, and encompass various values of the functionally graded parameter. Accurate results of shear deformation theories with various order of expansion are achieved. Finally, a gap in the literature is covered and benchmarks solution are provided.

Развитие взглядов К. Маркса на историческую свободу в трех социальных формах

Nowadays, under the order of the logical expansion of Western capital, human beings are faced with various survival problems. Whether it is the natural environment, ecology, energy or social, financial, economic crisis, crisis of faith, etc., the root causes of unfavorable scenarios are closely related to the lifestyle dominated by the logic of capital. By analyzing and modernly exploring the Marxist concept of freedom in three major social forms, the authors have tried to find a new way to resolve the above-mentioned existential crisis. At the same time, the discussion of Marx’s concept of historical freedom is significant for the modern theory of socialism with Chinese characteristics. Marx’s view of freedom is the theoretical system of Marx’s (Engels) basic views on the root of human freedom, the essence of freedom, the basic content of freedom, the value function of free-dom and the way to realize freedom. To fully understand K. Marx’s point of view on this issue, it is necessary to associate his theory of three social formations with the study of human freedom in the process of historical de-velopment. The theory of the three major social formations is an extremely important content of Marx’s view of history.

Discrete analogue of the Weil-Petersson volume in double scaled SYK

We show that the connected correlators of partition functions in double scaled SYK model can be decomposed into “trumpet” and the discrete analogue of the Weil-Petersson volume, which was defined by Norbury and Scott. We explicitly compute this discrete volume for the first few orders in the genus expansion and confirm that the discrete volume reduces to the Weil-Petersson volume in a certain semi-classical limit.

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.