Generalized Perturbation Method Research Articles

On application of the relative entropy concept in reliability assessment of some engineering cable structures

The main research problem studied in this work is an uncertain response and reliability assessment of the spatial cable structures due to the environmental stochasticity as well as material and geometrical imperfections. Some popular cable structures are analyzed for this purpose using the Stochastic Finite Element Method (SFEM) implemented with the use of three different techniques, namely the iterative generalized perturbation method, semi-analytical approach as well as the Monte-Carlo simulation. Uncertainty quantification delivered in this study is based on the series of FEM analyses of both static and dynamic structural problems. They enable the Least Squares Method determination of the structural polynomial responses linking extreme stresses and deformations with several uncorrelated uncertainty sources. Reliability assessment, fundamental in durability and Structural Health Monitoring, is completed using a comparison of the First Order Reliability Method (FORM) with probabilistic distance formulated by Bhattacharyya. Input uncertainties are assumed to be Gaussian according to the Maximum Entropy Principle. They have specific expected values following engineering design demands or the provisions of designing codes, whereas their standard deviations do not exceed the 10% level. The methods presented and the results obtained in this study may serve for further reliability analyses of large-scale civil engineering structures completed with both steel cables and also reinforced concrete plates like suspended bridges, for instance.

Dispersive Modal Characteristics of Guided Waves Propagating in Damaged Rails

The dispersive modal characteristics of propagating guided waves are useful for efficiently detecting defects in high-speed railway rails due to their advantages. This paper presents an effective method for directly analyzing the effect of defects in rails on the dispersive modal characteristics of propagating guided waves, which can be utilized for the defect detection in rails. By using the semianalytical finite element method and from the characteristic equations of the guided wave propagation in waveguides, a general perturbation method is developed to provide an exact relationship between the perturbations of structural stiffness caused by damage and the perturbations of dispersive modal characteristics of propagating guided waves. Thus, the phase velocity and group velocity for the damaged waveguide can be accurately predicted. From the obtained propagating guided wave modes, a mode selection index used for selecting effective guided waves for damage detection is introduced by evaluating the nodal displacements and energy concentrations on the rail surfaces. Finally, a numerical study for a high-speed rail is given to demonstrate the effectiveness of the proposed method for rail defect detection and propagating mode selection. The results of the numerical study show that the dispersive modal properties of propagating modes are affected by the location and size of defects in the rail, and the proposed method can give useful information for effective detection of defects in rails.

A New General Perturbation Method for Determining the Long-Term Motion of Comets

A number of authors have used special perturbation methods to propagate Comet Halley back before its oldest observation in 239 BC. Unfortunately, results from these studies vary drastically because it is so difficult to accurately model nongraviatational forces acting on comets. In contrast, general perturbation methods do not need to model any forces and can be more accurate over long periods of time. Regrettably, the most recent general perturbation method used for Comet Halley introduced a lot of subjectivity. A new general perturbation method integrating Halley’s Comet back in time is presented here. This new method uses least squares, based solely on math. Therefore, it does not introduce any subjectivity. It also permits statistical analysis of the model’s accuracy. Using this model, Halley’s Comet is propagated back to 2317 BC, and with the derived equations it can easily be integrated back much further in time. Results are very similar to two previous studies by other authors, varying by less than five years when propagated back over 2,200 years. This same new general perturbation method is also applied to Comet Swift-Tuttle. Results with Swift-Tuttle compare reasonably well with the only other known research that integrated this comet back in time.

The heuristically-based generalized perturbation theory

The generalized perturbation method is described relevant to ratios of bi-linear functionals of the real and adjoint neutron fluxes of critical multiplying systems. Simple linear analysis for optimization and sensitivity studies are then feasible relative to spectrum and space-dependent quantities, such as Doppler and coolant void reactivity effects in fast reactors.

Ab Initio Study of Stability, Local Order, and Phase Diagram For a Series of bcc-based Transition Metal Alloys

A parameter-free electronic structure approach is applied to the study of stability and chemical order in the 15 substitutional body-centered cubic (bcc)-based alloys made of the six transition metals of groups 5 (V, Nb, Ta) and 6 (Cr, Mo, W) of the periodic table. The method is based on a Green’s function description of the electronic structure of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with a generalized mean-field approach. In contrast to the results summarized in the assessed phase diagrams, stability and ordering trends are predicted in a broad range of alloy composition for at least seven alloys, and explanation is found in their electronic structure properties. Short-range order results, thermodynamics analysis, and bcc-based phase diagrams are also presented.

Short-range order in face-centered cubic VCoNi alloys

Concentrated solid solutions including the class of high entropy alloys (HEAs) have attracted enormous attention recently. Among these alloys a recently developed face-centered cubic (fcc) equiatomic VCoNi alloy revealed extraordinary high yield strength, exceeding previous high-strength fcc CrCoNi and FeCoNiCrMn alloys. Significant lattice distortions had been reported in the VCoNi solid solution. There is, however, a lack of knowledge about potential short-range order (SRO) and its implications for most of these alloys. We performed first-principles calculations and Monte Carlo simulations to compute the degree of SRO for fcc VCoNi, namely, by utilizing the coherent-potential approximation in combination with the generalized perturbation method as well as the supercell method in combination with recently developed machine-learned potentials. We analyze the chemical SRO parameters as well as the impact on other properties such as relaxation energies and lattice distortions.

Tight-binding modeling of interstitial ordering processes in metals: Application to zirconium hydrides

We present here a theoretical study of ordering processes in metal-hydrogen compounds based on a generalized perturbation method and on tight-binding coherent potential approximation. This approach is illustrated for zirconium hydrides, in which case we demonstrate that a cluster expansion of the ordering energy can be limited to effective pair interactions, the leading one being between hydrogen atoms in third-neighbor positions. These results are quantitatively confirmed by comparison to density functional theory calculations and qualitatively interpreted through orbital symmetry analysis. The method is then applied first to draw a preliminary Zr-H phase diagram and then to characterize the effect of lattice deformation on the ordering processes in zirconium hydrides.

Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime-Switching Approach

We develop a new approach to estimating DSGE models with occasionally binding borrowing constraints and apply it to Mexico's business cycle and financial crisis history. We propose a new endogenous regime-switching specification of the borrowing constraint, develop a general perturbation method to solve the model, and estimate it using Bayesian methods. The estimated model fits the data with well-behaved shocks, identifying three crisis episodes of varying duration and intensity: the early-1980s Debt Crisis, the mid-1990s Tequila Crisis, and the late-2000s Global Financial Crisis. The estimated crisis episodes are much more persistent and in line with the data than traditional models.

Two-component pulse in uniaxial media

A theory of self-induced transparency (SIT) for the two-component pulse in anisotropic uniaxial media is developed. The system of equations of SIT for extraordinary wave in uniaxial media by means of generalized reduction perturbation method is reduced to the coupled nonlinear Schrodinger equations for auxiliary functions. It is shown that in the theory of SIT, the second derivatives play a significant role that leads to the formation of a vector 0π pulse oscillating with the sum and difference of the frequencies. Explicit analytical expressions for the profile and parameters of the two-component nonlinear wave are presented. It is obtained along with scalar 2π pulse, the vector 0π pulse is also the basic pulse of SIT. The conditions for existence of the nonlinear extraordinary wave depend on the direction of propagation.

Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate.

Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime-Switching Approach

We estimate a workhorse DSGE model with an occasionally binding borrowing constraint. First, we propose a new specification of the occasionally binding constraint, where the transition between the unconstrained and constrained states is a stochastic function of the leverage level and the constraint multiplier. This specification maps into an endogenous regime-switching model. Second, we develop a general perturbation method for the solution of such a model. Third, we estimate the model with Bayesian methods to fit Mexico's business cycle and financial crisis history since 1981. The estimated model fits the data well, identifying three crisis episodes of varying duration and intensity: the Debt Crisis in the early-1980s, the Peso Crisis in the mid-1990s, and the Global Financial Crisis in the late-2000s. The crisis episodes generated by the estimated model display sluggish and long-lasting build-up and stagnation phases driven by plausible combinations of shocks. Different sets of shocks explain different variables over the business cycle and the three historical episodes of sudden stops identified.

An Empirical Study of Applying Statistical Disclosure Control Methods to Public Health Research

Patient data or information collected from public health and health care surveys are of great research value. Usually, the data contain sensitive personal information. Doctors, nurses, or researchers in the public health and health care sector do not analyze the available datasets or survey data on their own, and may outsource the tasks to third parties. Even though all identifiers such as names and ID card numbers are removed, there may still be some occasions in which an individual can be re-identified via the demographic or particular information provided in the datasets. Such data privacy issues can become an obstacle in health-related research. Statistical disclosure control (SDC) is a useful technique used to resolve this problem by masking and designing released data based on the original data. Whilst ensuring the released data can satisfy the needs of researchers for data analysis, there is high protection of the original data from disclosure. In this research, we discuss the statistical properties of two SDC methods: the General Additive Data Perturbation (GADP) method and the Gaussian Copula General Additive Data Perturbation (CGADP) method. An empirical study is provided to demonstrate how we can apply these two SDC methods in public health research.

Estimating Macroeconomic Models of Financial Crises: An Endogenous Regime Switching Approach

We estimate a workhorse DSGE model with an occasionally binding borrowing constraint. First, we propose a new specification of the occasionally binding constraint, where the transition between the unconstrained and constrained states is a stochastic function of the leverage level and the constraint multiplier. This specification maps into an endogenous regime-switching model. Second, we develop a general perturbation method for the solution of such a model. Third, we estimate the model with Bayesian methods to fit Mexico's business cycle and financial crisis history since 1981. The estimated model fits the data well, identifying three crisis episodes of varying duration and intensity: the Debt Crisis in the early-1980s, the Peso Crisis in the mid-1990s, and the Global Financial Crisis in the late-2000s. These crisis episodes display sluggish and long-lasting build-up and recovery phases driven by plausible combinations of shocks.

The Effect of Thermal Parameters on the Flow Temperature of a Magnetized Plasma in a Sphere

The effect of thermal parameters on the flow temperature of a magnetized plasma in a sphere was studied. The study models astrophysical environments such as the Sun, which have spherical outline. The governing equations of the problem were obtained based on the Navier-Stokes equations under the Boussinesq’s approximation. The solutions to the resulting equations were sought by means of the general perturbation method and the results were graphically represented with radial distance, r = 1.0 on the figures corresponding to the surface of the sphere. The thermal parameters; particularly, the radiation parameter, N2 and free convection parameter, Gr. were investigated in this study with a view to determine the effect of varying these parameters on the plasma flow temperature. Increasing both N2 and Gr. led to a decrease in the plasma flow temperature in the sphere. However, above the sphere (i.e. at radial distances, r >1.0) where the plasma density is sparse, increasing N2 and Gr. produced a corresponding increase in the plasma flow temperature. The decrease in the plasma flow temperature within the sphere with increase in the thermal parameters was observed to be more significant between radial distances, r = 0.25 and r = 0.7 (i.e., 0.25 ≤ r ≤ 0.7) than between r = 0.7 and r = 1.0 (i.e., 0.7 ≤ r ≤ 1.0). This is attributable to the prevalence of partially ionized heavy elements within 0.7 ≤ r ≤ 1.0 (corresponding to the convection zone of the solar interior) which trap the high energy photons thereby reducing the rate of radiative heat loss.

MHD Fluid Flow of an Exponentially Varying Plasma Density in a Radiating and Slowly Rotating Hot Sphere

The study presents the effect of density variation on the flow structure of a plasma gas in a slowly rotating and radiating hot sphere. The problem which is solved by general perturbation method shows that the plasma temperature decreases to a minimum at a radial distance of 1.4 solar radii and then increased to a maximum value at a radial distance of 3.5 solar radii, for various radiation parameters, N2. The sudden increase in temperature profile when the radial distance is 1.4 solar radii, indicates the heating up of the upper regions of the solar atmosphere.

Incorporating Solar Activity into General Perturbation Analysis of Atmospheric Friction

A new parameter is introduced, termed the density index, which enables the solar activity cycle to be captured in a new analytical atmospheric density model. Consequently, a new solar activity model is developed that uses a single independent variable per solar cycle to describe the solar activity across that cycle, as indicated by the index. These models are combined and applied to a well-known general perturbation method for satellite orbit lifetime analysis, which is first modified using modern mathematical tools to remove simplifications in the derivation. Validation against historical data shows an improvement in orbit lifetime estimates from an average error of 50.44% with a standard deviation of 24.96% to an average error of 3.46% with a standard deviation of 3.25%. Furthermore, the new method with applied atmospheric and solar activity models is found to compare favorably against other general and special perturbation methods, including third-party and commercial software, the most accurate of which was found to have an average error of 6.63% and standard deviation of 7.00%. A case study, the UKube-1 spacecraft, is presented, and it is found that the spacecraft was inserted into an orbit 54 km lower than required to comply with best-practice guidelines and that, with confidence, its orbit will decay in June years, and June months if the next solar cycle is an average magnitude cycle.

Interplanetary Coronal Mass Ejection effects on thermospheric density as inferred from International Space Station orbital data

The solar activity induces long term and short term periodical variations in the dynamics and composition of Earth’s atmosphere. The Sun also shows non periodical (i.e., impulsive) activity that reaches the planets orbiting around it. In particular, Interplanetary Coronal Mass Ejections (ICMEs) reach Earth and interact with its magnetosphere and upper neutral atmosphere. Nevertheless, the interaction with the upper atmosphere is not well characterized because of the absence of regular and dedicated in situ measurements at high altitudes; thus, current descriptions of the thermosphere are based on semi empirical models.In this paper, we present the total neutral mass densities of the thermosphere retrieved from the orbital data of the International Space Station (ISS) using the General Perturbation Method, and we applied these densities to routinely compiled trajectories of the ISS in low Earth orbit (LEO). These data are explicitly independent of any atmospheric model. Our density values are consistent with atmospheric models, which demonstrates that our method is reliable for the inference of thermospheric density. We have inferred the thermospheric total neutral density response to impulsive solar activity forcing from 2001 to the end of 2006 and determined how solar events affect this response. Our results reveal that the ISS orbital parameters can be used to infer the thermospheric density and analyze solar effects on the thermosphere.

Ricci curvature bounds for weakly interacting Markov chains

We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of spin systems including the Ising and Curie–Weiss models, a class of hard-core models and random walks on groups induced by a conjugacy invariant set of generators.

New perturbative method for analytical solutions in single-field models of inflation

We propose a new parametrization of the background equations of motion corresponding to (canonical) single-field models of inflation, which allows a better understanding of the general properties of the solutions and of the corresponding predictions in the inflationary observables. Based on the tools of dynamical systems, the method suggests that inflation comes in two flavors: power-law and de Sitter. Power-law inflation seems to occur for a restricted type of potentials, whereas de Sitter inflation has a much broader applicability. We also show a general perturbative method, by means of series expansion, to solve the new equations of motion around the critical point of the de Sitter type, and how the method can be used for arbitrary models of de Sitter inflation. It is then argued that for the latter there are two general classes of inflationary solutions, given in terms of the behavior of the tensor-to-scalar ratio as a function of the number $N$ of $e$-folds before the end of inflation: $r \sim N^{-1}$ (Class I), or $r \sim N^{-2}$ (Class II). We give some examples of the two classes in terms of known scalar field potentials, and compare their general predictions with constraints obtained from observations.

Inherent instability by antibonding coupling in AgSbTe2

In the present paper, an inherent instability in the ternary chalcogenide compound AgSbTe2 is described from the electronic structure viewpoint. Our calculations, which are based on the cluster expansion method, suggest nine stable crystal structures involving the most stable structure with symmetry. The effective pair interactions calculated by the generalized perturbation method point out that the stability of these structures originates from the number of linear arrangements of the Ag–Te–Sb atomic bonds. Moreover, it is found that AgSbTe2 has a special electronic structure, where the dominant components of the top of the valence band are the Te-5p antibonding states. Such an antibonding contribution leads to an inherent instability, such that the system spontaneously forms various mutation phases caused by charge-compensated defect complexes. We propose that these mutation phases play an important role in the thermal conductivity and thermoelectric efficiency in AgSbTe2.