Second-order Expression Research Articles

Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations

This paper focuses on the study of robust two-stage quadratic multiobjective optimization problems. We formulate new necessary and sufficient optimality conditions for a robust two-stage multiobjective optimization problem. The obtained optimality conditions are presented by means of linear matrix inequalities and thus they can be numerically validated by using a semidefinite programming problem. The proposed optimality conditions can be elaborated further as second-order conic expressions for robust two-stage quadratic multiobjective optimization problems with separable functions and ellipsoidal uncertainty sets. We also propose relaxation schemes for finding a (weak) efficient solution of the robust two-stage multiobjective problem by employing associated semidefinite programming or second-order cone programming relaxations. Moreover, numerical examples are given to demonstrate the solution variety of our flexible models and the numerical verifiability of the proposed schemes.

Long-Range Configuration Interaction with an Ab Initio Short-Range Correction and an Asymptotic Lower Bound†.

Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to reference data is used, and the method is applicable to ground and excited states. The formulas derived are rigorous when the physical interaction is approached. In this regime, the second-order expression provides a lower bound to the long-range full configuration interaction energy. A long-range/short-range separation of the interaction between electrons at a distance of the order of one atomic unit provides total energies within chemical accuracy, and, for the systems studied, provide better results than short-range density functional approximations.

Second-order spectral line shift comparisons

The second-order spectral line width formulae from the projection operator and kinetic theory methods were recently compared. It was shown that a systematic expansion of the projection operator width expression including initial correlations formally agrees with the second-order kinetic theory result. It is now shown that the second-order dynamic shifts are also formally the same. The static shifts, however, differ due to an ad hoc treatment of electron-electron correlations in the projection operator method. The approximation is necessary in order to screen the radiator-electron interactions. The differences, however, are expected to be small. The results suggest using the rigorous and more compact second-order width and shift expressions from the kinetic theory method as the starting point for spectral line shape calculations. At line center, however, the projection operator second-order expression for the width and shift simplifies and reduces to the kinetic theory result.

Sorption behavior of selected fission products on spent alum sludge

The spent alum sludge was employed for the removal of specific fission products including 137Cs, 85Sr, 152+154Eu, 99Mo, and 99Tc radionuclides from radioactive waste. The physicochemical features of spent alum sludge were investigated. The results illustrated that the uptake percentages were 94.2, 90.5, 87.6, 87.1, and 76.6%, correspondingly, for 99Mo, 152+154Eu, 99Tc, 85Sr, and 137Cs. The kinetic studies illustrated that the adsorption process obeyed Langmuir kinetics which is a combination of first-order and second-order expressions. The findings demonstrated that the spent alum sludge can be applied successfully as a low-cost and effective adsorbent for the treatment of radioactive waste.

Quantum Dichotomies and Coherent Thermodynamics beyond First-Order Asymptotics

We address the problem of exact and approximate transformation of quantum dichotomies in the asymptotic regime, i.e., the existence of a quantum channel E mapping ρ1⊗n into ρ2⊗Rnn with an error ϵn (measured by trace distance) and σ1⊗n into σ2⊗Rnn exactly, for a large number n. We derive second-order asymptotic expressions for the optimal transformation rate Rn in the small-, moderate-, and large-deviation error regimes, as well as the zero-error regime, for an arbitrary pair (ρ1,σ1) of initial states and a commuting pair (ρ2,σ2) of final states. We also prove that for σ1 and σ2 given by thermal Gibbs states, the derived optimal transformation rates in the first three regimes can be attained by thermal operations. This allows us, for the first time, to study the second-order asymptotics of thermodynamic state interconversion with fully general initial states that may have coherence between different energy eigenspaces. Thus, we discuss the optimal performance of thermodynamic protocols with coherent inputs and describe three novel resonance phenomena allowing one to significantly reduce transformation errors induced by finite-size effects. What is more, our result on quantum dichotomies can also be used to obtain, up to second-order asymptotic terms, optimal conversion rates between pure bipartite entangled states under local operations and classical communication. Published by the American Physical Society 2024

Oxytocin and corticotropin-releasing hormone exaggerate nucleus tractus solitarii neuronal and synaptic activity following chronic intermittent hypoxia.

Chronic intermittent hypoxia (CIH) in rodents mimics the hypoxia-induced elevation of blood pressure seen in individuals experiencing episodic breathing. The brainstem nucleus tractus solitarii (nTS) is the first site of visceral sensory afferent integration, and thus is critical for cardiorespiratory homeostasis and its adaptation during a variety of stressors. In addition, the paraventricular nucleus of the hypothalamus (PVN), in part through its nTS projections that contain oxytocin (OT) and/or corticotropin-releasing hormone (CRH), contributes to cardiorespiratory regulation. Within the nTS, these PVN-derived neuropeptides alter nTS activity and the cardiorespiratory response to hypoxia. Nevertheless, their contribution to nTS activity after CIH is not fully understood. We hypothesized that OT and CRH would increase nTS activity to a greater extent following CIH, and co-activation of OT+CRH receptors would further magnify nTS activity. Our data show that compared to their normoxic controls, 10days' CIH exaggerated nTS discharge, excitatory synaptic currents and Ca2+ influx in response to CRH, which were further enhanced by the addition of OT. CIH increased the tonic functional contribution of CRH receptors, which occurred with elevation of mRNA and protein. Together, our data demonstrate that intermittent hypoxia exaggerates the expression and function of neuropeptides on nTS activity. KEY POINTS: Episodic breathing and chronic intermittent hypoxia (CIH) are associated with autonomic dysregulation, including elevated sympathetic nervous system activity. Altered nucleus tractus solitarii (nTS) activity contributes to this response. Neurons originating in the paraventricular nucleus (PVN), including those containing oxytocin (OT) and corticotropin-releasing hormone (CRH), project to the nTS, and modulate the cardiorespiratory system. Their role in CIH is unknown. In this study, we focused on OT and CRH individually and together on nTS activity from rats exposed to either CIH or normoxia control. We show that after CIH, CRH alone and with OT increased to a greater extent overall nTS discharge, neuronal calcium influx, synaptic transmission to second-order nTS neurons, and OT and CRH receptor expression. These results provide insights into the underlying circuits and mechanisms contributing to autonomic dysfunction during periods of episodic breathing.

Understanding Stokes Drift Mechanism via Crest and Trough Phase Estimates

Abstract By providing mathematical estimates, this paper answers a fundamental question—“what leads to Stokes drift”? Although overwhelmingly understood for water waves, Stokes drift is a generic mechanism that stems from kinematics and occurs in any nontransverse wave in fluids. To showcase its generality, we undertake a comparative study of the pathline equation of sound (1D) and intermediate-depth water (2D) waves. Although we obtain a closed-form solution x(t) for the specific case of linear sound waves, a more generic and meaningful approach involves the application of asymptotic methods and expressing variables in terms of the Lagrangian phase θ. We show that the latter reduces the 2D pathline equation of water waves to 1D. Using asymptotic methods, we solve the respective pathline equation for sound and water waves, and for each case, we obtain a parametric representation of particle position x(θ) and elapsed time t(θ). Such a parametric description has allowed us to obtain second-order accurate expressions for the time duration, horizontal displacement, and average horizontal velocity of a particle in the crest and trough phases. All these quantities are of higher magnitude in the crest phase in comparison to the trough phase, leading to a forward drift, i.e., Stokes drift. We also explore particle trajectory due to second-order Stokes waves and compare it with linear waves. While finite amplitude waves modify the estimates obtained from linear waves, the understanding acquired from linear waves is generally found to be valid.

Third-Order Intrinsic Aberration Modification with Second-Order Accuracy Transfer of Pupil Coordinates and Extrinsic Aberration of Plane-Symmetric Optical System with a Two-Dimensional Field Light Source

A plane-symmetric optical system with a two-dimensional field light source, such as a soft X-ray and vacuum ultraviolet optical system, is widely used for synchrotron radiation source devices, microscopes and so on. Therefore, this paper studied third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration of these kinds of optical systems. First, we discuss the extrinsic aberration calculation method and derive the corresponding aberration expressions; in addition, we apply optical geometric relations and the polynomial fitting method to obtain a second-order accuracy transfer relationship expression of the pupil coordinates between adjacent optical surfaces and derived the modification calculation expressions of the intrinsic aberration caused by the above factor. Finally, the third-order intrinsic aberration modification with second-order accuracy transfer of pupil coordinates and extrinsic aberration expressions derived in this paper are applied to calculate ray spot diagrams of two soft X-ray and vacuum ultraviolet optical systems with meridional and sagittal field angle light sources, and these results are compared with those obtained from the ray-tracing software Shadow; this showed that the calculation accuracy of the aberration expressions is sufficient.

A Unified Wide-Speed Range Sensorless Control Method for Switched Reluctance Machines Based on Unsaturated Reluctance

A unified unsaturated-reluctance-based wide speed range sensorless control method for switched reluctance machines (SRMs) is proposed in this paper. Firstly, the sensitivity analysis of the estimated position to the possible reluctance calculation error is analyzed. This analysis reveals the feasible regions with low sensitivity and low risk of entering saturation. Then, the unsaturated reluctance in these feasible regions is obtained and modeled. A simple second-order rational expression is proposed to fit the highly nonlinear unsaturated reluctance curve. With this simple model, the rotor position can be analytically calculated only by solving a simple quadratic problem. Based on the above-presented analysis, a wide-speed range sensorless control is developed. The rotor position is universally estimated from the real-time reluctance value and the proposed analytical model. The high-frequency voltage injection and normal conduction phase are combined to calculate the phase reluctance over the wide-speed range. The concerns of calculating reluctance at the low-speed range are also discussed. A 5.1 kW four-phase 8/6 SRM is used to verify the proposed method. Various steady state and transient state experimental results prove the effectiveness of the proposed sensorless control method.

Arsenic removal by highly efficient MnFe2O4/TiO2/g-C3N4 and MnFe2O4/TiO2/GO adsorbents from a groundwater sample, Bardsir, Iran

In this study, MnFe2O4/TiO2/GO and MnFe2O4/TiO2/g-C3N4 spinel ferrites nanoparticles were used, and synthesized via the co-precipitation method, for the removal of arsenic from groundwater in the Bardsir region, Iran. The magnetic adsorbents were characterized by XRD, VSM, BET, FE-SEM, EDS, RAMAN, and FTIR analyses. The effects of pH, adsorbent dosage, contact time, initial arsenic concentration, and temperature on the adsorption process were investigated. MnFe2O4/TiO2/GO and MnFe2O4/TiO2/g-C3N4 were utilized to minimize the concentration of arsenic. The arsenic concentration was reduced from the initial amount of 17.8 mg/l to 197 µg/l and 177 µg/l using MnFe2O4/TiO2/GO and MnFe2O4/TiO2/g-C3N4, which indicates the adsorption capacity of 331 (mg/g) and 332 (mg/g), and the removal efficiency of 98.89% and 99.01%, respectively. Moreover, the adsorption rate for MnFe2O4/TiO2/GO and MnFe2O4/TiO2/g-C3N4 was very fast and occurred in 5 (min) and 15 (min), respectively. The results of kinetics studies were well correlated with the pseudo-second-order model, with the coefficient of determination values of 1 for both adsorbents. These nanoparticles could remove arsenic by following the Freundlich isotherm model. The thermodynamics studies showed that arsenic adsorption was an exothermic and spontaneous process. This article also presents a numerical simulation containing the second-order kinetic expression using COMSOL Multiphysics software. The experimental data and the numerical modeling results were in solid agreement. Furthermore, after five adsorption–desorption cycles, the adsorption capacity of the adsorbents remained constant as in the first cycle. Overall, a simple synthesis method, high adsorption capacity, fast kinetics, easy magnetic separation, and reusability demonstrate that MnFe2O4/TiO2/GO and MnFe2O4/TiO2/g-C3N4 are high-performance adsorbents for arsenic removal from aqueous systems.

Semi-Analytical Large Deformation and Three-Dimensional Stress Analyses of Pressurized Finite-Length Thick-Walled Incompressible Hyperelastic Cylinders and Pipes

This research is devoted to semi-analytical stress and large deformation analyses of finite-length thick-walled incompressible Mooney–Rivlin hyperelastic cylindrical pressure vessels/pipes with fixed ends, employing the three-dimensional theory of hyperelasticity. The formulation accounts for the thickness reduction in both radial and axial directions. The governing system of equations and the boundary conditions are assembled using a large-weights penalty method, after utilizing central, forward, and backward second-order point collocation expressions for the discretization of the thick hollow cylinder in both longitudinal and radial directions. The resulting coupled highly nonlinear two-dimensional equations are solved by the Newton–Raphson iterative updating technique. The results include the radial, axial, and three-dimensional distributions of the deformations and all the stress components. Comprehensive parametric studies are accomplished to evaluate the effects of the hyperelasticity parameters, boundary conditions, and thickness and length-to-radius ratios of the pressure vessel/pipe. Results reveal that the sections located in the vicinity of the fixed edges and the mid-section of the cylinder undergo the highest stresses, at low and high pressures, respectively. Moreover, while the pipe undergoes an overall expansion due to the internal pressure, it experiences a bending moment that induces compressive stresses at the outer boundary, due to the fixed edge. The magnitudes of the radial deformation and the circumferential stress significantly grow by increasing the cylinder length and the nonlinearities in the cylinder responses and behaviors increase by increasing the cylinder length.

Order-by-order anisotropic transport coefficients of a magnetised fluid: a Chapman-Enskog approach

We derive the first and second-order expressions for the shear, the bulk viscosity, and the thermal conductivity of a relativistic hot boson gas in a magnetic field using the relativistic kinetic theory within the Chapman-Enskog method. The order-by-order off-equilibrium distribution function is obtained in terms of the associate Laguerre polynomial with magnetic field-dependent coefficients using the relativistic Boltzmann-Uehling-Uhlenbeck transport equation. The order-by-order anisotropic transport coefficients are evaluated in powers of the dimensionless ratio of kinetic energy to the fluid temperature for finite magnetic fields. In a magnetic field, the shear viscosity (in all order) splits into five different coefficients. Four of them show a magnetic field dependence as seen in a previous study [1] using the relaxation time approximation for the collision kernel. On the other hand, bulk viscosity, which splits into three components (in all order), is independent of the magnetic field. The thermal conductivity shows a similar splitting but is field-dependent. The difference in the first and second-order results are prominent for the thermal conductivities than the shear viscosity; moreover, the difference in the two results is most evident at low temperatures. The first and second-order results seem to converge rapidly for high temperatures.

Magnetic CoFe2O4@carbon yolk-shell nanoparticles as catalysts for the catalytic wet peroxide oxidation of paracetamol: kinetic insights

<p>This work focuses on the use of carbon-coated magnetic cobalt ferrite nanoparticles as catalysts for catalytic wet peroxide oxidation (CWPO) of the emerging concern pollutant paracetamol (PCM). The magnetic core of the catalyst is composed of CoFe2O4 developed by a sol-gel method. The core is subsequently coated with a formaldehyde-resorcinol resin and TEOS, further carbonized at 600 ºC, and etched with NaOH to create a yolk-shell structure denoted as CoFe2O4@void@C. X-ray diffraction (XRD), transmission electron microscopy (TEM), and Fourier transformed infra-red (FTIR) analysis revealed that the uncoated core is composed of a CoFe2O4 cubic spinel structure with a crystallite size of 53 nm calculated using the Williamson-Hall (W-H) method, matching very well the average size observed by TEM (53.51  4.2 nm). Comparing the performances of CoFe2O4@void@C and the bare CoFe2O4 in the CWPO of paracetamol, total organic carbon (TOC) removals of 58% and 46% are obtained respectively after 24 h of reaction. An empirical kinetic model based on second-order and autocatalytic expressions was developed to suitably describe the decomposition of H2O2 and the removal of paracetamol using CoFe2O4@void@C as catalyst. The disappearance of TOC was well-described (r2 = 0.98) by a lumped kinetic model as the sum of TOCA, TOCB and TOCC, where TOCA is the TOC of the PCM, TOCB refers the intermediate products and TOCC is the TOC of the final products obtained during the CWPO of PCM.</p>

Second-order gauge-invariant formalism for the cosmological observables: complete verification of their gauge-invariance

Accounting for all the relativistic effects, we have developed the fully nonlinear gauge-invariant formalism for describing the cosmological observables and presented the second-order perturbative expressions associated with light propagation and observations without choosing a gauge condition. For the first time, we have performed a complete verification of the validity of our second-order expressions by comparing their gauge-transformation properties from two independent methods: one directly obtained from their expressions in terms of metric perturbations and the other expected from their nonlinear relations. The expressions for the cosmological observables such as galaxy clustering and the luminosity distance are invariant under diffeomorphism and gauge-invariant at the observed position. We compare our results to the previous work and discuss the differences in the perturbative expressions. Our second-order gauge-invariant formalism constitutes a major step forward in the era of precision cosmology and its applications in the future will play a crucial role for going beyond the power spectrum and probing the early universe.

Second-order approximate expressions of P- and SV-plane-wave reflection coefficients at the solid/solid media interface

To completely use large incident angle seismic data and improve the accuracy of amplitude-variation-with-offset inversion, especially for density information, we have derived second-order approximate expressions of the P- and SV-wave reflection coefficients at the solid/solid media interface. Vectors and Hessian matrices are used to describe the first- and second-order terms of the approximate expressions. The second-order approximations are then rewritten in a simple form. Furthermore, different pseudosecond-order approximations with different power series of the ray parameter p are derived based on the Taylor expansion of the second-order approximation of the P-wave reflection coefficient for the incident P wave (PP-wave reflection coefficient) according to the ray parameter p. By establishing four different single-phase medium models, we have verified that the accuracies of the second-order approximate expressions were remarkably higher than those of the first-order approximations. Furthermore, the pseudo p2 second-order approximation of the PP-wave reflection coefficient is highly consistent with the exact analytical expression.

Linear mode analysis from spin transport equation

We provide a linear analysis on normal modes of the spin Boltzmann equation proposed by Weickgenannt et al. [Phys. Rev. D 104, 016022 (2021)], where the nondiagonal or polarized part of the transition rate is neglected to ensure the Hermitian property of a linearized collision operator. As an instrumental element of spin kinetic theory, the conservation of total angular momentum is explicitly considered; thus, our analysis is relevant to the recent investigation on the issue of local spin polarization. By treating the linearized collision operator as an evolution operator, solving the normal modes turns out to be a degenerate perturbation problem in quantum mechanics. The dispersion relations of spinless modes are in accordance with well-known calculations, while the frequencies of spin modes are also determined up to second-order in wave vectors; the second-order expressions are only formal solutions to be further determined. Moreover, the relaxation of spin density is related to our linear mode analysis, which shall play a big role in investigating the issues of the local spin polarization in the relativistic heavy-ion collisions.

Modelling of “Water-in-glass” Solar Water Heaters Installation

As part of the ICaRE4Farms European project, a model of a solar water heater installation has been developed. This model is intended to estimate thermal performance of a specific arrangement of several “Water-in-Glass” solar collectors. In this solar field, the WiG collectors are arranged either in serial or in parallel, thus requiring the creation of two models. In this paper, the serial Evacuated Tubes collector’s model is presented. The operational efficiency of a single in-series solar collector is expressed through a second-order expression in accordance with the ISO 9806-1. Its coefficients have been determined thanks to an optimization tool in order to compute thermal performance with reliability. In-situ data from a working installation were compared to simulated values. Two experimental sequences are presented: in May and in September 2021. Results showed that the model is reliable in terms of both collectors’ temperature and energy balance.

A general justification for hybrid functionals in DFT by means of linear response theory* *To the memory of Enrico Clementi, an outstanding human being; in recognition of his pioneering work in quantum chemistry and in tribute to his leadership and long-lasting accomplishments.

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn–Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy’s constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

Performance Analysis of RIS-Assisted FSO Communications over Fisher–Snedecor F Turbulence Channels

The Fisher–Snedecor (F-S) F distribution has recently been introduced as a tractable turbulence-induced (TI) fading model that fits well with the experimental data. This paper provides a performance evaluation of a free-space optical (FSO) re-configurable intelligent surface (RIS)-assisted communications (ACs) link over the F-S F TI fading channels, assuming the intensity modulation–direct detection (IM–DD) technique. In particular, novel and closed-form (C-F) analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio (SNR) in terms of Gaussian hyper-geometric functions are efficiently derived. Capitalizing on the obtained results, novel C-F analytical expressions for the moment generating function (MMGF), outage probability (OP), average bit error rate (BER) and ergodic channel capacity (Cγ) of the FSO RIS-ACs system over the F-S F TI fading channels are provided and numerically evaluated under the various TI fading severity conditions. Furthermore, the second-order (S-O) statistical expressions for the level crossing rate (LCR) and average fade duration (AFD) are obtained and thoroughly examined for various FSO RIS-ACs system model parameters.

Mechanical properties of tissue-mimicking composites formed by material jetting additive manufacturing

Capitalizing on features including high resolution, smooth surface finish, large build volume, and simultaneous multi-color/multi-material printing, material jetting additive manufacturing enables the fabrication of full-scale anatomic models. The ability to print materials that resemble relevant, compliant tissues has especially motivated implementation of material jetting for patient-specific surgical planning or training models. In an effort to broaden the material selection for the material jetting process, and to provide materials that more closely mimic the functional needs for a wider variety of tissues, a composite material system is explored that uses non-curing fluid dispersed into a photo-curable medium. The material properties of the composites are examined through both thermal and mechanical analysis (dynamic mechanical analysis, Shore hardness testing, puncture testing, and tensile testing).Higher contributions of non-curing fluid generally reduce part strength and stiffness, and exponential and second-order polynomial expressions are appropriate fits for many of the mechanical properties as functions of non-curing fluid concentration. Through the fundamental exploration of the impact of an added diluent on material properties, the study advances knowledge on the process-property relationship for multi-material jetting. Additionally, better understanding of the mechanical property space offered by these materials will expand the capabilities of material jetting in the context of biomedical applications. The collection of mechanical properties serve as reference data sets to facilitate quicker screening for tissue-mimicking, medical models.