Linear Summation Research Articles

Experimental and Theoretical Study of Coating Spalling under High-Cycle Fractional Loading

An experimental and theoretical study of contact fatigue damage accumulation at the coating-substrate interface has been carried out for the case of frictional contact between a smooth coating and a rough counterbody. Coatings were synthesized via low-temperature thermal decomposition of metal (Al, Zr) carboxylate solutions, which resulted in the formation of nanoscale amorphous nanocrystalline oxide layers 20–400 nm thick (depending on the concentration of the film-forming solution and the number of loading cycles) on the substrate surface (quartz glass). The investigation included coating deposition, determination of coating mechanical properties by indentation, development of the friction test procedure, stress calculation at the coating-substrate interface by modeling high-cyclic frictional loading, and the choice of a damage accumulation model for the coating-substrate interface that relates the stress state to the number of cycles to coating spalling. Preliminary tests revealed the coating compositions and coating deposition techniques that provide the highest spalling resistance under cyclic contact loading. Parameters in the relation for contact fatigue damage accumulation were determined and the model was verified by analyzing the experimental load dependence of the number of cycles to coating spalling on the microscale. It has been shown that the linear damage summation model conventionally used for describing failure due to fatigue damage accumulation in some materials can be applied to investigate the coating-substrate interface whose properties depend not only on the properties of the interfacing materials but also on the coating deposition technique.

Standardization of the Evaluation Index System for Low-Carbon Cities in China: A Case Study of Xiamen

The construction of a reasonable evaluation index system for low-carbon cities is an important part of China’s green development strategy in urban areas. In this study, based on the theoretical framework for the concept of low-carbon cities, the perspectives from three index systems—that is, the Drivers, Pressures, State, Impact, Response model of intervention (DPSIR), a complex ecosystem, and a carbon source/sink process—were integrated to extract common indicators from existing evaluation index systems for low-carbon cities. Subsequently, a standardized evaluation index system for low-carbon cities that contained five indicators—carbon emission, low carbon production, low carbon consumption, low-carbon policy, and social economic development—was established. Thereafter, Xiamen was selected for an empirical analysis by determining the indicator weight with an entropy weight method and by carrying out a comprehensive evaluation using a linear summation model. The results showed that the weights of the five selected primary indicators for the evaluation of low-carbon cities were: low-carbon production > low-carbon consumption > social economic development > carbon emission > low-carbon policy. Among the secondary indicators, the average entropy weight of “pollution emission” was the highest at 0.1591, while the average entropy weight of “urbanization rate” was the lowest at 0.0360. Furthermore, the comprehensive index of low-carbon development in 2015 was higher than that in 2010, while the rate of economic growth was greater than the growth rate of carbon emission, which indicated that the relative decoupling of economic growth from carbon emission was basically achieved.

Spectroscopic ellipsometry investigations of Cd-Se thin film electrochemically prepared

Binary Cadmium selenium (Cd-Se) thin film deposited onto glass substrate coated by indium tin oxide (ITO) using electrodeposition method at room temperature. Structural, morphological and optical properties has been investigated by X-ray diffraction (XRD), scanning electron microscope (SEM) and variable angle spectroscopic ellipsometry (VESA). XRD pattern shows that the nature film is polycrystalline where both (hexagonal) Se and (hexagonal) CdSe crystalline phases coexist. Based on the (SEM) images, it was found that micro-structures consist of dense layers or agglomerates suggesting an acceptable adhesion between ITO layers and Cd-Se films. VESA measurements on the Cd-Se are presented in the energy range of 1.–5 eV with different incident angles and at room temperature. The experimental data of SE were fit using a linear summation from Gaussian and Tauc-Lorentz oscillator functions. Each function was employed to fit a range of absorption spectrum from ultraviolet, visible and infrared regions. Optical constants such as pseudo refractive index, pseudo extinction coefficient, real and imaginary parts of the pseudo dielectric function were determined. The optical energy band gap (Eg) of prepared film is 2.16 and 1.14 eV for the direct allowed and indirect allowed transitions, respectively.

Influence of simultaneous variations in operating parameters on burnup credit criticality analysis for PWR spent fuel assemblies

Abstract This study attempted to thoroughly investigate the impact of single and compound effects on burnup credit calculations for PWR spent fuel assemblies originating from various operating parameters. Three operating parameters were considered, including fuel temperature, boron concentration, and axial burnup profile. The single and compound effects defined in this study represent the influence caused by simultaneous variations of one and multiple operating parameters on the curve of effective multiplication factor ( k eff ) versus burnup ( B ), respectively. All the calculations were performed using SCALE 6.1 computer code together with the ENDF/B-VII 238-group data library. In addition, two geometrical models were established based on the Westinghouse 17 × 17 PWR optimized fuel assembly and GBC-32 storage cask. The results revealed that an increase of fuel temperature or boron concentration induces a positive reactivity deviation (or the change of k eff , Δ k ), the opposite is also true when a decrease of fuel temperature or boron concentration is considered. Moreover, the utilization of non-uniform axial burnup profile leads to a positive Δ k . Additionally, in most of the compound effects, Δ k resulting from the compound effects was not a linear summation of the Δ k ’s resulting from the associated single effects. In particular, such Δ k discrepancy increases as B increases, which could influence the precise assessment of burnup credit to some extent. The mechanisms of both the single and compound effects were studied by the analysis of the spectral distribution of fission. From this analysis, an increase of either fuel temperature or boron concentration leads to a harder neutron spectrum, while a non-uniform axial burnup profile leads to a softer one.

Methods of approximation theory in research of harmonic analysis and wavelets

In this paper, we give a brief introduction about applications of approxiamtion theory of functions in harmonic analysis and wavelet research.We start from Korovkins theorem to introduce applications of test functions in wavelet research. Then we present boundedness of singular integrals by using Jackson approximation.In addition, applications of regular linear summation and approximation in edge detection and inverse Fourier transform are stated. We also introduce some new results in signal reconstruction by sparse data.

Optical Communication Using Linear Sums of Optical Receiver Modes: Proof of Concept

We demonstrate the feasibility of an optical communication system that transmits linear sums of optical receiver modes (ORMs) as optical signals called ORM signals. The ORMs are inherent modes of conventional direct-detection optical receivers for wavelength-division multiplexing systems. Two lowest order ORMs are used to build ORM signals having distinct received voltage waveforms from each other. The optical receiver used has a Fabry–Perot filter as its optical filter and a fourth-order Bessel filter as its electrical filter. With these filters, corresponding ORMs are evaluated numerically and the ORM signals are generated using digital-to-analog converters. The received voltage waveforms after the receiver electrical filter are in good agreement with our analysis.

Contribution of the Kinetics of Inelastic Deformations to the Summation of Fatigue Damage to Steels

We propose a method for the evaluation of the accumulation of fatigue defects and variations of inelastic strains under cyclic loading with variable stress amplitudes. This method is based on the earlier developed model of ultimate exhaustion of cyclic plasticity. It is shown that, for materials with unstable inelastic deformations under cyclic loading, the fatigue damage does not obey the law of linear summation. We discovered a difference between the accumulation of fatigue defects in cyclically hardened and softened materials. This difference and nonlinearity are caused by the kinetics of inelastic deformations in different groups of materials. Hence, it is proposed to take this fact into account in estimating the degree of fatigue damage in order to decrease the computation error. In addition, we propose a scheme for the improvement of the results of evaluation of the total fatigue life under irregular loading by using the individual fatigue curves for the specimens with an aim of minimization of errors caused by the spread of experimental results.

Micropools of reliable area MT neurons explain rapid motion detection

Many models of perceptually based decisions postulate that actions are initiated when accumulated sensory signals reach a threshold level of activity. These models have received considerable neurophysiological support from recordings of individual neurons while animals are engaged in motion discrimination tasks. These experiments have found that the activity of neurons in a particular visual area strongly associated with motion processing (MT), when pooled over hundreds of milliseconds, is sufficient to explain behavioral timing and performance. However, this level of pooling may be problematic for urgent perceptual decisions in which rapid detection dictates temporally precise integration. In this paper, we explore the physiological basis of one such task in which macaques detected brief (~70 ms) transients of coherent motion within ~240 ms. We find that a simple linear summation model based on realistic stimulus responses of as few as 40 correlated neurons can predict the reliability and timing of rapid motion detection. The model naturally reproduces a distinctive physiological relationship observed in rapid detection tasks in which the individual neurons with the most reliable stimulus responses are also the most predictive of impending behavioral choices. Remarkably, we observed this relationship across our simulated neuronal populations even when all neurons within the pool were weighted equally with respect to readout. These results demonstrate that small numbers of reliable sensory neurons can dominate perceptual judgments without any explicit reliability based weighting and are sufficient to explain the accuracy, latency, and temporal precision of rapid detection. NEW & NOTEWORTHY Computational and psychophysical models suggest that performance in many perceptual tasks may be based on the preferential sampling of reliable neurons. Recent studies of MT neurons during rapid motion detection, in which only those neurons with the most reliable sensory responses were strongly predictive of the animals' decisions, seemingly support this notion. Here we show that a simple threshold model without explicit reliability biases can explain both the behavioral accuracy and precision of these detections and the distribution of sensory- and choice-related signals across neurons.

Linear Summation Underlies Direction Selectivity in Drosophila

While linear mechanisms lay the foundations of feature selectivity in many brain areas, direction selectivity in the elementary motion detector (EMD) of the fly has become a paradigm of nonlinear neuronal computation. We have bridged this divide by demonstrating that linear spatial summation cangenerate direction selectivity in the fruit fly Drosophila. Using linear systems analysis and two-photon imaging of a genetically encoded voltage indicator, we measure the emergence of direction-selective (DS) voltage signals in the Drosophila OFF pathway. Our study is a direct, quantitative investigation of the algorithm underlying directional signals, with the striking finding that linear spatial summation is sufficient for the emergence of direction selectivity. A linear stage of the fly EMD strongly resembles similar computations in vertebrate visual cortex, demands a reappraisal of the role of upstream nonlinearities, and implicates the voltage-to-calcium transformation in the refinement of feature selectivity in this system. VIDEO ABSTRACT.

Simulation of the Propagation of Circumferential Crack in the Cylindrical Element Structure Exposed to Cyclic Loadings

The purpose of these studies was to work out the methods for the computation of crack development in the plate and axisymmetric elements of structures at cyclic loading for the plasto-elastic arrangement using the conception of the accumulation of scattered damages in the material. In the domain in question, we simulated the processes of alternating-sign plasto-elastic deformation and the material crack resistance was estimated using the fatigue test data for smooth specimens. Thermal and elastically-deformed states of the structure were determined for different loading modes using the finite elements method. The material damageability was assessed for the curves of low-cycle fatigue and for the range of plasto-elastic deformations on the route of probable crack propagation using the hypothesis of linear summation. As soon as a critical value of the damageability is achieved the crack is propagated stepwise for the specified step. As an example, consideration was given to the kinetics of circumferential crack in the cylindrical element exposed to the axial-symmetric cyclic loading. The contact of crack edges was taken into consideration for compressing loading semicycles. The obtained data agree with the data obtained using the Newman method. The suggested technique can be used for the estimation of survivability of the elements of steam turbines (heat rotor grooves at start-up-stop modes, blade and disk interlocks, etc.).

Some evaluation of cubic Euler sums

P. Flajolet and B. Salvy [15] prove the famous theorem that a nonlinear Euler sum Si1i2⋯ir,q reduces to a combination of sums of lower orders whenever the weight i1+i2+⋯+ir+q and the order r are of the same parity. In this article, we develop an approach to evaluate the cubic sums S12m,p and S1l1l2,l3. By using the approach, we establish some relations involving cubic, quadratic and linear Euler sums. Specially, we prove the cubic sums S12m,m and S1(2l+1)2,2l+1 are reducible to zeta values, quadratic and linear sums. Moreover, we prove that the two combined sums involving multiple zeta values of depth four∑{i,j}∈{1,2},i≠jζ(mi,mj,1,1)and∑{i,j,k}∈{1,2,3},i≠j≠kζ(mi,mj,mk,1) can be expressed in terms of multiple zeta values of depth ≤3, here 2≤m1,m2,m3∈N. Finally, we evaluate the alternating cubic Euler sums S1¯3,2r+1 and show that it are reducible to alternating quadratic and linear Euler sums. The approach is based on Tornheim type series computations.

Cyclic viscoplastic analysis for steam generator material of Indian fast breeder reactor

AbstractCreep‐fatigue interaction behavior of grade 91 steel at 823 K has been studied. Creep component has been introduced with hold times 1, 10, and 30 minutes in tension and compression in continuous strain cycling. Fatigue life reduced due to application of hold and reduction was found to be more in compressive hold. The effect of various factors such as mean stress, stress relaxation, oxidation, microstructure, and inelastic strain accumulation on significant reduction in fatigue life in compression hold has been investigated. The oxidation has been observed as the key parameter that caused significant fatigue life reduction in compressive hold as compared with tensile hold. Chaboche unified viscoplasticity model has been used to understand the material's cyclic elasto‐viscoplastic behavior. The simulation results were in agreement with the experimental results. Fatigue lives under creep‐fatigue condition were estimated using frequency‐modified strain energy damage function method and linear damage summation method. Frequency‐modified strain energy damage function method under estimated the fatigue lives whereas linear damage summation method overestimated the lives.

Studies on creep-fatigue interaction behaviour of Alloy 617M

In this investigation, response of Alloy 617 M to creep-fatigue interaction loading has been studied. The creep-fatigue interaction tests were conducted in air environment at a constant strain rate of 3 × 10−3 s−1 and strain amplitude of ± 0.4% with hold periods of 1 min, 10 min and 30 min at peak tension or compression at 973 K. The material showed initial hardening to a saturation followed by reduction in stress initiated by crack nucleation, propagation and final failure. The fatigue life decreased in presence of hold period. The decrease in fatigue life was more in tensile hold than in compressive hold. The fatigue life showed saturating trend for higher hold periods. Fractographic studies revealed significant intergranular creep cavitation under tensile hold whereas compressive hold exhibited transgranular fatigue striations in association with intergranular creep cavitation. Significant stress relaxation was found to take place during hold and was more in compressive hold than under tensile hold. The creep and fatigue damage have been assessed based on linear damage summation rule. Creep damage fraction was assessed from the stress relaxation considering the average stress, minimum stress and integrated stress over the relaxation curve. The creep-fatigue damage assessment considering integration of creep damage during stress relaxation showed most conservative compared to the other two approaches.

High temperature fatigue and creep-fatigue behaviors in a Ni-based superalloy: Damage mechanisms and life assessment

The low cycle fatigue (LCF) and creep-fatigue behaviors of Ni-based GH4169 superalloy are investigated by uniaxial strain-controlled fully-reversed testing at 650 °C. Compared with LCF tests, the effects of tensile and compressive strain hold times on creep-fatigue lifetimes are experimentally explored with varying total strain ranges in the present work. In order to elucidate the damage mechanisms under complex loading waveforms, an additional series of tests with both tensile and compressive hold times are carried out at a given total strain range of 2.0%. Posterior to the cyclic tests, main-crack-failure modes and secondary cracking modes are studied via optical microscopy (OM), scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) techniques. Main-crack failure mechanisms are examined by the fracture appearance observations. Cracking modes are explored through quantitative characterization on the distributions of secondary cracks in the longitudinal cross sections under different loading waveforms. Moreover, a generalized life model based on linear damage summation (LDS) framework and energy dissipation criterion (EDC) is elaborated to estimate the damage mechanisms of fatigue, creep and oxidation. The prediction results can well establish the correlations between the reductions of numbers of cycles to failure and the presences of different damage mechanisms under respective loading waveforms.

Creep-Fatigue Behaviors and Life Assessments in Two Nickel-Based Superalloys

The aim of this paper is to investigate different factors, including dwell time, strain range, and strain ratio on creep-fatigue endurances in nickel-based Inconel 718 and GH4169 superalloys. We also summarize classic approaches for life assessments based on the generalizations of Coffin–Manson equation, linear damage summation (LDS), and strain-range partitioning (SRP) method. Each approach does have some degree of success in dealing with a specific set of creep–fatigue data. In order to evaluate the prediction capabilities of the validated approaches, a Bayesian information criterion (BIC) allowing for maximum likelihood and principle of parsimony is used to select the best performing model.

Activity-dependent synaptic integration and modulation of bilateral excitatory inputs in an auditory coincidence detection circuit.

Binaural excitatory inputs to coincidence detection neurons in nucleus laminaris (NL) play essential roles in interaural time difference coding for sound localization. Here, we show that the two excitatory inputs are physiologically nearly completely segregated. Synaptic integration shows linear summation of EPSPs, ensuring high efficiency of coincidence detection of the bilateral excitatory inputs. We further show that the two excitatory inputs to single NL neurons are symmetrical in synaptic strength, kinetics and short-term plasticity. Modulation of the EPSCs by metabotropic glutamate receptors (mGluRs) is identical between the two excitatory inputs, maintaining balanced bilateral excitation under neuromodulatory conditions. Unilateral hearing deprivation reduces synaptic excitation and paradoxically strengthens mGluR modulation of EPSCs, suggesting activity-dependent anti-homeostatic regulation, a novel synaptic plasticity in response to sensory manipulations. Neurons in the avian nucleus laminaris (NL) receive bilateral excitatory inputs from the cochlear nucleus magnocellularis, via morphologically symmetrical dorsal (ipsilateral) and ventral (contralateral) dendrites. Using in vitro whole-cell patch recordings in chicken brainstem slices, we investigated synaptic integration and modulation of the bilateral inputs to NL under normal and hearing deprivation conditions. We found that the two excitatory inputs onto single NL neurons were nearly completely segregated, and integration of the two inputs was linear for EPSPs. The two inputs had similar synaptic strength, kinetics and short-term plasticity. EPSCs in low but not middle and high frequency neurons were suppressed by activation of group I and II metabotropic glutamate receptors (mGluR I and II), with similar modulatory strength between the ipsilateral and contralateral inputs. Unilateral hearing deprivation by cochlea removal reduced the excitatory transmission on the deprived dendritic domain of NL. Interestingly, EPSCs evoked at the deprived domain were modulated more strongly by mGluR II than at the counterpart domain that received intact input in low frequency neurons, suggesting anti-homeostatic regulation. This was supported by a stronger expression of mGluR II protein on the deprived neuropils of NL. Under mGluR II modulation, EPSCs on the deprived input show transient synaptic facilitation, forming a striking contrast with normal hearing conditions under which pure synaptic depression is observed. These results demonstrate physiological symmetry and thus balanced bilateral excitatory inputs to NL neurons. The activity-dependent anti-homeostatic plasticity of mGluR modulation constitutes a novel mechanism regulating synaptic transmission in response to sensory input manipulations.

Linear combinations of primitive elements of a finite field

We examine linear sums of primitive roots and their inverses in finite fields. In particular, we refine a result by Li and Han, and show that every p>13 has a pair of primitive roots a and b such that a+b and a−1+b−1 are also primitive roots mod p.

ИНЖЕНЕРНЫЕ МЕТОДЫ ПРОГНОЗИРОВАНИЯ ОСТАТОЧНОГО РЕСУРСА ОБОРУДОВАНИЯ

One of the most important indicators of reliability of technical objects is their durability. Probabilistic and statistical methods used for group assessment of service life of marine equipment at the stage of its design are unsuitable for individual assessment of a residual resource during operation due to the great values of coefficients of the resource variation and significant discrepancies between the proposed and actual operation models. Improving the reliability of estimates can be achieved by controlling the actual operation and monitoring of diagnostic parameters which characterize degradation of the actual technical state of equipment. The article considers on specific examples the features of predictive extrapolation of time-series observations over diagnostic parameter and application of forecasting method based on the actual history of operational loadings. It is stated that the extrapolation method, in spite of such advantages as using a minimum number of controlled parameters and versatility, has a number of shortcomings that reduce its effectiveness in the evaluation of residual resource of multi-mode objects. To extend the use of extrapolative forecasting there have been proposed special methods of adjusting time series using the Euler method, linear and nonlinear regression models and the estimation approach of residual resource, which provides a preliminary study of physico-chemical deterioration of technical condition of equipment and subsequent measurement of the equivalent hours of the resource using results of the check operation and the hypotheses of linear summation of damage.

High-Temperature Creep-Fatigue Behavior of Alloy 617

This paper presents the high-temperature creep-fatigue testing of a Ni-based superalloy of Alloy 617 base metal and weldments at 900 °C. Creep-fatigue tests were conducted with fully reversed axial strain control at a total strain range of 0.6%, 1.2%, and 1.5%, and peak tensile hold time of 60, 180, and 300 s. The effects of different constituents on the combined creep-fatigue endurance such as hold time, strain range, and stress relaxation behavior are discussed. Under all creep-fatigue tests, weldments’ creep-fatigue life was less than base metal. In comparison with the low-cycle fatigue condition, the introduction of hold time decreased the cycle number of both base metal and weldments. Creep-fatigue lifetime in the base metal was continually decreased by increasing the tension hold time, except for weldments under longer hold time (>180 s). In all creep-fatigue tests, intergranular brittle cracks near the crack tip and thick oxide scales at the surface were formed, which were linked to the mixed-mode creep and fatigue cracks. Creep-fatigue interaction in the damage-diagram (D-Diagram) (i.e., linear damage summation) was evaluated from the experimental results. The linear damage summation was found to be suitable for the current limited test conditions, and one can enclose all the data points within the proposed scatter band.

Linearization of excitatory synaptic integration at no extra cost.

In many theories of neural computation, linearly summed synaptic activation is a pervasive assumption for the computations performed by individual neurons. Indeed, for certain nominally optimal models, linear summation is required. However, the biophysical mechanisms needed to produce linear summation may add to the energy-cost of neural processing. Thus, the benefits provided by linear summation may be outweighed by the energy-costs. Using voltage-gated conductances in a relatively simple neuron model, this paper quantifies the cost of linearizing dendritically localized synaptic activation. Different combinations of voltage-gated conductances were examined, and many are found to produce linearization; here, four of these models are presented. Comparing the energy-costs to a purely passive model, reveals minimal or even no additional costs in some cases.