Additive Scheme Research Articles

Factorized Schemes for First and Second Order Evolution Equations with Fractional Powers of Operators

Abstract Many non-local processes are modeled using mathematical models that include fractional powers of elliptic operators. The approximate solution of stationary problems with fractional powers of operators is most often based on rational approximations introduced in various versions for a fractional power of the self-adjoint positive operator. The purpose of this work is to use such approximations for the approximate solution of nonstationary problems. We consider Cauchy problems for the first and second order differential-operator equations in finite-dimensional Hilbert spaces. Estimates for the proximity of an approximate solution to an exact one are obtained when specifying the absolute and relative errors of the approximation of the fractional power of the operator. We construct splitting schemes based on the additive representation with a rational approximation of the operator’s fractional power. The stability and accuracy of factorized two-level additive operator-difference schemes for the first order evolution equation and three-level schemes for a second order equation are established.

Multi-Stages Iterative Process for Conservative Economic Finite-Difference Schemes Realization for the Problem of Nonlinear Laser Pulse Interaction with a Medium

We consider a problem of laser pulse interaction with a nonlinear medium which is accompanied by different nonlinear phenomena. Among them, we highlight the laser pulse self-action, optical bistability realization, formation of laser-induced complicated spatio-temporal structures. For computer modeling of these strongly nonlinear effects, using robust conservative numerical methods is required. Well-known, there are two widely applied approaches for the construction of numerical method: the conservative finite-difference schemes and additive finite-difference schemes (the split-step methods or decomposition methods). The first ones are non-economic, as a rule, while the second type of the methods is economic ones, however they possess well-known disadvantages. In our study, we joint advantages of both approaches by developing an original multi-stage iterative process for the conservative finite-difference scheme realization. Using computer simulation results, we demonstrate the feasibility of the proposed approach for investigating certain nonlinear optical phenomena.

HTPB Heat of Formation: Literature Survey, Group Additive Estimations, and Theoretical Effects

Hydroxyl-terminated polybutadiene (HTPB) is a common ingredient in rocket propellants, but its thermochemical properties (composition, density, and heat of formation) are not well defined. A survey of the literature and thermochemical databases indicated wide ranges for these properties, especially heat of formation. Six group additive schemes were used to estimate the heat of formation of HTPB and analyze the effects of hydroxyl functionalization and curing reactions. Good agreement is observed between the methods for HTPB isomer units, but cumulative differences result in significant disparities for larger, practical polymers. Increased hydroxyl functionality and the curing reaction are predicted to yield nonnegligible decreases in the heat of formation. The heat of formation of propellant-grade, isophorone-diisocayante-cured HTPB R-45M () was computed as or . Chemical equilibrium analyses were completed for solid propellants composed of ammonium perchlorate and HTPB, and for hybrid rocket engines based on HTPB burning with liquid oxygen or nitrous oxide, where the heat of formation of HTPB was varied within a reasonable range. The chemical equilibrium analysis computations indicated that combustion gas properties and theoretical propellant performance can vary up to 5% within practical operating conditions for the range of HTPB heats of formation implemented.

Integrating remote sensing data in optimization of a national water resources model to improve the spatial pattern performance of evapotranspiration

Hydrological models have traditionally been calibrated and evaluated against point-scale observations, such as streamflow, emphasizing the temporal, but not necessarily the spatial component of a model. The main goal of this study is to improve the spatial pattern performance of simulated actual evapotranspiration (AET), a key variable in the land–atmosphere interface, for the entire land-phase of Denmark. This is achieved by integrating fully distributed remote-sensing (RS) data and robust objective functions in the regionalization and optimization of the national water resources model of Denmark (DK-model). For this, monthly spatial patterns of MODIS16 ET at 1 km resolution are used as a reference RS ET estimate in the model calibration. We applied a gradient-based nonlinear Gauss-Marquardt-Levenberg (GML) algorithm for parameter estimation via inverse modeling. The proposed optimization framework includes three calibration strategies: Cal01 represents the traditional calibration approach against discharge and groundwater head observations only, Cal02 expands Cal01 by means of a spatial pattern-oriented objective function, namely the spatial efficiency (SPAEF) metric, targeting ET pattern performance, Cal03 adds to Cal02 an additional parameter regionalization scheme, where the original fixed land use class dependent distribution and seasonal development of leaf area index (LAI), crop coefficient (Kc) and root depth (RD) are replaced with empirical schemes driven by distributed vegetation (NDVI) and soil texture (clay fraction) data. Our results reveal that a significant improvement in the simulated spatial patterns of AET is obtained when combining regionalization schemes and a spatial pattern oriented objective function in Cal03, which is highlighted by a Copula analysis also. At the same time, a very limited trade-off in the model performance of AET patterns, streamflow and groundwater-heads is observed. Finally, the regionalization scheme (Cal03) affected the simulated groundwater recharge according to changes of AET. The findings of this study contribute to further improve spatial representation and evaluation of hydrological models and highlight the need to carefully design regionalization schemes as well as objective functions in fully distributed models.

Theoretical substantiation of new features of rolling bearings operation under combined loading conditions

Rolling bearings are widely used in the products of aviation and space technology. To ensure their long-term trouble-free operation, it is necessary to have accurate and reliable information about the forces acting on the bearings. The required values of forces and, accordingly, the required durability of bearings are usually determined on the basis of the traditional design scheme of a double-support beam (smooth beam mounted on two hinged supports). The paper presents a new interpretation of the features of the operation of bearing units on ball radial single-row bearings installed according to the cross located arrangement. It is shown that under conditions of combined loading, including radial and axial forces, the generally accepted theoretical model of a doublesupport beam is not implemented. There is no single calculation model that adequately reflects the nature of the interaction of bearing parts over the entire range of external loads. In the most general case, this model can be represented by a sequence of five statically indeterminate calculation schemes, which are modified and transformed into one another. So, with an increase in the external radial force, the cantilevered beam with additional hinge support scheme is first implemented, which, then, is transformed into the double-sided jamming scheme, and that, later, is transformed into the two double hinge supports scheme. It is also possible to implement two intermediate transition schemes. A specific example shows that in the products of aviation and space technology, determining the durability of bearings based on the traditional model is not advisable, since it can give an overestimated value with an error of 28,37 to 26663,9 times.

Preliminary Study on Additive Manufacturing Scheme of Hydraulic Manifold Block rapid-solidifying SLM Forming

[Purpose/significance] In traditional manufacturing process, hydraulic manifold blocks are drilled into blank to form their complex flow channel structure This processing technology is complicated and the efficiency is low. Selective laser melting (Selective laser melting, SLM) is a kind of additive manufacturing technology. Compared with traditional processing technology, it is not sensitive to the complexity of the processed parts. It is especially suitable for machining parts with complex internal structure such as hydraulic manifold blocks. [Method/Process] Therefore, this article proposes an additive manufacturing scheme for rapid-solidifying SLM forming of hydraulic manifold block, introduces the materials required for SLM forming, the method of rapid-solidifying SLM forming, and analyzes the application effect of the new scheme in the additive manufacturing of hydraulic manifold block. [Result/Conclusion] The results show that the rapid-solidifying SLM is insensitive to the internal pore structure of the integrated block, and can accurately design and optimize the complex porous structure of the integrated block. Compared with other additive manufacturing technologies, the forming accuracy is higher. The microstructure and comprehensive mechanical properties of the post integrated block are better, and it has a very broad development prospect.

Energy intensity of hydrocarbons in liquid and solid states

Objectives. The increased use of unmanned aerial vehicles necessitates the search for jet fuels based on hydrocarbon materials with high energy intensity and physical density. The purpose of the work was to analyze the influence of various factors on the mass energy intensity of hydrocarbons. This analysis is required to substantiate the algorithm for locating energy-intensive CnHm structures.Methods. Combustion energy was calculated using additive procedures. The calculations were performed using Microsoft Excel.Results. During the analysis of the mass energy intensity of CnHm hydrocarbons, the m/n ratio was discovered to be the decisive factor for achieving high values of the mass energy intensity of hydrocarbons. The energy intensity decreases when moving from alicyclic to cyclic hydrocarbons, and this decrease is not compensated by the production of strain energy. An additive scheme that allows the molar volume of hydrocarbons to be predicted with sufficient accuracy is proposed for calculating the volumetric enthalpies of combustion.Conclusions. According to the thermodynamic analysis, n-alkanes have the highest mass energy intensities. The technology for extracting n-alkanes from oil fractions is well developed, and a decrease in the hydrogen content in the fuel results in a decrease in the mass energy intensity. It appears improbable that the mass and volumetric energy intensities of hydrocarbons seem will reach their maximum values simultaneously. Hydrocarbons that have a high m/n value, 2, 3, 4, 5, 6-membered rings, and phenyl fragments may have relatively high mass and volumetric energy intensities at the same time.

Z-DNA as a Touchstone for Additive Empirical Force Fields and a Refinement of the Alpha/Gamma DNA Torsions for AMBER.

Although current AMBER force fields are relatively accurate for canonical B-DNA, many noncanonical structures are still described incorrectly. As noncanonical motifs are attracting increasing attention due to the role they play in living organisms, further improvement is desirable. Here, we have chosen the Z-DNA molecule, which can be considered a touchstone of the universality of empirical force fields, since the noncanonical α and γ backbone conformations native to Z-DNA are also found in protein-DNA complexes, i-motif DNA, and other noncanonical DNAs. We show that spurious α/γ conformations occurring in simulations with current AMBER force fields, OL15 and bsc1, are largely due to inaccurate α/γ parametrization. Moreover, stabilization of native Z-DNA substates involving γ = trans conformations appears to be in conflict with the correct description of the canonical B-DNA structure. Because the balance of the native and spurious conformations is influenced by nonadditive effects, this is a difficult case for an additive dihedral energy scheme such as AMBER. We propose new α/γ parameters, denoted OL21, and show that they improve the stability of native α/γ Z-DNA substates while keeping the canonical DNA description virtually unchanged, thus representing a reasonable compromise within the additive force field framework. Although further extensive testing is needed, the new modification appears to be a promising step toward a more reliable description of noncanonical DNA motifs and provides the best performance for Z-DNA molecules among current AMBER force fields.

Improvement of copper sulfide flotation using a new collector in an optimized addition scheme

Improvement of copper sulfide flotation using a new collector in an optimized addition scheme

Applications of optimal nonlinear control to a whole-brain network of FitzHugh-Nagumo oscillators.

We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the internode coupling strengths are derived from diffusion tensor imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially nonsparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the network's state-space decomposes into regions of low- and high-activity fixed points separated by a high-amplitude limit cycle, all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states, and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the system's location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for noninvasive brain stimulation.

Order of torsion for reduction of linearly independent points for a family of Drinfeld modules

Let q be a power of the prime number p, let K=Fq(t), and let r⩾2 be an integer. For points a,b∈K which are Fq-linearly independent, we show that there exist positive constants N0 and c0 such that for each integer ℓ⩾N0 and for each generator τ of Fqℓ/Fq, we have that for all except N0 values λ∈Fq‾, the corresponding specializations a(τ) and b(τ) cannot have orders of degrees less than c0log⁡log⁡ℓ as torsion points for the Drinfeld module Φ(τ,λ):Fq[T]⟶EndFq‾(Ga) (where Ga is the additive group scheme), given by ΦT(τ,λ)(x)=τx+λxq+xqr.

Transient stability improvement of power system with UPFC control by using transient energy function and sliding mode observer based on locally measurable information

This paper proposes a non-linear technique to improve the transient stability of power systems with a unified power flow controller (UPFC) based on locally measurable information. The proposed method is developed by applying the direct Lyapunov function. The whole control system contains both elementary control approach and an additional control scheme. In the elementary control, the TEF method is investigated for modeling the damping control of the power system with UPFC. In the additional control, the time-derivative signals of the controller are estimated with a 2nd order SMO. The significance of the study is in the use of a complete UPFC model. The other main feature of the proposed method is its robustness properties against changes in the system topology. The simulation results in the case of a single machine connected to an infinite bus, the IEEE 14-bus, and the IEEE 9-bus power system illustrate the efficiency of the proposed control technique under severe disturbances. The results reveal that the proposed control technique for UPFC reduces the first swing of oscillations acceptably and increases stability margins significantly.

AN INNOVATIVE BOUNDARY ELEMENT FORMULATION FOR BUILDING SLABS

Slab supported by beams (i.e. beam-slab floor) is a common practice in the construction of buildings. Modeling this slab type using the boundary element method (BEM) is an essential step to provide seamless frameworks for the analysis of buildings with complex geometries. However, one of the most challenging difficulties that have been facing research efforts in this area is its theoretical setting with limited applicability to practical building slabs. This limitation is addressed in this research work and a practical BEM-based formulation for the slab-beam floor is presented. The presented formulation discretizes the connection area between the slab, and beams and columns into cells (supporting cells). The centroids of these cells are used to carry out an additional collocation scheme which is required to solve the resulting system of equations. To generate the slab stiffness matrix, the generalized displacements that correspond to the supporting cells’ degrees of freedom are set to unity (one at a time). By assembling the generated slab stiffness matrix with beams and columns stiffness matrices using the stiffness analysis method, the overall stiffness matrix is obtained. Hooke’s law is then applied to calculate the generalized displacements and straining actions are obtained in the post-processing phase. The developed formulation is applied to an example to validate its results by comparing it with the analytical solution.

QUANTUM CHEMICAL SIMULATION OF THE INHIBITORY EFFECT OF AQUEOUS SOLUTIONS OF INORGANIC COPPER(II) SALTS ON THE COMBUSTION OF HYDROCARBONS

Introduction. The search for chemicals that would have an effective fire extinguishing effect and the development of new fire extinguishers based on them is an extremely important problem of fire safety. It is known from the literature that new aqueous fire extinguishing agents (AFEAs) based on dissolved inorganic salts of transition metals, in particular, copper(II) chloride salts, have a rather efficient inhibitory effect on the hydrocarbon flame. However, the mechanism of inhibition of hydrocarbon combustion by this class of substances is not completely ascertained. However, it is reliable information about the processes that take place in the flame after the bringing in there of the aerosol of the mentioned AFEA will allow a systematic search for more optimal chemical composition of dissolved inorganic salts of d-metals. Purpose. The purpose of the work is to reveal the peculiarities of the interaction of concentrated aqueous solutions of copper(II) chloride salts with chemically active flame particles.Methods. Quantum chemical calculations of the chemical activity of radicals that appear in the flame and the physicochemical processes that occur in the flame after the bringing on there of AFEA aerosol.Results. The mechanism of a fire-extinguishing effect of aqueous solutions of inorganic copper(II) salts on a hydrocarbon flame is investigated by a calculation method. The sequence of stages of chemical processes that occur in the flame during the inhibiting combustion of hydrocarbons by AFEAs—concentrated solutions of CuCl2 and K2[CuCl4]—and the thermal effects of all reactions that accompany each of these stepwise transformations were ascertained. The stages of the interaction of gaseous Cu2Cl4 molecules with ×OH and ×H radicals in flame with the formation of first a radical-molecular complex and then a molecular complex are decisive in the process of inhibition and display the processes of interruption of chain reactions, i.e. deactivation of radicals in a flame.Conclusion. Thus, using the method of quantum chemical calculations the mechanism of inhibition of hydrocarbon combustion by copper(II) salts was offered. The mechanism of this process is considered to be associative, the decisive elementary act of which is carried out according to the scheme of addition of active radicals of a flame (×OH particles) to gaseous molecules Cu2Cl4 with the formation of radical-molecular complex [{Cu(×OH)Cl2}2] and with its subsequent deactivation by ×H particles.

Accounting for land model error in numerical weather prediction ensemble systems: toward ensemble-based coupled land/atmosphere data assimilation

AbstractThe ensembles used in the NOAA National Centers for Environmental Prediction (NCEP) global data assimilation and numerical weather prediction (NWP) system are under-dispersed at and near the land surface, preventing their use in ensemble-based land data assimilation. Comparison to offline (land-only) data assimilation ensemble systems suggests that while the relevant atmospheric fields are under-dispersed in NCEP’s system, this alone cannot explain the under-dispersed land component, and an additional scheme is required to explicitly account for land model error. This study then investigates several schemes for perturbing the soil (moisture and temperature) states in NCEP’s system, qualitatively comparing the induced ensemble spread to independent estimates of the forecast error standard deviation in soil moisture, soil temperature, 2m temperature, and 2m humidity. Directly adding perturbations to the soil states, as is commonly done in offline systems, generated unrealistic spatial patterns in the soil moisture ensemble spread. Application of a Stochastically Perturbed Physics Tendencies scheme to the soil states is inherently limited in the amount of soil moisture spread that it can induce. Perturbing the land model parameters, in this case vegetation fraction, generated a realistic distribution in the ensemble spread, while also inducing perturbations in the land (soil states) and atmosphere (2m states) that are consistent with errors in the land/atmosphere fluxes. The parameter perturbation method is then recommended for NCEP’s ensemble system, and it is currently being refined within the development of an ensemble-based coupled land/atmosphere data assimilation for NCEP’s NWP system.

Spontaneous exfoliation of large-sized graphene oxide with low defect concentration by simple wet chemistry

The conventional Hummers' method involves intercalation, oxidation, hydrolysis, and exfoliation reactions for graphene oxide (GO) preparation, which generate atomic scale defects in the basal plane and unzip the plane to diminish lateral size. In this paper, processing conditions of the Hummers’ method was engineered, especially graphite material, dose-by-dose injection of KMnO4 oxidant, oxidation temperature, and exfoliation conditions, for less defect concentration and larger size of GO. Natural graphite material processed under 10 °C throughout the whole reaction steps and dose-by-dose addition scheme of the oxidant result in GOs with reduced defect density. Additional carboxylation reaction facilitates the exfoliation of GO sheets, showing ∼35 μm in diameter and mass yield of 140%. This simple wet chemistry-based methodology reported here paves a way to facile and scaled-up production of large-sized GOs with low defect concentration.

Spurious softening in the macroscopic response predicted by the additive tangent Mori–Tanaka scheme for elastic–viscoplastic composites

The Mori–Tanaka (MT) scheme is a well-established mean-field model that combines simplicity and good predictive capabilities. The additive tangent MT scheme is a popular variant of the method that is suitable for elastic–viscoplastic composites. This work is concerned with the analysis of some intrinsic features of the additive tangent MT scheme, in particular, of spurious softening in the macroscopic response that may be encountered when the Perzyna-type viscoplasticity model is used. The resulting non-monotonic macroscopic stress–strain response is clearly non-physical, but it also has a negative impact on the efficiency and robustness of the MT model when it is used as a local constitutive model in concurrent multiscale finite-element computations. As shown in the paper, the spurious softening is more pronounced when the so-called soft isotropization is employed to compute the viscoplastic Hill tensor, but it is also observed, although for a much narrower range of material parameters, in the case of the hard isotropization and when no isotropization is applied. Moreover, the softening is promoted at low strain rates, for high elastic contrast, and for high volume fractions of inclusions. Nevertheless, if the soft isotropization is avoided, the additive tangent MT scheme proves to be a feasible and computationally robust mean-field model that can be successfully employed in finite-element computations.

Enhancing gas production from Class II hydrate deposits through depressurization combined with low-frequency electric heating under dual horizontal wells

Class II hydrate deposits are characterized by a mobile water zone (WZ) underneath the hydrate-bearing layer (HBL) and are encountered in permafrost and deep-sea sediments. In this work, an efficient method of depressurization combining low-frequency electric heating under dual horizontal wells is proposed to exploit Class II hydrate deposits, in which two parallel horizontal wells are arranged in the HBL and the WZ. Based on the geological parameters in the Mallik deposit, the energy recovery behaviors are studied through a numerical simulation approach. Electric heating significantly improves hydrate dissociation and gas production compared with the depressurization method. However, gas production lags electric heating for a long time, and the energy efficiency ratio decreases with time in the later stage. To address these shortcomings, two additional electric heating schemes are designed and optimized. The results show that the additional wellbore heating at the beginning of production accelerates the dissociation of hydrates near the production well, thus greatly reducing the lag time. When electric heating is terminated after the 800th day, the cumulative gas production is reduced by 9.1%, but the energy efficiency ratio is improved as high as 48.71, which confirms the great potential of the proposed method.

Reliability of histopathologic diagnosis of fibrotic interstitial lung disease:\xa0an international collaborative standardization project

BackgroundCurrent interstitial lung disease (ILD) diagnostic guidelines assess criteria across clinical, radiologic and pathologic domains. Significant interobserver variation in histopathologic evaluation has previously been shown but the specific source of these discrepancies is poorly documented. We sought to document specific areas of difficulty and develop improved criteria that would reduce overall interobserver variation.MethodsUsing an internet-based approach, we reviewed selected images of specific diagnostic features of ILD histopathology and whole slide images of fibrotic ILD. After an initial round of review, we confirmed the presence of interobserver variation among our group. We then developed refined criteria and reviewed a second set of cases.ResultsThe initial round reproduced the existing literature on interobserver variation in diagnosis of ILD. Cases which were pre-selected as inconsistent with usual interstitial pneumonia/idiopathic pulmonary fibrosis (UIP/IPF) were confirmed as such by multi-observer review. Cases which were thought to be in the spectrum of chronic fibrotic ILD for which UIP/IPF were in the differential showed marked variation in nearly all aspects of ILD evaluation including extent of inflammation and extent and pattern of fibrosis. A proposed set of more explicit criteria had only modest effects on this outcome. While we were only modestly successful in reducing interobserver variation, we did identify specific reasons that current histopathologic criteria of fibrotic ILD are not well defined in practice.ConclusionsAny additional classification scheme must address interobserver variation in histopathologic diagnosis of fibrotic ILD order to remain clinically relevant. Improvements to tissue-based diagnostics may require substantial resources such as larger datasets or novel technologies to improve reproducibility. Benchmarks should be established for expected outcomes among clinically defined subgroups as a quality metric.

A new framework for teaching scientific reasoning to students from application-oriented sciences

About three decades ago, the late Ronald Giere introduced a new framework for teaching scientific reasoning to science students. Giere’s framework presents a model-based alternative to the traditional statement approach—in which scientific inferences are reconstructed as explicit arguments, composed of (single-sentence) premises and a conclusion. Subsequent research in science education has shown that model-based approaches are particularly effective in teaching science students how to understand and evaluate scientific reasoning. One limitation of Giere’s framework, however, is that it covers only one type of scientific reasoning, namely the reasoning deployed in hypothesis-driven research practices. In this paper, we describe an extension of the framework. More specifically, we develop an additional model-based scheme that captures reasoning in application-oriented practices (which are very well represented in contemporary science). Our own teaching experience suggests that this extended framework is able to engage a wider audience than Giere’s original. With an eye on going beyond such anecdotal evidence, we invite our readers to test out the framework in their own teaching.