Practical Calculation Method Research Articles

Large-eddy simulation studies for predicting plume concentrations around nuclear facilities using an overlapping technique

We propose, in emergency response to nuclear accidents, a practical and quick local-scale atmospheric dispersion calculation method using an overlapping technique. First, we pre-calculated large-eddy simulations (LESs) of plume dispersion around an actual nuclear facility under idealised atmospheric conditions with 36 wind-direction cases and made a dataset of the 10-minute averaged concentrations for each wind direction case. Then, we conducted LESs of plume dispersion for 1-hour periods under realistic atmospheric conditions using the meteorological data and estimated the spatial distributions of the 1-hour averaged concentrations by overlapping the pre-calculated concentration data depending on the frequency of the mean wind directions. It is shown that the concentration distribution patterns are well reproduced in comparison to those under the realistic conditions. It is concluded that the atmospheric dispersion calculation method using the overlapping technique has potentially a high performance in emergency responses to nuclear accidents.

A Short-Circuit Calculation Method for DFIG-Based Wind Farms

Short-circuit calculations for wind farms are crucial for determining equipment ratings and providing basic information for protection coordination. In this paper, a practical calculation method of short-circuit currents (SCCs) is proposed for doubly fed induction generator (DFIG)-based wind farms. The improved calculation method of the SCCs in single DFIG is developed based on electromagnetic transient analysis. Combined with the traditional method of calculating the SCCs of the power system, an equivalent model of the DFIG-based wind farm used for SCCs is studied. The equivalent model and expressions for SCCs are later validated through PSCAD/EMTDC-based simulation results, and a comparison with the national standard calculation method is analyzed. The results show that the calculation method proposed in this paper has better accuracy and practicability, which are important elements in the electrical design of DFIG-based wind farms.

Mechanical behavior of the reinforced concrete frame with masonry filling Comportement mécanique des portiques en béton armé avec remplissage en maçonnerie

Masonry is often used in the most of reinforced concrete structure constructions as a filling material that is important on structural characteristics. Structural contribution in the calculations was neglected or misunderstood, mainly due to the lack of a practical calculation methods and an appropriate regulatory tool.The analysis of frames filled with masonry is very complex. This complexity is linked from one part to the difference in the nature of elements and its behavior that make up the masonry itself (brick and mortar) and their interaction, and on the other part, for the large dispersion that characterizes the bricks as well as the execution's quality parameters which make it difficult to define reliable criteria for the masonry. The objective of this work is to experimentally highlight the influence of the hollow brick masonry filler, commonly used in Morocco, on reinforced concrete frames subject to lateral stresses, to deepen understanding the seismic behavior of the masonry structures by evaluating the structural performance of a specimen wall. These experimental results will be compared to those found by modeling prototypes, using SAP 2000 software, based on various approaches and models as well as other results deduced from the other researchers. The experimental study was carried out according to standard NF EN 1052-3 on two reinforced concrete frames, of dimensions (2m X 1.6m), the one with the masonry filling, and the other without filling in order to determine the initial characteristic resistance to the shearing of the masonry walls. The obtained results showed that a filling has a beneficial effect on rigidity which can be doubled compared to an empty frame. in the same way the lateral resistance. But this effect is much contrasted; it depends a lot on the characteristics essentially of the materials (bricks and concrete). This is the main reason, which justifies the divergence of the results deduced from the nine models that we used.

Schwinger-Keldysh diagrammatics for primordial perturbations

We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use a quasi-single-field inflation model as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case (m<3H/2) that has been previously studied, and the heavier scalar case (m>3H/2) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large.

A new fast approach for well production prediction in gas-condensate reservoirs

Prediction of gas-condensate well production is significant for sensible decision making for the reservoir development plan, infrastructure investment, and produced gas and condensate sales contract. Typically, time-consuming numerical simulation with fine grids or local grid refinement around the well is implemented in order to capture the effects of condensate blockage and predict gas-condensate well deliverability. In addition, in the commencement of the reservoir lifetime, the numerical simulation predicts erroneous results due to high uncertainty in reservoir data. A simple analytical model can estimate gas-condensate well production reasonable with a limited number of input data. On the other hand, uncertainty studies require repetitious usage of the analytical calculation. Therefore, a faster and more practical method for calculation of gas-condensates well flow rate has a precious value. In this paper, a fast analytical method is introduced for prediction of gas and condensate production profiles based on the two-phase pseudo-pressure integral and material balance equation. Proposed analytical model in contrast to previous ones, predicts the exact plateau time. As the result, it does not need iteration in each reservoir pressure step to compute the relevant flowing bottom-hole pressure during the constant gas production period. The model is expanded to take into account the high-velocity phenomena in near the wellbore region. It is also extended for the first time for different well geometries including vertical, deviated, horizontal, and hydraulic-fractured wells. Additionally, the analytical model is validated using fine grid numerical simulation for a wide range of rock and fluid properties. The developed analytical model can be used as a fast engineering tool for evaluating the uncertainty in well and reservoir data to choose the best strategy for reservoir development.

A nonmonotone scaled conjugate gradient algorithm for large-scale unconstrained optimization

ABSTRACTThis paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden–Fletcher–Goldfarb–Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under appropriate assumptions, the method is proven to possess global convergence for nonconvex smooth functions, and R-linear convergence for strongly convex functions. Preliminary numerical results and related comparisons show the efficiency of the proposed method in practical computation.

Decentralized MRAC for Large-Scale Interconnected Systems With State and Input Delays by Integrators Inclusion

This paper investigates the problem of decentralized model reference adaptive control (MRAC) for a class of large-scale systems with time-varying delays in the interconnected terms and state and input delays. The upper bounds of interconnection terms with time-varying delays and external disturbances are assumed to be completely unknown. By integrators inclusion, a dynamic input delay compensator is established for input delay compensation and it is used as a practical method for state calculation x(t + R). Also, a method is presented for a class of decentralized feedback controllers, which can evolve the closed-loop system error uniformly bounded stable. As a numerical example, the proposed technique is applied to an unstable open-loop system to show the feasibility and effectiveness of the method.

Calculation of Tyre Pyrolytic Oil Combustion Products Using the Method of Gibbs Free Energy Minimization

This paper presents a practical and economical method of calculation based on thermodynamic equilibrium, which allows to evaluate quantitatively and qualitatively the emissions of combustion products of alternative fuels in search state, such as tyre pyrolytic oil which can be used in equipment such as compression ignition engine, boilers, furnaces and gas turbine combustion chambers.

Pixel-wise estimation of noise statistics on iterative CT reconstruction from a single scan.

As iterative CT reconstruction continues to advance, the spatial distribution of noise standard deviation (STD) and accurate noise power spectrum (NPS) on the reconstructed CT images become important for method evaluation as well as optimization of algorithm parameters. Using a single CT scan, we propose a practical method for pixel-wise calculation of noise statistics on an iteratively reconstructed CT image, which enables accurate calculation of noise STD for each pixel and NPS. We first derive the noise propagation from measured projections to an iteratively reconstructed CT image provided that the projection noise is known. We then show that the model of noise propagation remains approximately unchanged for extra simulated noise added on the measured projections. To compute the noise STD map and the NPS map on an iteratively reconstructed CT image from a single scan, we first iteratively reconstruct the CT image from the measured projections using an existing reconstruction algorithm. The same measured projections are added by different sets (a total of 32 sets in our implementation) of projection noise simulated from an estimated projection noise model, and are then used to iteratively reconstruct different CT images. The calculations of the noise STD map and the NPS map are finally performed on the entire stack of these different reconstruction images. We evaluate our method on an anthropomorphic head phantom, and demonstrate the clinical utility on a set of head and neck patient CT data, using two iterative CT reconstruction algorithms: the penalized weighted least-square (PWLS) algorithm and the total-variation (TV) regularization. In the head phantom case, repeated scans are acquired to generate the ground truths of noise STD and NPS maps. Using only one single scan, the proposed method accurately calculates the noise STD maps with a root-mean-square error (RMSE) of less than 5HU. In the NPS map estimation, we compare the result of our proposed method with that of the conventional method which calculates the NPS maps on a uniform region of interest on one CT image. Our method outperforms the conventional method on the NPS map estimation with RMSE reduced by 92%. The implementation of the proposed method on the patient data successfully provides the noise STD values around complex structures and a high-quality NPS map. The proposed method accurately calculates noise STD for each pixel and NPS on an iteratively reconstructed CT image, with no requirement of repeated CT scans. It provides a detailed evaluation of imaging performance of different iterative reconstruction methods on the same CT dataset.

A Novel Gauged Vector Potential Formulation for 3-D Motional Eddy-Current Problems Using Edge Elements

The accurate computation of motional eddy currents is essential for the design of electromagnetic devices such as eddy-current brakes. When the conductors are uniform in the moving direction, it is convenient to formulate and solve the problem within a fixed coordinate system without needing to use two or more coordinate systems and connecting the fields in each region. Because ungauged magnetic vector potential (MVP) formulation can be solved using only iterative linear solvers, which are not so robust as direct solvers, it is desirable to impose proper gauge condition to ensure that the formulation has a unique solution. In this paper, a novel gauged formulation for motional eddy-current problems using finite edge element approximation of the MVP is proposed. Both transient and steady-state motional eddy-current problems are studied. A dummy scalar variable is introduced in the non-conducting region to enforce the Coulomb gauge, together with the gauge condition in the conducting region, to ensure that the resultant linear system can be solved using direct linear solvers. Three-dimensional numerical examples are presented to showcase the accuracy and usefulness of the proposed method for practical engineering computation.

Approximate estimation of wrinkle wavelength and maximum amplitude using a tension-field solution

Membrane-based space structures such as solar sails, inflatable antennas and sunshields have attracted attention for use on future advanced space science and engineering missions. Since these membrane-based space structures are easily deformed by small disturbances, a practical calculation method for the surface configuration of the deformed membranes is required to realize the membrane structures without failure. This study formulates an equation to estimate the wrinkle wavelength and maximum amplitude appearing on thin membranes based on a tension-field solution. The equation calculates the wrinkle wavelength and maximum amplitude using three wrinkling parameters, which are the major principal stress in the wrinkled region, the length of the wrinkle line, and the wrinkle strain. Because these wrinkling parameters are given by a traditional wrinkling analysis using tension-field theory, the formulated equation reveals an approximate wrinkle wavelength and a maximum amplitude appearing on the thin membranes without cumbersome bifurcation analysis and has characteristics applicable to various types of structures. By conducting a wrinkling analysis using tension-field theory for the two classical membrane models, which have wrinkling phenomena appearing across the entire membrane and in part of the membrane, a wrinkle wavelength and maximum amplitude are estimated from the formula. Comparing the estimated results with those given by wrinkling analysis using shell theory, it is observed that the estimate appropriately captures the wrinkle wavelength and maximum amplitude in the wrinkled region where tension-field theory is applicable. The equation presented in this study offers a new, practical approach to estimate the wrinkled membrane surface configuration.

A Practical Method for Computation of Laplace Inverses by Post–Widder’s Formula

In this note, a novel method for parametric inversion of Laplace transforms by means of the Post–Widder formula is developed. In brief, the coefficients of the MacLaurin series equivalent of the sequence, which converges to Post–Widder’s formula at infinity, are calculated by means of the iterated Aitken transform. Subsequently, the asymptotic values of such coefficients are obtained using the diagonal Pade approximants in a computationally efficient manner. Our method revives the classical Post–Widder formula from the practical viewpoint.

Practical calculation method to estimate the absolute boron concentration in tissues using 18F-FBPA PET

PurposeThe purpose of this study was to establish a practical method to estimate the absolute boron concentrations in the tissues based on the standardized uptake values (SUVs) after administration of 4-borono-phenylalanine (BPA) using 4-borono-2-18F-fluoro-phenylalanine (18F-FBPA) PET.MethodsRat xenograft models of C6 glioma (n = 7, body weight 241 ± 28.0 g) were used for the study. PET was performed 60 min after intravenous injection of 18F-FBPA (30.5 ± 0.7 MBq). After the PET scanning, BPA-fructose (167.3 ± 18.65 mg/kg) was administered by slow intravenous injection to the same subjects. The rats were killed 60 min after the BPA injection and tissue samples were collected from the major organs and tumors. The absolute boron concentrations (unit: ppm) in the samples were measured by inductively coupled plasma optical emission spectrometry (ICP-OES). The boron concentrations in the tissues/tumors were also estimated from the 18F-FBPA PET images using the following formula: estimated absolute boron concentration (ppm) = 0.0478 × [BPA dose (mg/kg)] × SUV. The measured absolute boron concentrations (mBC) by ICP-OES and the estimated boron concentrations (eBC) from the PET images were compared.ResultsThe percent difference between the mBC and eBC calculated based on the SUVmax was −5.2 ± 21.1% for the blood, −9.4 ± 22.3% for the brain, 1.6 ± 21.3% for the liver, −14.3 ± 16.8% for the spleen, −9.5 ± 27.5% for the pancreas, and 3.4 ± 43.2% for the tumor. Relatively large underestimation was observed for the lung (−48.4 ± 16.2%), small intestine (−37.8 ± 19.3%) and large intestine (−33.9 ± 11.0%), due to the partial volume effect arising from the air or feces contained in these organs. In contrast, relatively large overestimation was observed for the kidney (34.3 ± 29.3%), due to the influence of the high uptake in urine.ConclusionsThe absolute boron concentrations in tissues/tumors can be estimated from the SUVs on 18F-FBPA PET using a practical formula. Caution must be exercised in interpreting the estimated boron concentrations in the lung, small intestine and large intestine, to prevent the adverse effects of overexposure, which could occur due to underestimation by partial volume effect using PET.

Investigation of the longitudinal wind power spectra at the gorge terrain

This study investigates the fundamental characteristics of the longitudinal wind power spectra at the gorge terrain. First, a simplified V-shaped gorge terrain model, representing usual deep-cutting gorge terrains where long-span bridges usually straddle, was introduced for the wind tunnel test. The longitudinal wind power spectra at the gorge center were analyzed in detail and compared with those of the simulated oncoming wind. Then, a practical calculation method was proposed to directly calculate the power spectra values at the gorge terrain based on the oncoming wind field and minimum wind parameters at the gorge center. Finally, an infield V-shaped deep-cutting gorge terrain model was also introduced for the wind tunnel test, and the obtained wind power spectra further validated the proposed calculation method. The results show that for both gorge terrain models, the power spectra values in the low-frequency range become closer to those of the oncoming wind with the measurement positions moving away from the ground, while good agreements are always found in the high-frequency range for all of the specified measurement positions. The proposed calculation method can calculate the power spectra values at these two gorge terrains with relatively high accuracy. It is hoped that this study can more conveniently provide informative guidelines for determining the wind power spectra values for similar gorge terrains in engineering practices than traditional wind tunnel tests or computational fluid dynamics numerical simulations.

Fundamental study on mixing layer and horizontal circulation in open-channel flows with rectangular embayment zone

A part of mean kinetic energy in a main-channel is used for production of a large-scale horizontal circulation in the side cavity. However, the details of the mechanism such as energy transport are poorly understood. Therefore, we conducted PIV measurements in a laboratory flume and compared space distributions of mean velocity components and Reynolds stress by varying a cavity geometry. In particular, a practical calculation method of Reynolds stress was also developed and its accuracy was examined by comparison with the measured data. Furthermore, contributions of components in an energy transport equation were revealed quantitatively.

DFT calculation of isotropic hyperfine coupling constants of spin adducts of 5,5-dimethyl-1-pyrroline-N-oxide in benzene and water

Isotropic hyperfine coupling constants (HFCCs) of spin adducts of 5,5-dimethyl-1-pyrroline-N-oxide (DMPO) are calculated by DFT method with solvation effect. Geometries of ring conformers and rotational conformers of trapped radicals are optimized and their HFCCs are calculated. Boltzmann weighted average of HFCCs of low energy conformations shows very good agreement with the experimental value in benzene. Two or four water molecules hydrogen bonded to the spin adduct have to be explicitly incorporated in the case of water. The results show time-independent averaging of relevant conformers is a very practical method for calculation of HFCCs of DMPO spin adducts.

Methods of traction rolling stock fire safety analysis

Aim. Fire safety of a protection asset is the state of a protection asset that is characterized by the capability to prevent the occurrence and development of fire, as well as the effects of hazardous factors of fire on people and property [1]. The traction rolling stock (TRS) is one of the primary protection assets on railway transport. Managing TRS fire safety involves a large volume of information on various TRS types: possible fire-hazardous conditions, fire safety systems, parameters of TRS-related processes. That means that efficient management must be built upon analysis that allows identifying trends and factors of fire hazard development. The analysis should be organized in such a way as to allow its results to be used in evaluation of composite safety indicators [2]. The required applied nature of such analysis is also obvious. Given the above, it should be noted that the applied research indirectly solves the task of using the results of fundamental research to address not only cognitive, but also societal issues [3]. The aim of this article is to structure the most efficient applied and theoretic methods of analysis and to develop a structure for systems analysis of TRS fire safety. Methods. The multitude of factors that affect the condition of TRS can be divided into two groups: qualitative and quantitative. Importantly, it is impossible to completely research the impact of all the elements of a complex technical system that is TRS on fire safety. We have to examine a part of the whole, i.e. a sample, and then use probabilistic and statistical methods to extrapolate the findings of sample examination to the whole [4]. An analysis of a data set requires a correctly defined sample. At this stage, the quality of information is the most important criterion. The list of raw data was defined based on the completeness of the description, reliability of the sources. Then, in a certain sequence, the data was analyzed by means of qualitative and semi-quantitative methods. First, given the impossibility to establish evident connections (destroyed by the hazardous effects of fire) between the condition of units that preceded the fire, the Pareto analysis was used. The research involved root cause analysis (Ishikawa diagram). Subsequently, cluster analysis of fire-hazardous situations was used. The main purpose of cluster analysis consists in establishing generic sequences of events that entail TRS fires. For that purpose, a description of possible fire-hazardous states of traction rolling stock is required, i.e. a multitude of events and states must be described. Dependability analysis can be successfully performed by representing the safety state information in terms of the theory of sets [5]. The sets of hazardous fire-related TRS events are represented in the form of partially ordered sets. Processing of such sets that are non-numeric in their nature cannot be performed by means of statistical procedures based on addition of parametric data. For that reason the research used mathematical tools based on the notion of type of distance. A part of data that have quantitative characteristics was analyzed statistically. Results. The TRS fire safety data analysis methods presented in this article that include methods of numeric and non-numeric data processing allowed developing a formatted list of fire hazard factors that enable the creation of a practical method of TRS fire risk calculation. An algorithm is proposed for application of qualitative and quantitative methods of analysis of data of various numerical natures. An example is given of the algorithm’s application in the analysis of diesel engine fire safety. The proposed method can be used for analyzing anthropogenic safety in terms of listing the factors involved in risk assessment.

Fast Calculation Method of Energy Flow for Combined Electro-Thermal System and Its Application

In recent years, Combined electro-thermal system has developed rapidly. In order to provide the initial data for the analysis of the combined electro-thermal system, a practical energy flow calculation method for the combined electro-thermal system is proposed in this paper. Based on the detailed analysis of the topology structure of the heating network and its hydraulic and thermodynamic model, the forward-backward sweep method for the heat flow of the heating network is established, which is more suitable for the actual radial heating network. The electric and thermal coupling model for heating source, such as thermoelectric unit and electric boiler is established, and the heat flow of heating network and the power flow of power grid are calculated orderly, thus a fast calculation method for the combined electro-thermal system is formed. What’s more, a combined electro-thermal system with two-stage peak-shaving electric boiler is used as the example system. This paper validates the effectiveness and rapidity of this method through the example system, and analyzes the influence for the energy flow of combined electro-thermal system caused by the operating parameters such as the installation location of electric boiler, the outlet water temperature of heat source and the outlet flow rate, etc.

EVALUATING THE EFFECTIVENESS OF BUDGETARY CONTROL IN UKRAINE

Introduction. Provision of sustainable development requires efficiency in the management of public financial resources. Every year the number of detected financial irregularities supervisory authorities increases. Reduce the amount of possible financial irregularities by increasing the efficiency of budgetary control. The main purpose of the scientific research is to evaluate the efficiency of budgetary control in Ukraine. Results.The effectiveness of budgetary control is a complex economic category .It is characterized by certain criteria and depends on many parameters and factors. In assessing the effectiveness of budgetary control and the development of practical methods of calculation and formation performance criteria should take into account not only the economic component but also various other components efficiency. Monitoring the effectiveness of budgetary control carried out according to certain criteria by examining different interrelated indicators. In our opinion, the most thoroughly evaluate the effectiveness of budgetary control are the following criteria: performance criteria, the criterion of concentration, structuring criterion, criterion validity, criterion dynamism. Conclusion. The introduction of a single integrated system of indicators to assess the effectiveness of budgetary control will help assess the achievement of goals to improve the efficiency of budget resources of the state through a set of criteria: performance, concentration, structuring, efficiency and agility. Using the general method facilitate assessment of the effectiveness of public spending as between different supervisory authorities and between the different territorial units of those bodies.

Graph method for evaluation of process safety in railway facilities

Aim. Industrial safety (OS) is the state of protection of operating personnel from harmful effects of manufacturing processes, energy, equipment, objects, conditions and schedule of work [1]. The most efficient evaluation of OS in railway transportation is ensured by composite indicators, one of which is the risk assessment indicator. That is also reflected in the Russian legislation that stipulates the requirement to evaluate fire, occupational and other types of risks that affect industrial safety. According to the definition set forth in GOST 33433-2015 [2] risk is a combination of the probability and consequences of an event. The most complicated task related to risk assessment is the choice of the evaluation model for the probability of an undesired event. The model must enable practical applicability of evaluation results for planning of risk compensation measures. Currently, there are a large number of probability evaluation methods that can be divided into two large groups, i.e. expert and quantitative. Expert methods have several well-known shortcomings. The quantitative methods require the construction of a system of equations or an analytical model. In the context of railway facilities the construction of analytical models of probability evaluation is of principal interest due to the possibility of demonstration of the factors that are taken into consideration by the model. The aim of the article is to formalize the analytical method for evaluation of the probability of railway facility transfer into a hazardous state (in the context of industrial safety). Methods . Undesirable events that cause industrial safety incidents in railway facilities are random; they can be represented as a random process. A random system development process, including objects transition from a safe state into hazardous (undesirable) states, i.e. system state change in time, can under some assumptions be described with a semi-Markov process. In general, the construction and solution of semi-Markov models comes down to building a system of homogenous differential equations. This procedure always involves mathematical difficulties. [3] shows the possibility of representation and solution of semi-Markov models with a coupled graph model. Such models are highly visual, and allow formalizing the wanted system states, as well as paths of transition from safe into hazardous states. The main problem of modelling random processes of industrial safety state changes is the requirement to identify the complete list of hazardous states and preceding non-hazardous or pre-hazardous states. The processes typical to railway facilities are characterized by a multitude of states that cause various events. The concept of “state” usually characterizes an instantaneous image, a “cross-section” of a system. Thus, at the first stage of construction and solution of a model of random process of a system’s industrial safety state change, the finite sets of safe and hazardous states of the railway facility under consideration are identified in accordance with the known hazardous state criterion [4]. As the process of state change of a system’s industrial safety in railway transportation is random in time, in this article system operation is described with a semi-Markov process with the assumption that the discrete process is described with an embedded Markov chain. The set of system states and their connections are represented with a directed state graph with defined topological concepts [3]. For a constructed model, the article provides the proof of the theorem identifying the probability of system transition from an initial non-hazardous into a hazardous state, as well as the formula for calculation of such probability. Results . The graph method for evaluation of industrial safety in railway facilities developed in this article includes both the rules of construction of a system’s safety states graph and the tool for evaluation of the probability of system transition into a specific hazardous state. The graph is the basis of the practical method for calculation and forecasting of industrial safety incidents. The article provides the proof of the theorem identifying the probability of system transition from an initial non-hazardous into a hazardous state, as well as an example of application of graph method for evaluation of probability of fire in a fixed facility. The proposed probability evaluation method can be used in planning of industrial safety measures in terms of specification of new states or rules of transition into associated states.