Offshore floating nuclear power plant (FNPP) is characterized by its small and mobility, which is not only able to provide safe and efficient electric energy to remote islands, but to the oil and gas platforms. The safety digital control system (DCS) cabinet, as a carrier for the electronic devices, plays a significant role in ensuring the normal operation of the nuclear power plant. To satisfy the requirements of cabinet used in the sea environment, such as well rigidity, shock load resistance, good seal and corrosion resistance, etc, more and more attention is focused on the cast aluminum cabinet. However, the cast aluminum structure may cause larger weight of cabinet, which inevitability affects the mobility of cabinet, and increases the carried load of ship as well. Therefore, seeking for an effective approach to design a light weight cast aluminum cabinet for the offshore FNPP is definitely necessary. In this work, a frame of cast aluminum cabinet with lightweight is obtained successfully via structure topology optimization design, it is found that the weight of the frame can be reduced to 50% after optimization iterations. Subsequently, the natural frequency of the optimized cast aluminum cabinet is calculated by using ABAQUS, it is seen that the first mode frequency of the frame is beyond 30 Hz, which can meet the basic stiffness requirement. Accordingly, dynamic design analysis method (DDAM) is performed to verify the ability of the optimized cast aluminum cabinet in resisting sudden shock load, and the shock response characteristics of the cabinet are determined. Numerical results support that the optimized frame of cabinet possesses good resistance to high level shock. However, for the assembled cast aluminum cabinet, the vertical shock circumstance turns out to be the most critical condition, high stress and deformation regions occurs at the bracket and column. Reinforcements are proposed to make the bracket stiffer in this shock loading condition.

The Mini-Plate 2 (MP-2) irradiation test is a fueled experiment designed for irradiation in multiple test locations in the Advanced Test Reactor (ATR) at the Idaho National Laboratory (INL). The experiment is a drop-in test where small aluminum-clad fuel plate samples (mini plates) are cooled directly by the ATR Primary Coolant System (PCS) water. The MP-2 fuel plate experiment will be irradiated in several different irradiation locations of the ATR. This fueled experiment contains aluminum-clad fuel mini plates consisting of monolithic U-Mo. Four different types of fuel plates with fuel meat thickness and cladding are part of the MP-2 test. A thermal analysis has been performed on the MP-2 experiment. A method for calculating Departure from Nucleate Boiling Ratio (DNBR) and Flow Instability Ratio (FIR) during a reactivity transient using the commercial finite element and heat transfer code ABAQUS is discussed. At the start of an ATR cycle the heat generation rate of the fueled experiment is high and the heat rate multiplier from the outer shim control cylinders is low, while the reverse is true at the end of the ATR cycle. Thermal analyses at 10-day increments during the cycle calculate the DNBR and FIR during a reactivity transient. This technique calculates DNBR for the fuel plate surfaces and FIR for all water components for each finite element surface and node at various times during the ATR cycle. Heat rates vary with time during the transient calculations that are provided by a detailed physics analysis. Oxide growth on the fuel plates is also incorporated. Results from the transient calculations are displayed with the ABAQUS post processor. By calculating these parameters at each location in the finite element model, conservatism is replaced with accuracy. This allows for a greater margin for the thermal hydraulic safety parameters.

Radiation damage in structural materials for nuclear applications is not well-understood, especially when linking the atomic scale damage mechanisms to the macroscopic effects. On a microscopic level, particle radiation creates defects that can accumulate in the material. Defects can also interact with existing features in the material. Since both defects and features have different energies associated with them, investigation of the resulting energy spectrum in a macroscopic sample may offer insight into the connection between microscopic damage and macroscopic properties. In alloys, changes in the size and number of precipitates will be reflected in the amount of energy required to dissolve the precipitates during thermal analysis. This can then be studied using differential scanning calorimetry (DSC). This work explores the sensitivity of the DSC measurement to detect irradiation-induced instability in metastable and secondary phase precipitates in the high-strength aluminum alloy 7075-T6 for extremely low doses of helium-ion and neutron irradiation. The precipitates in aluminum 7075-T6 are expected to grow or shrink, changing the energy spectrum measured by DSC. The magnitude of the change can then be compared to a model of irradiation-induced phase instability. This will demonstrate the ability of this thermal analysis technique to help bridge the gap between microscopic radiation effects and macroscopic properties.

The Mini-Plate 2 (MP-2) irradiation test is a fueled experiment designed for irradiation in multiple test locations in the Advanced Test Reactor (ATR). MP-2 is considered a non-instrumented drop-in test where small aluminum-clad fuel plate samples are cooled directly by the ATR Primary Coolant System (PCS) water. The MP-2 fuel plate experiment will be irradiated in several different irradiation locations of the ATR. This fueled experiment contains aluminum-clad fuel mini plates consisting of monolithic U-Mo. Four different types of fuel plates were analyzed. A thermal analysis has been performed on the MP-2 experiment to be irradiated in the ATR at Idaho National Laboratory (INL). A new technique for calculating Departure from Nucleate Boiling Ratio (DNBR) and Flow Instability Ratio (FIR) using the commercial finite element and heat transfer code ABAQUS is demonstrated. This new technique calculates DNBR for the fuel plate surfaces and FIR for all water components for each finite element surface and node. Pressure drop data is fed into the calculations in order to geometrically calculate the water saturation temperature. Results from the DNBR and FIR calculations are displayed with the ABAQUS post processor named Viewer. By calculating these parameters at each location in the finite element model, conservatism is replaced with accuracy. This allows for a greater margin for the thermal hydraulic safety parameters.

In this study, we analyze and compare the temperature profiles, and temperature gradient profiles of UN, U 3 Si 2 and U 3 O 8 aluminum (Al) dispersed nuclear fuels to propose safer nuclear fuels with enhanced thermal conductivity. To calculate the electronic and lattice thermal conductivities, we use EPW, BoltzTrap and ShengBTE codes implemented with Quantum Espresso. Maxwell-Eucken approximation is used to get the effective thermal conductivity of the considered dispersed fuels. The temperature and temperature gradients are calculated by solving the steady state heat conduction equation for a cylindrical fuel rod. Results show that these fuels have reduced the centerline temperature which will prevent fuel melting, as well it will reduce the thermal stress which leads to cracking the pellet.

Advanced Thermal Reactor (ATR) FUGEN is the heavy water-moderated, boiling light water-cooled, pressure tube-type reactor. The commercial operation of FUGEN started on Mar. 1978 and terminated on Mar. 2003 and the decommissioning of FUGEN has been carried out since the decommissioning plan was approved in 2008. In order to perform the decommissioning work such as dismantling and decontamination safely and reasonably, technology development for the decommissioning has been promoted actively. This paper describes a part of technology development as follows. (1) Technology development on reactor dismantling The reactor of FUGEN is made of various materials such as stainless steel, carbon steel, zirconium alloy and aluminum which have relatively high activity concentration by operation for 25 years. With consideration of these characteristics, the reactor will be dismantled under water remotely in order to shield the radiation and prevent dust from migrating from water to air generated by the cutting considering the usage of zirconium alloy which is likely to be oxidized. In addition, laser cutting method whose features are fast cutting speed and less secondary waste in cutting will be applied for reactor dismantling. However, laser cutting method has no experiences to be applied to dismantlement of reactor facilities. Therefore, laser cutting for actual dismantled objects in air was demonstrated in controlled area in FUGEN using laser cutting system composed of articulated robot and laser cutting head. As a result, safety and applicability of laser cutting system was confirmed. From now on, primary cutting work in air, cutting demonstration with a relatively high dose rate and mock-up test in water for dismantling the actual reactor will be carried out. (2) Technology development on investigation of contamination It is necessary to evaluate radioactive inventory in the facilities accurately in order to reflect the evaluated data to dismantling plan appropriately. Therefore, the investigation of the contamination for the facilities has been carried out for safe and reasonable decommissioning work. The in-situ simple investigation method for the contamination of inner pipes which is mostly dominated by Co-60 is started to develop using the portable NaI(Tl) spectrometer. This method complements conventional investigation method to take samples from the pipes and to analyze them by radiochemical method to figure out the contamination of the whole facility.

Boron Carbide (B 4 C) particle-reinforced aluminum matrix composite is the key material for use as neutron absorber plate in spent fuel storage racks as well as new fuel and in-containment fuel storage racks for GENIII advanced passive nuclear power plants in China. This material has once depended upon importing with high expense and restricted delivery schedule by foreign supplier. Therefore it has meaningful practical significance to realize the localized manufacturing for this material in China. More importantly, since it’s the first time for this material to be used in domestic plant, particular care should be taken to assure the formal supplied neutron absorber material products exhibit high stabilized and reliable service in domestic nuclear engineering. This paper initiates and proposes a principle design framework from technical view in qualification requirements for this neutron absorber material so as to guide the practical engineering application. Aiming at neutron absorber materials supplied under practical manufacturing condition in engineering delivery, the qualification requirements define B 4 C content, matrix chemistry, 10 B isotope, bulk density, 10 B areal density, mechanical property and microstructure as key criteria for material performance. The uniformity assessment as to different locations of this material is also required from at least three lots of material. Only qualified material meeting all of the qualification requirements should proceed to be verified by lifetime testing such as irradiation, corrosion and thermal aging testing. Systematic and comprehensive performance assessments and verification for process stabilization could be achieved through the above qualification. The long-term service for this neutron absorber material in reliable and safe way could be convincingly expected in spent fuel storage application in China.

In chemical researchers view, hot functional test is a verification of the Nuclear Power Plant before first fuel loading and commercial operation, which is the preparation for staffs, documents, instruments and sampling systems. So, chemistry department should use its own language, knowledge and experience to express their thoughts and what they have seen during the engineering commissioning period. As the first commercial operation nuclear power plant after Fukushima nuclear accident, during the four units commissioning period, chemical researchers accumulated a lot of good experience and feedbacks in the aspect of construction and commissioning for new nuclear power plant. For example, in order to ensure the personnel skill level, we must make special plans which include staff training, laboratory construction, instrument and on-line system commissioning, and all of these should be timely adjusted and changed in order to be consistent with the engineering progress. In order to ensure the water quality of pipe flushing in different stages, such as cold functional test, hot functional test, we should set a strictly water chemical standard which based on the HAF103, and the standard should have some differences in different stage for one unit. In order to ensure the water chemistry in good performance especially after the unit going into commercial operation, the maintenance plan for equipment and system must be formulated, and then, a detailed monitoring plan must be executed. At the same time, a strict system flushing controlling mode can also provide a great benefits for water chemistry quality, especially in the period of start-up. In addition to these above experiences, chemistry researchers of Ningde nuclear power plant also accumulated a lot of good practices and feedbacks about dealing with some abnormal water quality activities, which can’t be founded in commercial operation unit. For example, the aluminum (Al) content in the primary increased rapidly and beyond the specification limits in hot functional test and so on. This article will share the good practices and feedbacks of the first phase of Fujian Ningde nuclear power plant. We hope these good practices and experience feedbacks can provide good reference for the other new nuclear plants in the stage of design, construction, operation and maintenance in the future.

The U.S. High Performance Research Reactor conversions fuel development team is focused on developing and qualifying the uranium-molybdenum (U-Mo) alloy monolithic fuel to support conversion of domestic research reactors to low enriched uranium. Several previous irradiations have demonstrated the favorable behavior of the monolithic fuel. The Full Size Plate 1 (FSP-1) fuel plate experiment will be irradiated in the northeast (NE) flux trap of the Advanced Test Reactor (ATR). This fueled experiment contains six aluminum-clad fuel plates consisting of monolithic U-Mo fuel meat. Flow testing experimentation and hydraulic analysis have been performed on the FSP-1 experiment to be irradiated in the ATR at the Idaho National Laboratory (INL). A flow test experiment mockup of the FSP-1 experiment was completed at Oregon State University. Results of several flow test experiments are compared with analyses. This paper reports and shows hydraulic analyses are nearly identical to the flow test results. A water channel velocity of 14.0 meters per second is targeted between the fuel plates. Comparisons between FSP-1 measurements and this target will be discussed. This flow rate dominates the flow characteristics of the experiment and model. Separate branch flows have minimal effect on the overall experiment. A square flow orifice was placed to control the flowrate through the experiment. Four different orifices were tested. A pressure differential versus flow rate curve for each orifice is reported herein. Fuel plates with depleted uranium in the fuel meat zone were used in one of the flow tests. This test was performed to evaluate flow test vibration with actual fuel meat densities and reported.

The U.S. High Performance Research Reactor Conversions fuel development team is focused on developing and qualifying the uranium-molybdenum (U-Mo) alloy monolithic fuel to support conversion of domestic research reactors to low enriched uranium. Several previous irradiations have demonstrated the favorable behavior of the monolithic fuel. The Full Scale Plate 1 (FSP-1) fuel plate experiment will be irradiated in the northeast (NE) flux trap of the Advanced Test Reactor (ATR). This fueled experiment contains six aluminum-clad fuel plates consisting of monolithic U-Mo fuel meat. Three different types of fuel plates with matching pairs for a total of six plates were analyzed. These three types of plates are: full burn, intermediate power, and thick meat. A thermal analysis has been performed on the FSP-1 experiment to be irradiated in the ATR at the Idaho National Laboratory (INL). A thermal safety evaluation was performed to demonstrate that the FSP-1 irradiation experiment complies with the thermal-hydraulic safety requirements of the ATR Safety Analysis Report (SAR). The ATR SAR requires that minimum safety margins to critical heat flux and flow instability be met in the case of a loss of commercial power with primary coolant pump coast-down to emergency flow. The thermal safety evaluation was performed at 26 MW NE lobe power to encompass the expected range of operating power during a standard cycle. Additional safety evaluations of reactivity insertion events, loss of coolant event, and free convection cooling in the reactor and in the canal are used to determine the response of the experiment to these events and conditions. This paper reports and shows that each safety evaluation complies with each safety requirement of the ATR SAR.

Monolithic, plate-type fuels are the proposed fuel form for the conversion of the research and test reactors to achieve higher uranium densities within the reactor core. This fuel type is comprised of a low enrichment, a high density U-10Mo alloy fuel-foil, which is sandwiched between diffusion barriers and encapsulated in a cladding material. To understand the irradiation performance, fuel-plates are being benchmarked for large number of parameters. In this work, effects of the cladding material were studied. In particular, a monolithic fuel-plate with U7Mo foil and Zry-4 cladding was simulated to explore feasibility of using Zircaloy as a surrogate cladding material. For this, a selected mini-plate from RERTR-7 tests was simulated first with as-run irradiation history. By using same irradiation parameters, a second case, a plate with U10Mo fuel and Al6061 cladding was simulated to make a comparative assessment. The results indicated that the plate with Zircaloy cladding would operate roughly 50 °C hotter compared with the plate with Aluminum cladding. Larger displacement profiles along the thickness for the plate with Zircaloy cladding were observed. Higher plastic strains occur for the plate with Aluminum cladding. The results have revealed that any pre-irradiation stresses would be relieved relatively fast in reactor and the fuel-foil would be essentially stress-free during irradiation. The fuel stresses however, develop at reactor shutdown. The plate with Zircaloy cladding would have higher residual stresses due to higher pre-shutdown temperatures. Similarly, the stresses magnitudes are higher in the foil core for the plates with Zircaloy cladding. Finally, pressure on the fuel is significantly higher for the plates with Zircaloy cladding. Overall, employing a Zircaloy as surrogate cladding material did not provide a better thermo-mechanical performance compared with the Aluminum cladding.

A typical sandstone uranium deposit, located in the Tuhar basin, was selected to compare the effect of oxygen as the oxidizer with that of hydrogen peroxide. Based on the feasibility study of oxygenation of ferrous and uranium minerals, batch leaching, pressure column leaching and field testing were carried through. The results of feasibility study and laboratory leaching indicate that ferrous ion is inaccessible to being oxidized by pressure oxygen in acidic solutions with pH 2–2.5, and oxygen can oxidize the uranium minerals. Recovery of uranium is proportional to the oxygen pressure. Additionally, the low concentrations of aluminium and ferric ion alleviate the potential precipitation of aluminum and iron significantly. The further field test confirmed the feasibility of oxygen in acid leach. Oxygen has some extent effects of increasing uranium level and considerable effects of anti-precipitation and clogging. In general, oxygen has better applicability in this deposit.

A procedure for Electron Beam Welding (EBW) was developed for the manufacturing of a follower fuel assembly made of an AA 6061-T6 aluminum straps for a U-Mo plate-type fuel proposed to be used in the future in Korea’s Kijang Research Reactor (KJRR) project. The initial welding trials of the weld samples were carried out with a high vacuum chamber using the EBW process. After investigating the welds, EB welding parameters for the full-sized samples were optimized for the required depth of penetration and weld quality. Subsequently, the weld samples made by the filler specimens showed higher shearing strengths than those of the non-filler specimens. This procedure made by EBW process was also confirmed based on the results of the shearing strength test, an examination of the macro-cross sections, and the fracture surfaces of the welded specimens.

In ESS, a pulsed proton beam of 5 MW mean power will hit a tungsten target to generate neutrons by spallation. The pulses are 2.86 ms long and occur with 14 Hz; the power within a pulse is 125 MW. Only centimeters from the target, the neutrons are moderated by liquid hydrogen in aluminium vessels. The deposited power heats the surrounding structures and fluids which are circulated and cooled. The hydrogen is operating at 15 bar and average temperature between 17 and 21 K, i.e. above the critical pressure 12.8 bar, but below the critical temperature 32.9 K. During the pulses, the peak heat deposition in the aluminium is 15 W/cm 3 and in the hydrogen 4 W/cm 3 . If the cooling of the aluminium is neglected during one pulse, the temperature increases to 34 K. That is above the critical temperature, where physical properties change strongly with temperature. Therefore the conjugate heat transfer has to be investigated in detail. This work includes 1D principal transient calculations of a general configuration as well as CFD simulations of the heating and cooling of a specific design. The 1D calculations are performed using GNU/Octave and the CFD using ANSYS/CFX. It is concluded that with an inlet temperature of 17 K, the wall temperature can be kept below the critical temperature in the general configuration and sufficient cooling can be ensured in the investigated specific design.

Monolithic plate-type fuel is a fuel form being developed for high performance research and test reactors to minimize the use of enriched material. These plate-type fuels consist of a high uranium density LEU foil contained within diffusion barriers and encapsulated within a cladding material. To benchmark this new design, effects of various geometrical and operational variables on irradiation performance have been evaluated. For this work, the effects of fuel foil centering on the thermo-mechanical performance of the mini-plates were studied. To evaluate these effects, a selected plate from RERTR-12 experiments, the Plate L1P756, was considered. The fuel foil was moved within the fuel plate to study the effects of the fuel centering on stress, strain and overall shape of the fuel elements. The thickness of the fuel foil, thickness of the Zr-liners and total thickness of the plate were held constant, except the centerline alignment of the fuel foil. For this, the position of the fuel foil was varied from the center position to a maximum offset corresponding to the minimum allowable aluminum cladding thickness of 0.1524 mm. Results for various offset cases were then compared to each other and to the ideal case of a centered fuel foil. Fabrication simulations indicated that the thermal expansion mismatch results in warping of the fuel plate during fabrication as the fuel plate is cooled from the HIP temperature when the fuel is not centered. Even if the model is constrained during cooling to simulate the rigid HIP can surrounding the fuel plate during cooling, warping is observed when the constraint is removed. Similarly, irradiation simulations revealed that the fuel offset causes virtually all irradiation-induced swelling to occur on the thin-cladding side of the plate. This is observed even for the smallest offset that was considered. The total magnitude of the swelling is approximately same for all offsets values.

Monolithic plate-type fuel is a fuel form being developed for high performance research and test reactors to minimize the use of enriched material. These fuel elements are comprised of a high density, low enrichment, U-Mo alloy based fuel foil, sandwiched between Zirconium liners and encapsulated in Aluminum cladding. The use of a high density fuel in a foil form presents a number of fabrication and operational concerns, such as: foil centering, flatness of the foil, fuel thickness variation, geometrical tilting, foil corner shape etc. To benchmark this new design, effects of various geometrical and operational variables on irradiation performance have been evaluated. As a part of these series of sensitivity studies, the shape of the foil corners were studied. To understand the effects of the corner shapes of the foil on thermo-mechanical performance of the plates, a behavioral model was developed for a selected plate from RERTR-12 experiments (Plate L1P785). Both fabrication and irradiation processes were simulated. Once the thermo-mechanical behavior the plate is understood for the nominal case, the simulations were repeated for two additional corner shapes to observe the changes in temperature, displacement and stress-strain fields. The results from the fabrication simulations indicated that the foil corners do not alter the post-fabrication stress-strain magnitudes. Furthermore, the irradiation simulations revealed that post-fabrication stresses of the foil would be relieved very quickly in operation. While, foils with chamfered and filleted corners yielded stresses with comparable magnitudes, they are slightly lower in magnitudes, and provided a more favorable mechanical response compared with the foil with sharp corners.

Great operational challenges are placed on nuclear power plants. These challenges are usually reflected in the expansion of fuel cycle length, long-time operation or power uprates. The one way is to optimize the equipment or replace it with equipment with higher efficiency. The second way is to optimize the fuel and its cladding. In this area it is possible to work mainly on the development of new materials which have better nuclear or mechanical properties. Nuclear power industry is a conservative one. It is necessary to have a detailed knowledge of materials properties of used equipment. Knowledge of the materials behavior is particularly required in the environment where the materials are exposed to neutron flux. This article focuses on new promising materials that can be used in a nuclear fuel, a nuclear reactor or its closest vicinity. Carbon nano materials can be included among these types of materials. Composite materials have generally improved mechanical and thermal properties with addition of nanoparticles. However the additives itself have an impact on the behavior of the neutron field. This article describes an experiment that examined the behavior of neutrons in carbon nano fibers, carbon nano tubes and nano wires of aluminum oxide. The main goal of the experiment was to determine how neutron scattering is affected, when the sample is exposed to neutron beam. The article presents results, including additional testing of nano materials. Additional tests were carried out to verify the purity and parameters of the investigated samples.

Micro arc oxidation (MAO) technology known as a newly surface treatment technology has got a widely application in the field of aviation, aerospace, automotive, electronics, and medical industry. Strength, toughness, hardness and corrosion of valve metal such as aluminum, magnesium, copper, zinc, zirconium and their alloys can be greatly improved by MAO technology. This paper tries to probe into the feasibility of using MAO technology in nuclear power industry. Aluminum and its alloys are used as structural materials such as the cladding of reactor fuel and all kinds of pipes in the low nuclear reactor. Zirconium alloys are widely used for the fuel cladding, cannula, catheter and other components of the fuel assemblies. Titanium and its alloys offer a unique combination of desirable mechanical properties which makes them to be the candidate materials for structural application in the field of nuclear energy. The surface of all these materials may be destroyed which increasing the risk of the nuclear accident due to the severe serving conditions. As a result, it is necessary to improve the corrosion and wear resistance behavior. With the urgent requirements of safety and durability of nuclear reactor, MAO technology must have a broad prospect in nuclear industry.

We present here an ellipsoidal timing detector in Radioactive Ion Beam Line in Lanzhou (RIBLL). The photons induced by radioactive beam ions passing through a thin plastic-scintillator foil BC422, emit from the foil center corresponding to one focal point of an aluminum ellipsoidal mirror and are reflected to another focus point at which the cathode of a photomultiplier tube locates. A time resolution of about 115ps is achieved for 12 N and the counting rate up to 10 8 pps is allowed. The simulation was carried out using GEANT4 Monte Carlo toolkit. The photons total collection efficiency following projectile from different position, photon collection efficiency and time resolution of photon to photocathode of 3 different cases were calculated. Also the main factors influencing the detector’s time resolution and some proposals are given.

The Monte Carlo (MC) simulation method, known to handle complex problems which may be formidable for deterministic methods, will always require validation with classic problems that have evolved historically from deterministic methods [1–5] based on Chandrasekhar’s method in radiative transfer, Fourier transforms, Green’s functions, Weiner-Hopf method etc which are restricted to simple geometries, such as infinite or semiinfinite media, and simple scattering laws too for practical application. This work compares deterministic results with MC simulation results for neutron flux in a slab. We consider mono-energetic transport problem in an infinite medium and in a 1-D finite slab with isotropic scattering. The transport theory solutions used in infinite geometry are the Green’s function solution and the spherical harmonics ( P 1 , P 3 ) solutions, while for the 1-D finite slab, we refer to a transport benchmark for which an exact solution is available. For diffusion theory, we consider the Green’s function infinite geometry solution, and the exact and eigen-function numerical solution for finite geometry (1-D slab). The objective of this work is to illustrate the results from all the methods considered especially near the source and boundaries, and as a function of the scattering probability. The results are plotted for six elements that include a strong absorber, such as gadolinium, and a strong “scaterrer” such as aluminium. The present work is didactic and focuses on problems which are simple enough, yet important, to illustrate the conceptual difference and computational complexity of the deterministic and stochastic approaches.