Experimental Ones Research Articles

Vibrations characteristics analysis of metal composite 17-4PH material extrusion additively manufactured parts under amplitude dependence property

The ultra-fuse 17-4 PH stainless-steel filament has emerged as a promising new material in the 3D printing field during this past decade. Since the introduction recently of the 17-4 PH stainless-steel filament in the material extrusion process, extensive research has been carried out on the mechanical performance (tensile strength, plasticity, and surface roughness) of the metal composite 17-4 PH stainless-steel material extrusion additively manufactured parts, however few of them mainly focused on the dynamic performance of the 17-4 PH stainless-steel material extrusion additively manufactured parts thus leaving a slight void, therefore to fill this gap a dynamic linear model of a metal composite filament ultra-fuse 17-4 PH stainless-steel material extrusion additively manufactured parts has been established in this study considering the amplitude dependence. Material extrusion additively manufactured plates have been built in x and z-direction, and based on the Jones-Nelson model an investigation of the natural frequency and response and damping ratio of ultra-fuse metal composite 17-4PH metal composite material extrusion specimens has been completed. Equations of the proposed dynamic model have been solved by the combination of the orthogonal polynomial method and energy method. The Newton-Raphson iteration has been employed to predict the natural frequencies and responses of the ultra-fuse 17-4 PH stainless-steel material extrusion manufactured parts. The results indicate that the predicted damping characteristics of the ultra-fuse metal composite 17-4 PH metal composite material extrusion parts have a good consistency with the experimental ones, meanwhile, when amplitude vibration increases from [0.25g…2.00g], the response of the ultra-fuse 17-4 PH metal composite material extrusion parts increase as well both for x and z-direction samples.

Unveiling the Neutral Difference and Its Automated Search

Given a differential characteristic and an existing plaintext pair that satisfies it (referred to as a right pair), generating additional right pairs at a reduced cost is an appealing prospect. The neutral bit technique, referred to as neutral differences throughout this paper, provides a solution to this challenge. Traditionally, the search for neutral differences has heavily depended on experimental testing, leading to limitations in the search range. In this work, we propose the neutral difference table and establish a link between boomerang cryptanalysis and neutral differences. Furthermore, we propose an automated search for neutral differences to address the problem of a limited search range of neutral differences, as previous approaches relied on experimental testing. This approach provides a basis for the subspace spanned by the neutral differences, and we apply this technique to both SPECK32 and LEA, where the predicted results closely match the experimental ones. Consequently, we present the improved differential-linear distinguishers for SPECK32 and LEA, along with the 18-round attacks on LEA192 and LEA256 with the lowest time complexity up to date.

Cyclic behaviour of welded stainless steel beam-to-column connections: Experimental and numerical study

This paper presents an experimental and numerical programme on six welded stainless steel beam-to-column connections subjected to cyclic loading. The test specimens were designed in accordance with Eurocodes and comprised an I-section beam made from 316 L stainless steel welded to an I-section column made from 304 L stainless steel. Each specimen was subjected to a quasi-static cyclic loading protocol and the load-displacement curves are monitored and reported. The results are analysed in terms of failure characteristics, skeleton curve, strain distribution and energy dissipation. Typical failure modes are combined global flexural and torsional buckling and localised web and flange buckling of the beams. The slope of skeleton curve in the hardening region and the energy dissipation capacity appeared to reduce with the section size. Numerical models capable of successfully replicating the experimentally observed response were developed. The load-displacement behaviour and the failure pattern were compared to the experimental ones, showing a good validation. Overall, it has been demonstrated that good hysteretic performance has been achieved for the welded stainless steel beam-to-column connections.

A Simultaneous Study on Wire-Loop, Plate-Loop, and Plate Antennas for Wideband Circular Polarization

We investigate three square-shaped antennas to increase the bandwidth of circular polarization. Each antenna has two adjacent corners excited with the same amplitudes and a phase difference of 90° using a branched feedline vertical to the ground plane. We evaluate the 3 dB axial ratio bandwidth as a function of the loop-arm width using the moment method. It is found that the axial ratio bandwidth reaches 38% for an arm width of 0.04 wavelengths, wider than that of a wire-loop antenna by a factor of three. The simulated results are verified by experimental ones.

Experimental study of organic enrichment on meiofaunal diversity

The organic enrichment effects on the meiofauna and nematofauna were assessed for field sediment and other experimental ones enriched with organic matters conducted in the laboratory for 4 weeks. Also, dissolved oxygen (DO) and pH were monitored for each one. The abundance and diversity of meiofaunal groups and nematofauna varied. Strong significant correlations were found between DO and the studied items. Nematoda was the most abundant group in the field sediment and other experimental ones; their counts increased with the increase in organic enrichments and were dominated by deposit feeders. Amphipoda, Ostracoda and predator/omnivore nematodes disappeared in highly organic-enriched sediments. Changes in DO and organic enrichments might be the more attributable reasons for the alteration of the meiobenthic assemblages. The generic compositions of Nematoda provide a good indicator for environmental alterations.

Impact of temporal resolution in single particle tracking analysis

Temporal resolution is a key parameter in the observation of dynamic processes, as in the case of single molecules motions visualized in real time in two-dimensions by wide field (fluorescence) microscopy, but a systematic investigation of its effects in all the single particle tracking analysis steps is still lacking. Here we present tools to quantify its impact on the estimation of diffusivity and of its distribution using one of the most popular tracking software for biological applications on simulated data and movies. We found important shifts and different widths for diffusivity distributions, depending on the interplay of temporal sampling conditions with various parameters, such as simulated diffusivity, density of spots, signal-to-noise ratio, lengths of trajectories, and kind of boundaries in the simulation. We examined conditions starting from the ones of experiments on the fluorescently labelled receptor p75NTR, a relatively fast-diffusing membrane receptor (diffusivity around 0.5–1 µm2/s), visualized by TIRF microscopy on the basal membrane of living cells. From the analysis of the simulations, we identified the best conditions in cases similar to these ones; considering also the experiments, we could confirm a range of values of temporal resolution suitable for obtaining reliable diffusivity results. The procedure we present can be exploited in different single particle/molecule tracking applications to find an optimal temporal resolution.

Electric Field Gradient in Chiral and Tetrahedral Molecules within High-Order LRESC Formalism.

In this work, we present the electric field gradient (EFG) given by the linear response elimination of the small component (LRESC) scheme up to the 1/c4 order (c is the speed of light in vacuum) in CHFClX (X = Br, I, At) chiral molecules, together with CHF2Br and CH2FX (X = Br, I, At) tetrahedral systems. The former could be good candidates for further parity violation studies, especially when heavy atoms are surrounding. In this context, the LRESC scheme demonstrates effective applicability to large tetrahedral and chiral molecules that incorporate heavy elements, with relativistic effects playing a crucial role. The LRESC results of EFG exhibit an excellent agreement with those calculated at the four-component level, giving differences of only hundredths order in a.u. (atomic units) for the bromine nucleus and less than 0.1 a.u. for the iodine nucleus. Regarding the other nuclei, for the chiral molecules, there is a heavy atom effect on the light atom (HALA) for chlorine and fluorine atoms as the substituent halogen atom becomes heavier. Furthermore, the electronic part of the EFG for the central carbon and the fluorine nuclei presents an important dependence with the environment in the molecules under study. With accurate calculations of the EFG and tabulated nuclear quadrupole moment, the nuclear quadrupole coupling constant is obtained within the LRESC scheme, including for the first time correlation effects on the spin-dependent corrections with this methodology, providing results close to the experimental ones for Cl, Br, and I atoms. At the Hartree-Fock level, the differences are around 6% for Br and I nuclei, and at the density functional theory level with the LDA and PBE0 functionals, the differences are no more than 2%.

Low-velocity impact behavior of two-way SFRC slabs strengthened with steel plate

Structural systems and structural elements can often suffer severe damage or even completely collapse under the effect of sudden dynamic impact loading, which is a different type of loading that is not considered during their design. Research on how structures behave under impact loading and how they can be strengthened to perform better against this type of loading has increased to avoid such undesirable severe damage. Within the scope of this study, it is aimed to improve the behavior and increase the performance of two-way steel fiber-reinforced concrete (SFRC) slabs, one of the leading structural elements that can be affected by impact loading, using steel fiber concrete (SFC) and placing steel plates on the surface of the RC slab. Within the scope of the study, the effects of placing FRC as layers in different positions within the slab and placing the steel plate on different surfaces of the slabs were examined. Impact loading was applied using a drop weight test setup designed by the authors, and the acceleration–time, displacement–time, and impact loading–time behaviors of the RC slabs were measured and interpreted. The use of fiber concrete in RC slabs and strengthened with steel plates increased the maximum acceleration values by an average of 3% and 113%, respectively. The use of fiber concrete in RC slabs reduced the maximum displacement and residual displacement values by an average of 2% and 25%, respectively. Placing steel plates on the slabs reduced the maximum displacement and residual displacement values by an average of 270% and 199%, respectively. In addition, the energy absorption capacities of RC slabs were calculated, and how they were affected by experimental variables was examined. Numerical analyses of the RC slabs tested in the study were also conducted using ABAQUS finite element software, and the results obtained were compared with the experimental ones.

Bridging theory and practice: CFD simulation and interactive VR for conduction heat transfer learning

AbstractSoftware simulation programs and virtual reality (VR) have become powerful tools for several educational purposes, and recently, they were used in a wide range of applications. In cases of inaccessibility to labs, workshops, or industries, as happened before in the coronavirus disease 2019 pandemic, these tools could be effectively integrated with practical lab experiments. In this study, a computational fluid dynamics (CFD) simulation and a VR module were utilized to simulate heat transfer by conduction through various experimental cases. The CFD simulation results were obtained using ANSYS/FLUENT software. Meantime, the experimental data were obtained by carrying out three experiments of heat conduction with different heat transfer rates through simple, composite, and different cross‐sectional area bars. At last, the experimental procedure and devices used were virtually constructed using SolidWorks software as three‐dimensional models, which were then extruded into VR and augmented reality models. It was found that the simulation results closely align with the experimental ones, and the temperature profile in both cases has the same behavior with small differences, which indicates the validity of the developed module to be used as a simulation of the actual experiments. In addition to improving knowledge of heat transfer principles, this combination of simulation and VR technology advances many Sustainable Development Goals (SDGs), including advancing quality education (SDG 4) and innovation in higher education (SDG 9). Additionally, this method assists in achieving the course learning objectives by mimicking real‐world lab experiments, guaranteeing that students graduate from the course with the required information and abilities.

High energy and high repetition rate QCW-LD end-pumped electro-optical Q-switched Yb:YAG laser

The quasi-continuous wave laser diode (QCW-LD) pumping is considered as the most efficient way for generating high energy nanosecond pulsed laser with repetition rate ranging from 50 to 1000 Hz. Here, a high efficiency, high repetition rate and high energy QCW-LD end-pumped electro-optical (EO) Q-switched Yb:YAG laser was demonstrated. The shortest pulse duration of 17.4 ns with a maximum single pulse energy of 5.1 mJ was obtained at the repetition rate of 100 Hz. As the repetition rate increases up to 500 Hz, the maximum output single pulse energy was obtained to be 5.38 mJ with the pulse width of 18.7 ns, corresponding to the slope efficiency of 21.6% and beam quality factor of M x 2=1.04, and M y 2=1.01. In addition, a theoretical study was carried by numerical simulation of the rate equations, and the results were agreed well with the experimental ones. The results show that QCW-LD pumping with Yb-doped crystals is a promising way for highly efficient, high-energy and high repetition rate nanosecond pulsed laser generation.

Chemoreactome screening of aquacobalamin and heptamethyl ester of cyanoaquacobyrinic acid cytotoxic effects on tumor cells with experimental confirmation on BT-474 and A549 cell

Background. The search for an effective and safe pharmacotherapy for tumor diseases includes the evaluation of the action of candidate molecules on various types of tumor cells. Vitamin B12 and its derivatives are promising molecules whose properties can be controlled through chemical modifications.Objective: conducting in silico chemoreactom screening and in vitro experimental study of aquacobalamin and heptamethyl ester of cyanoaquacobyrinic acid (HECСA).Material and methods. Chemoreactome screening was carried out on the basis of a problem-oriented theory of chemograph isomorphism analysis, which is an extension of the algebraic approach to machine learning and recognition problems. Trainable algorithms for calculating chemical distances between molecules were used, on the basis of which the values of half-maximal inhibitory concentration (IC50) were calculated. Screening was carried out for 470 cultures of human tumor cells, including SNB19 (astrocytoma), HCT116 (colon cancer), HeLa (cervical carcinoma), BT-474 (breast duct carcinoma), and A549 (lung carcinoma) cell lines. Dicyanocobyric acid heptamethyl ester ((CN)2Cby(OCH3)7) was obtained by boiling a solution of vitamin B12 in methanol with sulfuric acid (1.0 M) for 4 days. HECСA ((CN)(H2O)Cby(OCH3)7) was obtained by vacuum drying an aqueous solution of (CN)2Cby(OCH3)7 (pH 4.0 and 25 °С). The ester structure and purity were confirmed by 1H nuclear magnetic resonance data, elemental analysis, and MALDI-ToF (matrix-assisted laser desorption/ionization time of flight) mass spectroscopy. Experimental studies of tumor cell cultures were carried out using the MTT testwith aquacobalamin and HECСA on cell lines of immortalized (telomerized) fibroblasts (Fb-hTERT), lung carcinoma (A549), and breast duct cancer (BT-474).Results. Chemoreactome screening of the effects of molecules on tumor cells made it possible to obtain estimates of cell growth IC50 for 470 tumor cell lines. Depending on cell line and vitamin B12 derivative molecule, IC50 values varied in a fairly wide range: from 15 to 2000 nM. In vitro studies on cultures of two human tumor cell lines (BT-474 and A549) and telomerized Fb-hTERT fibroblasts confirmed the cytotoxic effect of aquacobalamin and its hydrophobic derivative HECСA. It was shown that aquacobalamin had weak cytotoxic properties in the concentration range of 3.125–200 µg/l (IC50 > 200 nM), and HECСA significantly reduces the survival of BT-474 and A549 tumor cell lines at high concentrations (100–200 µg/l, IC50 about 100 nM).Conclusion. Correspondence was shown between the results of in silico chemoreactome screening and in vitro cell culture studies: IC50 values for HECСA were significantly lower than for aquacobalamin, and the conversion factor from chemoreactome estimates to experimental ones was almost the same (2.64 for BT-474, and 2.63 for A549). The results of chemoreactome screening for other tumor cell lines can be used to plan further cell experiments with vitamin B12 derivatives.

How Much Should We Trust Instrumental Variable Estimates in Political Science? Practical Advice Based on 67 Replicated Studies

Abstract Instrumental variable (IV) strategies are widely used in political science to establish causal relationships, but the identifying assumptions required by an IV design are demanding, and assessing their validity remains challenging. In this paper, we replicate 67 articles published in three top political science journals from 2010 to 2022 and identify several concerning patterns. First, researchers often overestimate the strength of their instruments due to non-i.i.d. error structures such as clustering. Second, IV estimates are often highly uncertain, and the commonly used t-test for two-stage-least-squares (2SLS) estimates frequently underestimate the uncertainties. Third, in most replicated studies, 2SLS estimates are significantly larger in magnitude than ordinary-least-squares estimates, and their absolute ratio is inversely related to the strength of the instrument in observational studies—a pattern not observed in experimental ones—suggesting potential violations of unconfoundedness or the exclusion restriction in the former. We provide a checklist and software to help researchers avoid these pitfalls and improve their practice.

A model of heterogeneous undercooled liquid and glass accounting for temperature-dependent nonexponentiality and enthalpy fluctuation.

Dynamic heterogeneity is a fundamental characteristic of glasses and undercooled liquids. The heterogeneous nature causes some of the key features of systems' dynamics such as the temperature dependence of nonexponentiality and spatial enthalpy fluctuations. Commonly used phenomenological models such as Tool-Narayanaswamy-Moynihan (TNM) and Kovacs-Aklonis-Hutchinson-Ramos fail to fully capture this phenomenon. Here we propose a model that can predict the temperature-dependent nonexponential behavior observed in glass-forming liquids and glasses by fitting standard differential scanning calorimetry curves. This model extends the TNM framework of structural relaxation by introducing a distribution of equilibrium fictive temperature (Tfe) that accounts for heterogeneity in the undercooled liquid. This distribution is then frozen at the glass transition to account for the heterogeneous nature of the glass dynamics. The nonexponentiality parameter βKWW is obtained as a function of temperature by fitting the Kohlrauch-Williams-Watts (KWW) equation to the calculated relaxation function for various organic and inorganic undercooled liquids and glasses. The calculated temperature dependent βKWW shows good agreement with the experimental ones. We successfully model the relaxation dynamics far from equilibrium for two silicate systems that the TNM model fails to describe, confirming that temperature dependent nonexponentiality is necessary to fully describe these dynamics. The model also simulates the fluctuation of fictive temperature δTf during isothermal annealing with good qualitative agreement with the evolution of enthalpy fluctuation reported in the literature. We find that the evolution of enthalpy fluctuation during isothermal annealing heavily depends on the cooling rate, a dependence that was not previously emphasized.

Ultimate strength failure mechanism and optimization design of marine composite deck grillage structures with opening

In this paper, the ultimate bending strength and the failure mechanism of the marine composite deck grillage structure are experimentally and numerically investigated, before the optimization design is conducted to enhance the ultimate bearing capacity. The ultimate strength experiment of the composite deck grillage structure is first carried out. Based on the improved progressive failure method and the cohesive damage theory, the numerical simulation considering fiber failure, matrix failure, shear failure and adhesive layer failure is conducted and the predicted strains, load–displacement curves, and failure modes of the specimen are compared with the experimental ones to verify the accuracy of the present method. Both experimental and predicted results show that the stiffeners and the laminated deck near the opening are the stress concentration areas, and the matrix failure is main failure mode. The optimization results show that the suitable panel thickness can reduce the stress concentration effect and avoid premature fracture in localized areas due to stress concentration. The increase of the stiffener heights can significantly increase the ultimate strength and the bending stiffness. These findings can provide support for the design of composite deck grillage structures in ships.

Ductile damage and fracture characterizations in bi-cyclic biaxial experiments

This paper discusses novel extremely low-cycle bi-cyclic biaxial reverse experiments with large strains. Various tests with tension-compression-tension (TCT) shear cyclic loads, superimposed by either non-reverse or reverse cyclic loading patterns, are newly designed to investigate the plastic, damage, and fracture behavior. These experiments fill the gaps in carrying out complex reverse loading by utilizing 4mm thick biaxially loaded cruciform specimens. The deformed specimens in different loading stages are examined metallographically with micrographs to elucidate the influence of loading histories on the occurrence and evolution of micro-defects. In addition, scanning electron microscopy (SEM) is also used to analyze the fractured surfaces and verify the anisotropic damage mechanism. An advanced anisotropic cyclic plastic-damage continuum model is utilized to characterize the material behavior, including the Bauschinger effect, the stress-differential effect and the non-hardening effect after shear reverse loading as well as stress-state-induced damage mechanisms. Due to the utilization of the digital image correlation (DIC) technique, the numerical results can be compared with the experimental ones in both load–displacement curves and strain fields, respectively. The elastic strain triaxiality and strain Lode parameter are introduced, providing a novel perspective for analyzing the cyclic loading experiments.

Fracture prediction on hydrogen-charge notched samples using a stress-state-dependent phenomenological model

There is a consensus for transitioning to clean energy sources to meet the world’s energy demands. Hydrogen is a candidate to supply green energy. However, hydrogen embrittlement (HE) in materials is an issue that needs to be assessed. Based on the damage concept, a straightforward and robust computational framework is presented to predict the harmful effects on material resistance caused by the HE phenomenon. The adopted model framework builds upon dealing with the coupled mechanical diffusion problem in a simplified approach by considering the local equilibrium between hydrogen concentration at interstitial sites and Cauchy stresses. A modified version of the Mohr–Coulomb criterion dependent on the stress triaxiality and Lode angle introduces a damage indicator parameter. The proposed model is applied to study the brittle intergranular fracture of a high-strength AISI 4135 steel. A detailed description of the stress state and hydrogen-driven failure parameters are presented for two specimens with different notch radii. The proposed model is implemented in a VUMAT subroutine and made available for download to the technical community for research and educational use. After calibrating the model parameters, the numerical results yield good agreements of the predicted fracture strength of notched hydrogen-charged samples compared to the experimental ones. Maximum differences of around 10% among experimental and numerical tests are observed.

Multi-methodological analysis of hydrogen desorption from graphene

Chemisorption of hydrogen on graphene has been extensively investigated in last decades, but the reported values of over several eV, depending on different factors, such as the local structural environment, substrates or previously bound hydrogen.In this work, we combine Temperature-Programmed Desorption experiments with simulations using empirical reactive force fields and Density Functional Theory calculations. We observe that desorption occurs through processes with different activation energies, which we are able to identify by analyzing simulation data and post-processing experimental ones through a procedure based on Arrhenius fit with feedback. The result is the assignment of experimentally observed desorption peaks to different desorption processes, namely desorption from isolated sp3 H, or couples of H in conformation cis or trans, or edge sp3 or sp2 H.The protocol we outline is generally applicable and might be particularly useful in more complex cases with larger multiplicity of desorption peaks.

Biaxial Testing of EPDM Rubbers for Automotive Applications Using a Uniaxial Testing Machine

The FE-based structural design of components made of rubber materials requires an experimental characterization to calibrate a proper hyperelastic material model. A strain energy density (SED) parameter is typically adopted to describe the hyperelastic behavior of isotropic rubbers. This can be written as a function of the strain tensors, the strain invariants or the stretch ratios and proper material parameters. The latter must be calibrated on experimental data generated by testing rubber materials under different loading conditions, typically two among uniaxial tension, pure shear and biaxial tension. In this context, the mechanical behavior of Ethylene–Propylene–Diene Monomer (EPDM) rubbers, both in the dense and expanded configurations, which are typically employed to manufacture automotive seals, has been investigated. First, uniaxial tension tests have been performed. Afterwards, a new fixture has been developed to perform equi-biaxial tension tests using a uniaxial testing machine. The fixture has been adopted to test EPDM cruciform specimens under equi-biaxial tension loading. Finally, both uniaxial and equi-biaxial data have been employed to fit a Mooney–Rivlin material model for each tested EPDM rubber, which has been validated by comparing the results of FE simulations with the experimental ones.

Coupled fluid-structure simulation of a flapping wing using free multibody dynamics software

AbstractComputer simulations offer invaluable insights into fluid-structure interaction phenomena, increasing our understanding of complex behaviors within fluid flows and enabling predictions of consequential effects. This paper explores flapping wing simulation using an original toolchain based on free software. The structural domain is modeled using multibody dynamics, interfaced with arbitrary fluid dynamics solvers through a general-purpose multiphysics coupling library. The proposed toolchain is validated against benchmark models, demonstrating its effectiveness in various applications. Our study, inspired by experimental ones, applies this coupling to investigate the hydroelastic behavior of a flexible wing. Wing motion characteristics, structural properties, and convergence criteria are analyzed through numerical simulations. While achieving appreciable agreement with experimental data on wing motion ratios, challenges in dealing with large displacements have been identified. Nonetheless, the present study provides valuable insights into fluid-structure interactions, laying the groundwork for future refinements in computational modeling techniques and advancing the understanding of bio-inspired flight mechanisms.

Experimental and numerical study of thermal and electrical potential of BIPV/T collector in the form of air-cooled photovoltaic roof tile

Among renewable energy sources, Building-Integrated Photovoltaic/Thermal (BIPV/T) systems are gaining increasing interest. To improve their economic competitiveness, technologies that increase their efficiency are searched for. The paper is devoted to evaluating the impact of various air-cooling configurations on the thermal and electrical performance of a photovoltaic roof tile. A numerical model of the own experimental system was developed in the ANSYS Fluent software for a wide range of input variables. The original approach based on the SST k-ω turbulence model, Discrete Ordinates radiation model, and the use of Solar Load module were proposed. Such a numerical model allows representation of semi-transparent layers and variable solar irradiance, which is a unique realization of real system modelling. Numerous analyses conducted indicate a higher heat recovery potential for an airflow duct with a height of 25 mm for all configurations analysed. The highest value of recovered heat flux was approximately 330 W/m2 under conditions of a volumetric air flow rate of 7.5 m3/h and solar irradiance equal to 900 W/m2. Good agreement of the results of the multivariant CFD simulations with new experimental ones was confirmed. Insight into the flow phenomena behind the achieved thermal results supplemented the knowledge. The highest electrical efficiency obtained experimentally was 5.76 % for a channel with a height of 50 mm, volumetric flow rate equal to 7.5 m3/h and solar irradiance equal to 600 W/m2. The presented methodology and the results obtained can be useful in research devoted to optimising BIPV/T air-based cooling systems, which will then be tested in-situ. Moreover, new experimental data collection can be used for the verification of numerical models.