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At least 757 records · Page 42

Neural simulation-based inference of the Higgs trilinear self-coupling via off-shell Higgs production

One of the forthcoming major challenges in particle physics is the experimental determination of the Higgs trilinear self-coupling. While efforts have largely focused on on-shell double- and single-Higgs production in proton-proton collisions, off-shell Higgs production has also been proposed as a valuable complementary probe. In this article, we design a hybrid neural simulation-based inference (NSBI) approach to construct a likelihood of the Higgs signal incorporating modifications from the Standard Model effective field theory (SMEFT), relevant background processes, and quantum interference effects. It leverages the training efficiency of matrix-element-enhanced techniques, which are vital for robust SMEFT applications, while also incorporating the practical advantages of classification-based methods for effective background estimates. We demonstrate that our NSBI approach achieves sensitivity close to the theoretical optimum and provide expected constraints for the high-luminosity upgrade of the Large Hadron Collider. While we primarily concentrate on the Higgs trilinear self-coupling, we also consider constraints on other SMEFT operators that affect off-shell Higgs production.

Ghosh, Aishik [Univ. of California, Irvine, CA (Un↗

Double diffraction imaging of x-ray induced structural dynamics in single free nanoparticles

Abstract Because of their high photon flux, x-ray free-electron lasers (FEL) allow to resolve the structure of individual nanoparticles via coherent diffractive imaging (CDI) within a single x-ray pulse. Since the inevitable rapid destruction of the sample limits the achievable resolution, a thorough understanding of the spatiotemporal evolution of matter on the nanoscale following the irradiation is crucial. We present a technique to track x-ray induced structural changes in time and space by recording two consecutive diffraction patterns of the same single, free-flying nanoparticle, acquired separately on two large-area detectors opposite to each other, thus examining both the initial and evolved particle structure. We demonstrate the method at the extreme ultraviolet (XUV) and soft x-ray Free-electron LASer in Hamburg (FLASH), investigating xenon clusters as model systems. By splitting a single XUV pulse, two diffraction patterns from the same particle can be obtained. For focus intensities of about 2 × 10 12 W cm −2 we observe still largely intact clusters even at the longest delays of up to 650 picoseconds of the second pulse, indicating that in the highly absorbing systems the damage remains confined to one side of the cluster. Instead, in case of five times higher flux, the diffraction patterns show clear signatures of disintegration, namely increased diameters and density fluctuations in the fragmenting clusters. Future improvements to the accessible range of dynamics and time resolution of the approach are discussed.

Sauppe, M. (ORCID:0000000163123102)↗

On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations

Simulations of turbulent flow present challenges in terms of accuracy and affordability on modern highly-parallel computer architectures. A multigrid-reduction-in-time algorithm is used to provide a framework for separately evolving different scales of turbulence and for parallelizing the temporal domain, thereby increasing the concurrency. It is hypothesized that the space–time locality of the small scales of turbulence can be used to circumvent difficulties in applying temporal multigrid to flows dominated by inertial physics. For algorithms that fall well short of spectral accuracy (fourth-order is used in this work) attention must be paid to the accuracy of features on scales transferred between multigrid levels. Numerical experiments were performed using implicit large-eddy simulation. Results from applying the approach to an infinite-Reynolds number Taylor–Green flow and a double-shear flow at a Reynolds number of 11650 provide strong evidence that the approach has merit. The multigrid-reduction-in-time framework can be used to parallelize the temporal domain of a high-Reynolds-number turbulent flow and permit independent convergence of different scales. Establishing this foundation allows for future research in reducing the wall-clock time to solve turbulent flows while retaining the same accuracy as sequential solvers. In conclusion, current performance results from parallelizing the temporal domain are not competitive with those from sequential-in-time methods.

97 MATHEMATICS AND COMPUTING↗

Achievement of the Planetary Defense Investigations of the Double Asteroid Redirection Test (DART) Mission

NASA's Double Asteroid Redirection Test (DART) mission was the first to demonstrate asteroid deflection, and the mission's Level 1 requirements guided its planetary defense investigations. Here, we summarize DART's achievement of those requirements. On 2022 September 26, the DART spacecraft impacted Dimorphos, the secondary member of the Didymos near-Earth asteroid binary system, demonstrating an autonomously navigated kinetic impact into an asteroid with limited prior knowledge for planetary defense. Months of subsequent Earth-based observations showed that the binary orbital period was changed by –33.24 minutes, with two independent analysis methods each reporting a 1 σ uncertainty of 1.4 s. Dynamical models determined that the momentum enhancement factor, β , resulting from DART's kinetic impact test is between 2.4 and 4.9, depending on the mass of Dimorphos, which remains the largest source of uncertainty. Over five dozen telescopes across the globe and in space, along with the Light Italian CubeSat for Imaging of Asteroids, have contributed to DART's investigations. These combined investigations have addressed topics related to the ejecta, dynamics, impact event, and properties of both asteroids in the binary system. A year following DART's successful impact into Dimorphos, the mission has achieved its planetary defense requirements, although work to further understand DART's kinetic impact test and the Didymos system will continue. In particular, ESA's Hera mission is planned to perform extensive measurements in 2027 during its rendezvous with the Didymos–Dimorphos system, building on DART to advance our knowledge and continue the ongoing international collaboration for planetary defense.

79 ASTRONOMY AND ASTROPHYSICS↗

Hydrogen Bond Benchmark: Focal‐Point Analysis and Assessment of DFT Functionals

We performed a hierarchical, convergent ab initio benchmark study and systematically analyzed the performance of density functional approximations for describing hydrogen bonds in small neutral, cationic, and anionic complexes, as well as in larger systems involving amide, urea, deltamide, and squaramide moieties. Focal point analyses (FPA), extrapolating to the ab initio limit, were carried out using correlated wave function methods up to CCSDT(Q) for the small complexes and CCSD(T) for the larger systems, together with correlation-consistent Gaussian basis sets up to the complete basis set limit. Optimized geometries and vibrational frequencies were obtained at the CCSD(T) level. The resulting FPA hydrogen-bond energies converge within a few tenths of a kcal mol −1 . These reference data were used to evaluate 60 density functionals (including 12 dispersion-corrected), spanning the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. Overall, the meta-hybrid M06-2X provides the best performance for both hydrogen bond energies and geometries, while the dispersion-corrected GGAs BLYP-D3(BJ) and BLYP-D4 also yield accurate hydrogen-bond data and can serve as cost-effective options for studying large and complex systems.

coupled cluster theory↗

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of N = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in N = 4 DBI) are shown to be removable at O(ε 0 ) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nuclear fragmentation at the future electron-ion collider

We explore the potential of conducting low-energy nuclear physics studies, including nuclear structure and decay, at the future Electron-Ion Collider (EIC) at Brookhaven. By comparing the standard theory of electron-nucleus scattering with the equivalent photon method applied to Ultraperipheral Collisions (UPC) at the Large Hadron Collider (LHC) at CERN. In the limit of extremely high beam energies and small energy transfers, very transparent equations emerge. We apply these equations to analyze nuclear fragmentation in UPCs at the LHC and 𝑒𝐴 scattering at the EIC, demonstrating that the EIC could facilitate unique photonuclear physics studies. Furthermore, we have also shown that the fragmentation cross-sections at the EIC are about 1,000 times smaller than those at the LHC. At the LHC, the fragmentation of uranium nuclei displays characteristic double-hump mass distributions from fission events, while at the EIC, fragmentation is dominated by neutron emission and fewer few fission products, about 10,000 smaller number of events.

Bertulani, Carlos A. [East Texas A&M University, C↗

Robust Ferromagnetism in Highly Strained SrCoO 3 Thin Films

Epitaxial strain provides important pathways to control the magnetic and electronic states in transition-metal oxides. However, the large strain is usually accompanied by a strong reduction of the oxygen-vacancy formation energy, which hinders the direct manipulation of their intrinsic properties. Here, using a postdeposition ozone annealing method, we obtain a series of oxygen stoichiometric SrCoO 3 thin films with the tensile strain up to 3.0%. We observe a robust ferromagnetic ground state in all strained thin films, while interestingly the tensile strain triggers a distinct metal-to-insulator transition along with the increase of the tensile strain. The persistent ferromagnetic state across the electrical transition therefore suggests that the magnetic state is directly correlated with the localized electrons, rather than the itinerant ones, which then calls for further investigation of the intrinsic mechanism of this magnetic compound beyond the double-exchange mechanism.

36 MATERIALS SCIENCE↗

Updates to Relevance Vector Machine: Multiclass Classification, Variable Selection, and Proof-of-Concept Application to Safeguards Fresh Fuel Verification using List-Mode Neutron Collar Data

To expand the capabilities of safeguards authorities to verify the integrity of fresh fuel assemblies, Oak Ridge National Laboratory has retrofit the existing electronics of the JCC-71 uranium neutron coincidence collar, which contains 18 3 He neutron detectors and an external 241 AmLi(α, n) neutron interrogation source arranged to surround a fresh nuclear fuel assembly. The new electronics system allows analysts to record list-mode neutron multiplicity data in addition to the singles and doubles rates that are currently measured. Based on previous proof-of-concept research, analysis of these new data will identify off-normal fuel configurations in an assembly and characterize or localize the specific partial fuel defects. The purpose of this report it to document the analysis algorithm development and then to demonstrate its capability for the safeguards verification of fresh fuel assemblies using list mode neutron collar data. To analyze the complex list-mode data collected with the upgraded uranium neutron collar, multivariate classification algorithms are being developed using a novel classification method, the relevance vector machine. This approach may be applied to multiclass problems to estimate the probability that test data belongs to one of many possible classes of data. In addition, our method identifies the most useful variables/channels for making predictions, which illuminates the basis for the model’s predictions, and this interpretability is largely unique among data analytics methods. Variable selection occurs during model training and parameter tuning and does not need any external hyperparameter tuning routines. Finally, we apply the modified relevance vector machine to a simulated dataset of list-mode neutron collar data generated with the radiation transport code MCNP. The method can correctly identify off-normal fuel configurations, categorize the data according to four fuel defect scenarios, and rank the channels in the data according to prediction utility. For nuclear safeguards applications, it is concluded that this method has the potential to increase the sensitivity and reliability to detect missing fuel rods from a standard 17 x 17 Pressurized Water Reactor (PWR) fresh fuel assembly. Within this analysis, “off-normal” (i.e., missing fuel rods) were correctly classified in 17 simulated test scenarios with one quarter (25%) of the fresh fuel rods missing using a training data set of 58 simulated measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

2D gravity↗

Development and Characterization of Electrodes for Surface-Specific Attenuated Total Reflection Two-Dimensional Infrared Spectroelectrochemistry

Electrochemical interfaces still have remaining mysteries surrounding the interfacial region of the electrical double layer, despite being prevalent throughout the energy and water remediation industries. The electrical double layer is where many important dynamic processes such as catalysis and electron transfer occur. The goal of this work is to study the electrical double layer with two-dimensional infrared (2D IR) spectroscopy to experimentally access the details of the structural dynamics of this complex environment. However, there are several experimental challenges to applying 2D IR spectroscopy to this application, such as assuring the surface specificity of the spectrum, optimizing the signal strength while minimizing spectral distortions from dispersion and Fano line shapes, and selecting electrode materials that are both sufficiently IR compatible and conductive. Here we will discuss various considerations when designing 2D IR experiments of electrode interfaces utilizing several substrates and experimental configurations and demonstrate a robust method for 2D IR experiments of electrode interfaces under applied potential that combines nonconducting Si ATR wafers with conductive ITO and thin nanostructured films of plasmonically active Au functionalized with 3-mercapto-2-butanone (MCB). We show that layered electrodes on thin Si ATR wafers with MCB are sensitive to applied potential and that the distortions in the linear and 2D IR spectra are heavily dependent on the morphology of the Au surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Nitrogen Out-of-Plane (NOOP) Mechanism for Imine-Based Light-Driven Molecular Motors

Light-driven molecular motors have generated considerable interest due to their potential applications in material and biological systems. Recently, Greb and Lehn reported a new class of molecular motors, chiral N-alkyl imines, which undergo unidirectional rotation induced by light and heat. The mechanism of unidirectional motion in molecular motors containing a C═N group has been assumed to consist of photoinduced torsion about the double bond. In this work, we present a computational study of the photoisomerization dynamics of a chiral N-alkyl imine motor. We find that the location and energetics of minimal energy conical intersections (MECIs) alone are insufficient to understand the mechanism of the motor. Furthermore, a key part of the mechanism consists of out-of-plane distortions of the N atom (followed by isomerization about the double bond). Dynamic effects and out-of-plane distortions are critical to understand the observed (rather low) quantum yield for photoisomerization. Finally, our results provide hints as to how the photoisomerization quantum yield might be increased, improving the efficiency of this class of molecular motors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Noniterative finite amplitude methods for E 1 and M 1 giant resonances

The finite amplitude method (FAM) is a very efficient approach for solving the fully self-consistent random-phase approximation (RPA) equations. We use FAM to rederive the RPA matrices for Skyrme functionals, calculate the electric dipole ( E 1) and the magnetic dipole ( M 1) giant resonances, and compare the results with available experimental and evaluated data. For the E 1 transitions in heavy nuclei, the calculations reproduce well the resonance energy of the photoabsorption cross sections. In the case of M 1 transitions, we show that the residual interaction does not affect the transition strength of double-magic nuclei, which suggests that the spin terms in the Skyrme force currently neglected in the present computation could improve the agreement between FAM and experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Controlling substrate temperature with infrared heating to improve mechanical properties of large-scale printed parts

Additively manufactured parts made with polymer extrusion techniques can be 50-75% weaker in the z-direction (across layers) than in the x- and y-directions. This has been attributed to poor mobility of polymer chains and a low degree of entanglement across a cold deposition interface. This is particularly a challenge when printing large-scale parts, such as with the Big Area Additive Manufacturing (BAAM) system, because layer times can exceed several minutes. The current work presents a method for controlling the temperature of the substrate material on the BAAM just prior to deposition using infrared heating lamps. Additionally, long layer times were simulated by actively cooling the material following deposition of each layer. The effect of substrate temperature on the z-direction mechanical properties of 20% carbon fiber reinforced acrylonitrile butadiene styrene (ABS) was measured for an initial temperature ranging from 50 °C to 150 °C and a preheated temperature ranging from 150 °C to 220 °C. Infrared preheating proved to be very effective when applied to substrates that had cooled considerably, almost doubling the tensile strength and increasing the fracture toughness by a factor of 7x.

36 MATERIALS SCIENCE↗

Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte

Electroconvective (EC) instability and its influence on surface morphological perturbations (Morph) are important in many applications, including electrodialysis, batteries, and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the EC and Morph instabilities using two approaches. In the bulk analysis, we derive the asymptotic solutions for small and large wave numbers by neglecting the space charge layer and imposing a second kind electroosmosis slip velocity boundary condition on the electroneutral bulk region. In the full analysis, the instability of the entire region of the liquid electrolyte is analyzed using the ultraspherical spectral method. Both studies show that the flow significantly affects the EC instability. The imposed flow distorts the concentration field, causing a sheltering effect which hinders the ion transport from low- to high-concentration regions, and therefore suppresses the EC instability below a certain wave number. In combination with the viscous stabilization of the high wave number modes by the space charge layer, a sufficiently strong imposed flow can fully suppress the EC instability. The increment in the critical voltage for the instability onset is roughly proportional to the square root of the product of imposed velocity and double layer thickness. The imposed flow has a smaller effect on the Morph instability, except that it may remove the morphological modes resulting from the EC instability and thereby change the wave number of the most unstable mode.

42 ENGINEERING↗

Effects of Testosterone on Mixed-Muscle Protein Synthesis and Proteome Dynamics During Energy Deficit

Effects of testosterone on integrated muscle protein metabolism and muscle mass during energy deficit are undetermined. The objective was to determine the effects of testosterone on mixed-muscle protein synthesis (MPS), proteome-wide fractional synthesis rates (FSR), and skeletal muscle mass during energy deficit. This was a randomized, double-blind, placebo-controlled trial. The study was conducted at Pennington Biomedical Research Center. Fifty healthy men. The study consisted of 14 days of weight maintenance, followed by a 28-day 55% energy deficit with 200 mg testosterone enanthate (TEST, n = 24) or placebo (PLA, n = 26) weekly, and up to 42 days of ad libitum recovery feeding. Mixed-MPS and proteome-wide FSR before (Pre), during (Mid), and after (Post) the energy deficit were determined using heavy water (days 1-42) and muscle biopsies. Muscle mass was determined using the D3-creatine dilution method. Mixed-MPS was lower than Pre at Mid and Post (P < 0.0005), with no difference between TEST and PLA. The proportion of individual proteins with numerically higher FSR in TEST than PLA was significant by 2-tailed binomial test at Post (52/67; P < 0.05), but not Mid (32/67; P > 0.05). Muscle mass was unchanged during energy deficit but was greater in TEST than PLA during recovery (P < 0.05). The high proportion of individual proteins with greater FSR in TEST than PLA at Post suggests exogenous testosterone exerted a delayed but broad stimulatory effect on synthesis rates across the muscle proteome during energy deficit, resulting in muscle mass accretion during subsequent recovery.

Endocrinology & Metabolism↗

Cathodic Protection Modeling for Hanford Underground Double-Shell Tank Farms

Hanford stores millions of gallons of radioactive and chemically hazardous waste from the production of weapon materials in tank farms consisting of underground carbon-steel storage tanks surrounded by reinforced concrete. Six of these Hanford tank farms use double-shell storage tanks (DSTs). The DST farms were constructed from 1968 to 1986 with a planned 40–50 year design life, so some are already operating beyond their initial life expectancy. Ultrasonic testing (UT) has indicated significant thinning on the bottom of the secondary (outer) liner of these tanks, believed to arise from groundwater intrusion driving concrete side corrosion. There is no direct access to the steel/concrete interface between the tank and the concrete pad, making it difficult to apply a chemical-based mitigation strategy or to conduct repairs, but cathodic protection (CP) is a possible method to inhibit further concrete-side corrosion. Hanford already uses CP to protect below grade steel piping within the tank farms and connected to the tanks, but this system was not designed to protect the tank bottoms. CP design must account for the structures surrounding the DSTs, including the steel reinforcing bars (rebar) within the concrete pad and vault, various process lines, and the existing CP system. In this study, finite element analysis (FEA) modeling was carried out to simulate CP protection of 1) a single tank and CP anode to develop options for modeling the rebar and to compare to a simpler circuit model and 2) the entire Hanford AN tank farm as a representative example consisting of seven tanks, associated piping, and both existing and new CP anodes. Both circuit and FEA models predict that significant protective current could be delivered to the bottoms of the tanks with the addition of tank-protection anodes below the depth of the tanks. Simulations with only the existing pipe-protection anodes active confirmed that only a very small current to the tank bottoms is predicted under present conditions. Multiple simplified representations of the dome and wall rebar were tested to reduce the computational complexity of the tank-farm simulations, resulting in modeling the rebar as edge elements with a prescribed effective circumference that matches the real rebar surface area. The geometry of the rebar is also simplified into horizontal hoops around the tank walls and radial rebar over the dome with increased effective circumference to retain the target surface area. This simplification was found to greatly reduce the complexity and solution time of the models without large changes in current distributions, especially to the tank bottom. A range of values were tested for model parameters such as soil and concrete resistivities and polarization resistance to investigate their impact on the current and electric potential distributions. Depending on the parameters used, FEA simulations predict some risk of overprotection, particularly on the piping system; since overprotection can also lead to surface damage associated with hydrogen gas generation at the interface (e.g. hydrogen embrittlement or damage to coatings), this needs to be considered when refining the design of the new CP system. Comparison between the FEA models and the circuit model representation demonstrated that the circuit model could not match the predicted FEA current distribution, even when using the exact same surface areas. This discrepancy appeared to be at least partly attributable to the impact of the relative positions of the tank components and anodes to each other and to the ground surface. The FEA model accounts for the relative positions since it solves the governing equations in three dimensions, but the circuit model cannot account for the positioning. In particular, the circuit model underpredicts the current to the tank bottom and overpredicts the current to the dome compared to FEA for the baseline geometry. The FEA models omitted the electrically isolated rebar in the bottom concrete slab. However, a circuit based stray current model estimated that only 2.1% of the total current through the slab would stray into the rebar, corresponding to ~0.21 A for a target current density of 2 mA/ft2 to the tank bottom. The estimated corrosion driven by this amount of stray current is predicted to yield a lifetime of >400 years for the minimum rebar diameter, assuming an acceptable cross-section area loss of 10%.

d'Entremont, Anna [Savannah River National Laborat↗

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗