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At least 217 records · Page 12

Accuracy of approximations to the Navier-Stokes equations

The systems of truncated differential equations that have been proposed to reduce the complexity and large computational costs of solutions to the full Navier-Stokes equations are considered. These systems are computationally efficient and capture all the physically relevant behavior. The systems follow a certain hierarchy: (1) the classical boundary-layer equations with specified edge properties (usually the streamwise pressure distribution); (2) the coupled boundary-layer/inviscid equations; (3) the so-called thin-layer equations that discard streamwise diffusion; and (4) the Navier-Stokes equations. Consideration is given to each of these approximations applied to an incompressible, laminar-separating flow at low and moderate Reynolds numbers. It is pointed out that for any flow or region of flow for which viscous-inviscid interaction effects are small, classical boundary-layer equations will provide a satisfactory description of the viscous flow at a fraction of the computational cost of any higher approximations.

Murphy, J. D.↗

The effect of finite-amplitude baroclinic waves on passive, low-level, atmospheric constituents, with applications to comma cloud evolution

The redistribution of a low-level, passive constituent of the atmosphere under the influence of a growing baroclinic wave is examined by a series of analytical calculations based on a two-level, highly truncated model. It is shown that a constituent confined to the lower half of the atmosphere, and initially homogeneous in the horizontal, will tend to achieve maximum concentration in the low pressure/warm sector portion of the wave and minimum concentration in the high pressure/cold outbreak region with sharpest gradient between the maxima and minima roughly coinciding with the cold front. This distribution is further accentuated if an initial meridional gradient of the constituent exists. Assuming as a rough first approximation, that water vapor can be considered to be such a passive constituent, it is shown that the implied relative humidity field and cloud distribution will tend to evolve into the comma-type form commonly observed on satellite images of mid-latitude cyclone waves. Moreover, the solution is shown to replicate the complex flow regime associated with the comma formation, elucidating the dynamical roles of vertical motion and advection in the cloud evolution.

Saltzman, B.↗

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗

Performance of an aero-space plane propulsion nozzle

An inviscid and viscous analysis is provided for an exposed half nozzle that is used with a scramjet for thrust generation. The analysis is based on the inviscid theory of a two-dimensional, minimum length nozzle with a curved inlet surface, where the flow may be sonic or supersonic. Inlet conditions are prescribed and the gas is assumed to be perfect. Viscous, and when appropriate inviscid, nondimensional parametric results are provided for the thrust, lift, heat transfer, pitching moment, and a variety of boundary-layer thicknesses. In addition to global results, wall distributions of pressure, heat transfer, etc., are provided. The analysis demonstrates that the nozzle produces a considerable lift force whose magnitude may exceed the thrust and a significant pitching moment. The thrust is quite sensitive to the inlet Mach number; it rapidly decreases as the inlet Mach number increases There is little loss in the thrust as the nozzle's downstream wall is truncated. The corresponding decrease in lift and the pitching moment is moderate.

Emanuel, George↗

Quantifying Uncertainties In Neutron-Alpha Scattering With Chiral Nucleon-Nucleon And Three-Nucleon Forces

We report that modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Starting from NN potentials up to fifth order (N 4 LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confidence intervals for the 3N contact and contact-plus-one-pion-exchange low-energy constants (c E and c D ) contribute to the overall uncertainty budget of many-body calculations of neutron- 4 He (n-α) elastic scattering. We compute structure and reaction observables for three-, four-, and five-nucleon systems within the ab initio frameworks of the no-core shell model and no-core shell model with continuum. Using a small set of design runs, we construct a Gaussian process model (GPM) that acts as a statistical emulator for the theory. With this, we gain insight into how uncertainties in the 3N low-energy constants propagate throughout the calculation and determine the Bayesian posterior distribution of these parameters with Markov-Chain Monte Carlo. We find rapidly converging n-α phase shifts with respect to the chiral order. With the adopted leading-order 3N force, calculations based on the NN interaction at N 4 LO of Entem, Machleidt, and Nosyk are unable to reproduce the experimental phase shifts in the 3/2 - channel within the estimated chiral truncation errors. Closer agreement with empirical data is found when using an older parametrization of the NN interaction at order N 3 LO, and the position and width of the P-wave resonances can be used to reduce the uncertainty of the 3N low-energy constants. The present results point to a lack of spin-orbit strength when the newer parametrization of the chiral NN force up to fifth order is combined with the leading-order 3N force. The inclusion of higher-order 3N-force terms may be required to recover the missing strength. GPMs can act as fast and accurate emulators of ab initio many-body calculations of low-energy scattering and reactions of light nuclei, opening the way to a robust quantification of theoretical uncertainties grounded in the description of the underlying chiral Hamiltonian.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Numerical and Experimental Studies of the Natural Convection Flow Within a Horizontal Cylinder Subjected to a Uniformly Cold Wall Boundary Condition

Numberical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time dependent natural convection flow within a horizontal cylinder. The early time flow development and wall heat transfer is obtained after imposing a uniformly cold wall boundary condition on the cylinder. Solutions are also obtained for the case of a time varying cold wall boundary condition. Windware explicit differ-encing is used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first order accuracy is maintained in time and space. The results encompass a range of Grashof numbers from 8.34 times 10,000 to 7 times 10 to the 7th power which is within the laminar flow regime for gravitationally driven fluid flows. Experiments within a small scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer and also the decay of wall heat transfer with time.

Stewart, R. B.↗

The many-body expansion for aqueous systems revisited: 1. Water-water interactions

We revisit the Many-Body Expansion (MBE) for water-water interactions by examining the effects of the basis set, including those resulting from the Basis Set Superposition Error (BSSE) correction, on the various terms for selected sizes of water clusters up to n = 21. The analysis is performed at the second order Møller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality for the (H2O)n, n = 7, 10, 13, 16 and 21 clusters, for which we report either the complete MBE (n = 7, 10) or the one through the 6-body (n = 13) and the 5-body terms (n = 16, 21). Our results suggest that any sizeable contributions to the total cluster binding energy arising from the 5-body and larger terms are solely an artifact of the size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero at the Complete Basis Set (CBS) limit. The magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSEcorrected) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small, so that neglecting the correlation contribution in all terms above the 3-body results in an error of ??(0.1%). The BSSE correction to the largest 2-body term in the MBE was accurately estimated from the function ?? [1 + erf(-?? ??)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are separated by R, with the constants ??, ?? fitted to the calculated BSSE corrections for the individual 2-body terms of the clusters with each basis set. Our results unquestionably demonstrate that the MBE for water-water interactions converges to the 4-body term, since any finite terms above the 4-body are artifacts of the size of the basis set and can be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate many-body molecular dynamics simulations for aqueous systems.

Heindel, Joseph↗

Modal model reduction or model reduction of large space structures in frequency domain

Large space structures are characterized by a large number of modes, grouped frequencies, and small inherent damping. Model reduction techniques in time domain may not be effective due to small damping. The model truncation method is generally used. This method can not solve the problem of grouped frequencies, and will lose all the information about the higher order modes. A new method developed in this paper, which tries to minimize the error of interested transfer functions, makes use of all the information of the original system, and achieves improvement not only from a smaller error of transfer functions but also from better frequency distribution.

Mifang, Ruan↗

Flow and heat transfer in the wake of a triangular arrangement of spheres

This research work seeks to investigate the influence of spacing and heat transfer on the wake behavior of a triangular arrangement of spheres. Four experimental configurations have been investigated at three Reynolds numbers, Re 1 = 350, Re 2 = 700, and Re 3 = 1050. Two isothermal cases were investigated with spacing between the spheres of zero and one sphere diameter, and two cases were investigated with an applied heat flux at the same spacing conditions. The time resolved particle image velocimetry results revealed various flow phenomena including flow separations, von Karman vortex shedding, and Kelvin–Helmholtz instabilities. The turbulent statistics reveal the effect of proximity and heat transfer on the time averaged values of the wake size, turbulent strengths, and Reynolds shear stress in the wake of each sphere, namely, the laminarization effects from the addition of heat and the suppression of the lead sphere wake from the proximity of the trailing spheres. These results are complemented by the application of proper orthogonal decomposition (POD) to the flow fields, which extracts the coherent structures from the flow. Here the modes that describe the coherent structures are extracted and described in detail, which provide further insight into effects of the experimental conditions on the temporal behavior of the flow. Many of the low order modes are found to be associated in pairs, corresponding to asymmetric structures or advection of a given structure downstream. The capability of POD to produce reduced order models of the flow is then utilized to facilitate vortex identification analysis. A turbulent kinetic energy based mode truncation criteria, which has been found to enhance vortex identification capability, is applied to select the POD modes and temporal coefficients to be used in the reduced order modeling. The reconstructed velocity fields are then analyzed with vortex identification algorithms to extract the vortex cores and boundaries. The combination of these approaches allows the study of the effect of proximity and heat transfer on the vortex characteristics, such as size, strength, and distribution.

42 ENGINEERING↗

Some observations of surface pressures and the near wake of a blunt trailing edge airfoil

Experiments with a truncated and untruncated airfoils of profiles NACA 640A10, were carried out in subsonic wind tunnels in a velocity range of 19m/s to 54m/s corresponding to Reynolds numbers of 200,000 to 468,000 based on the chord. Airfoil spanned the test section to achieve two dimensionality of the model. Velocity measurements, pressure measurements, and vortex shedding in the wake were measured using a hotwire and pressure transducers. The measured chordwise static pressure distribution on the smooth trailing edge airfoil along the midspan plane, agreed with the theoretical results calculated on the basis of the potential flow for that airfoil. Boundary layer profiles measured in the midspan plane, behind the maximum thickness of the airfoil show no separation of the flow. Spanwise distribution of the measured static pressure on the upper surface of the airfoil shows uniformity for both configurations with and without the boundary layer trip. This uniformity of pressure distribution and separation indicates that the flow on the airfoil was uniform and two dimensional in character.

Digumarthi, R. V.↗

Analysis of the tapered slot antenna

A method for calculating the radiation pattern of end-fire tapered slot antennas with or without dielectric substrate is presented. The method involves a two-step procedure: (1) determine the field distribution of a traveling wave along the tapered slot, and (2) compute the radiation from this slot field by using the half-plane Green's function to account for termination effects. Acceptable estimates of the slot field usually can be obtained from a stepped approximation to the tapered geometry. The method has been verified by comparisons to measured patterns for various dielectric substrates and antenna dimensions. However, the effect of lateral truncation has not yet been successfully modeled. Experimental patterns showing this effect are presented.

Janaswamy, Ramakrishna↗

Disentangling long and short distances in momentum-space TMDs

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in Λ QCD /k T . We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over k T ≤ k$^{cut}_{T}$ in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near k$^{cut}_{T}$, such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the non-perturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Bifurcation and stability of low-order steady flows in horizontally and vertically forced convection

A nonlinear spectral model of two-dimensional, shallow Boussinesq convection which responds to heating in both the horizontal and vertical directions is examined. The governing partial differential system is converted to an infinite set of ordinary differential equations and truncated to a small set to permit detailed study of the number and types of transitions from one flow configuration to another. The Hadley number and the Rayleigh number are defined as the horizontal and vertical thermal forcing mechanisms, respectively, for inclusion in the nonlinear spectral model, which is composed of three equations. The model is then used to describe steady states, linearly stable solutions, and balancing factors in unstable stratification. The number and the distribution of the steady states are found to be qualitatively independent of the aspect ratio and the Prandtl number.

Yost, D. A.↗

One-Dimensional Glassy Behavior of Ultraconfined Water Strings

Water is renowned for its anomalous behaviors, which can be linked to a distributed H-bond network in bulk water. Ultraconfinement of the water molecule can remove H-bonding, leaving only molecular water. In natural cordierite crystals, water is trapped in an orthorhombic channel with an average diameter of 5.7 Å, running through the center of the unit cell parallel to the c-axis. Calorimetric measurements reveal the existence of a one-dimensional (1D) glass linked to this water. In these channels, water molecules in truncated, sparse 1D strings interact only via dipole–dipole correlations. Here, a physical 1D glass is formed from these strings. This unusual state can be explained by a modified Ising model. This model predicts a dependence of the glass transition temperature, Tg, on the size of these domains. This is confirmed experimentally.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electronic Excitation‐Driven β‐Ga 2 O 3 Metastability Transformation and Self‐Organization Mechanism: β→κ/γ/δ Phases

Here, irradiation-driven multiphase self-organization presents emergent opportunities for the customization of nanoscale engineering properties, dynamically tuning strain-field distributions and interfacial electronic structures. Responding to intense electronic excitation-induced energy deposition, the dominant phase transformations, with varying Gibbs free energy $Δ,G^o_f$ are confirmed as β → κ → γ → δ that are located in specific microregions for Gallium (III) oxide (Ga 2 O 3 ), as follows: (i) Surface-localized interstitial accumulation under compressive stress triggers β → δ via semi-coherent interface formation. (ii) Tensile stress within latent tracks drives vacancy-mediated oxygen layer truncation (4/12 periodicity along ⟨0001⟩), stabilizing coherent 4H (ABCB) κ and 3C (ABC) β (ABC) interfaces through strain-compensated octahedral distortion. (iii) Screw dislocation-mediated lattice relaxation induces β → γ via cation disordering (Ga 3+ occupancy at β-interstitial sites), forming metastable spinel γ with mixed occupancy across 16d/8a Wyckoff sites. Irradiation-driven β-Ga 2 O 3 →κ/γ/δ transitions, as mechanistically revealed via inelastic thermal spike (i-TS) calculations and molecular dynamics simulations, induce defect-mediated nonlinear photoresponse, critical for optoelectronic engineering.

Han, Xinqing [Shandong Univ., Jinan (China)]↗

Computationally efficient subglacial drainage modelling using Gaussian process emulators: GlaDS-GP v1.0

Subglacial drainage models represent water flow at the ice–bed interface through coupled distributed and channelized systems to determine water pressure, discharge, and drainage system geometry. While they are used to understand processes such as the relationship between surface melt and ice flow, the number of uncertain model parameters and the computational cost of running models makes it difficult to adequately explore the high-dimensional parameter space and evaluate uncertainty in model predictions. Here, we develop Gaussian process (GP) emulators that make fast predictions with associated uncertainty of subglacial drainage model outputs. Using a truncated principal component (PC) basis representation, we construct a GP emulator for diurnally averaged subglacial water pressure. We also explore emulation of scalar variables describing drainage efficiency and configuration. We train the emulators using ensembles of up to 512 simulations varying eight parameters of the Glacier Drainage System (GlaDS) model on a synthetic domain intended to represent an ice-sheet margin. The emulators make predictions ∼ 1000 times faster than GlaDS simulations, with errors <3 % for the water pressure field and ∼ 5 %–9 % for drainage efficiency and configuration. We apply the emulators to explore the eight-dimensional parameter space by computing variance-based parameter sensitivity indices, finding that three parameters (ice flow coefficient, bed bump aspect ratio, and the subglacial cavity system conductivity) explain 90 % of the variance in modelled water pressure in response to parameter changes. The GP emulator approach described here is well suited to integrating observational data with models to make calibrated, credible predictions of subglacial drainage.

58 GEOSCIENCES↗

Coherent Phonon Dynamics in Plasmonic Gold Tetrahedral Nanoparticle Ensembles

Coherent phonon modes supported by plasmonic nanoparticles offer prospective applications in chemical and biological sensing. Whereas characterization of these phonon modes often requires single particle measurements, synthetic routes to narrow size distributions of nanoparticles permit ensemble investigations. Recently, the synthesis of highly monodisperse gold tetrahedral nanoparticles with tunable edge length and corner sharpness has been developed. Herein, we characterize a size series of these nanoparticles in colloidal dispersion via transient absorption spectroscopy to examine their mechanical and plasmonic responses upon photoexcitation. Oscillations of transient absorption signals are observed in the plasmon resonance and correspond to the lowest order radial breathing modes of the nanoparticles, the frequencies of which are affected by edge length and truncation of the corners. Furthermore, quality factor values ranging from 10 to 15 are observed for the oscillations that convey potential utility in mass-sensing and plasmon-exciton coupling photonics schemes. Finite-difference time domain and finite element analysis calculations establish the specific optically-relevant phonon modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗