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At least 73 records · Page 4

Laplace-transform technique for deriving thermodynamic equations from the classical microcanonical ensemble

A direct and convenient method is presented for deriving expressions which equate any thermodynamic state function to averages of specific dynamical functions and their fluctuations over the classical microcanonical distribution. Specific expressions are obtained for a variety of thermodynamic quantities. The effect of various entropy definitions on the results are assessed, and the latter are compared to previous work in the literature. The derived formulas are applied to the analysis of molecular-dynamics computer simulations.

Pearson, E. M.↗

Mathematical Description of Dendrimer Structure

Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.

Majoros, Istvan J.↗

Riverine dissolved organic matter transformations increase with watershed area, water residence time, and Damköhler numbers in nested watersheds

Abstract Quantifying the relative influence of factors and processes controlling riverine ecosystem function is essential to predicting future conditions under global change. Dissolved organic matter (DOM) is a fundamental component of riverine ecosystems that fuels microbial food webs, influences nutrient and light availability, and represents a significant carbon flux globally. The heterogeneous nature of DOM molecular composition and its propensity for interaction (i.e., functional diversity) can characterize riverine ecosystem function across spatiotemporal scales. To investigate fundamental drivers of DOM diversity, we collected seasonal water samples from 42 nested locations within five watersheds spanning multiple watershed sizes (~ 5 to 30,000 km 2 ) across the United States. Patterns in DOM molecular richness, aromaticity, relative abundance of N-containing formulas, and putative biochemical transformations derived from high-resolution mass spectrometry were assessed across gradients of explanatory variables associated with watershed characteristics (e.g., watershed area, water residence time, land cover). We found that putative biochemical transformations were more strongly related to explanatory variables across watersheds than common bulk DOM parameters and that watershed area, surface water residence time and derived Damköhler numbers representing DOM reactivity timescales were strong predictors of DOM diversity. The data also indicate that catchment-specific land cover factors can significantly influence DOM diversity in diverging directions. Overall, the results highlight the importance of considering water residence time and land cover when interpreting longitudinal patterns in DOM chemistry and the continued challenge of identifying generalizable drivers that are transferable across watershed and regional scales for application in Earth system models. This work also introduces a Findable Accessible Interoperable Reusable (FAIR) dataset (> 300 samples) to the community for future syntheses.

54 ENVIRONMENTAL SCIENCES↗

Electric dipole moments in 5+3 flavor weak effective theory

A fully generic treatment of electric dipole moments (EDMs) is presented in the CP-violating and flavor-conserving weak effective field theory (WET) with five flavors of quarks and three flavors of leptons. We systematically analyze leading contributions to EDMs originating from QCD and QED renormalization group running between the electroweak scale and low energy scales of about 2 GeV. We include the full one-loop anomalous dimension and a subset of two-loop corrections, as well as threshold corrections at the bottom, charm and τ masses. This allows us to derive master formulae in the space of generic WET for the neutron and proton EDMs, for EDMs of diamagnetic atoms, and for the precession frequencies constrained in molecular EDM experiments, from which bounds on the electron EDM are extracted. In particular, our master formulae capture the contributions of WET CP-violating operators with heavy quark and lepton flavors. As an application, we study EDM constraints on the Yukawa couplings of the Higgs boson, in both the linear and non-linear realizations of electroweak symmetry breaking.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Computer program for calculation of ideal gas thermodynamic data

Computer program calculates ideal gas thermodynamic properties for any species for which molecular constant data is available. Partial functions and derivatives from formulas based on statistical mechanics are provided by the program which is written in FORTRAN 4 and MAP.

Gordon, S.↗

The molecular velocity of sound

The molecular velocity of sound was calculated according to Rao's formula and the temperature and concentration dependences of this value were studied in aqueous solutions of alkali and alkaline-earth halides. Study of relative association brought to light characteristic effects of ions. The variation of the relative association can be explained by a breaking of hydrogen bonds by ions and thermal agitation.

Auslaender, D.↗

On the possibility of analytical approximation of line forms during random disorders of the resonance frequencies in molecular vibration-rotation spectra for satellite sounding

The generalization spectral line contour concept and formulas for a two component mixture, as well as consequences of the general formula are discussed. The calculation procedure, initial information, calculation results and comparison of calculations with available experimental data, for radiation absorption in three CO2 bands are presented.

Fomin, V. V.↗

Theory for microwave thermal emission from a layer of cloud or rain

Microwave thermal emission from a layer of cloud or rain consisting of spherical particles has been investigated. Scattering effects are studied in great detail with both numerical and analytical approaches. In the absence of ground emission, it is found that scattering induces brightening for optically thin layers and vice versa for optically thick layers. As a function of observation angle, brightening occurs near nadir, while darkening occurs at large angles in the case of small optical thickness. For large optical thickness, darkening occurs at all angles because of backscattering effects. When the layer of cloud or rain is above an air layer and an ocean surface at a higher temperature, it is found that the darkening effect at large optical thickness is much more pronounced. The darkening effect is also larger for vertical polarizations because the ocean emits more vertically polarized components. The effect of thermal emission and molecular absorption by atmospheric gases is also taken into account. Results obtained from analytical formulas under single-scattering assumptions are compared and illustrated.

Tsang, L.↗

Ground and excited state gradients with end-to-end differentiable semiempirical quantum chemistry

Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born–Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree–Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bimolecular Chemistry in the Ultracold Regime

Advances in atomic, molecular, and optical physics techniques allowed the cooling of simple molecules down to the ultracold regime ([Formula: see text]1 mK) and opened opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques such as mass spectrometry and ion imaging significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short range. We discuss a series of studies on the reaction KRb + KRb → K 2 + Rb 2 initiated below 1 μK, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products.

Chemistry↗

Modification of a force field for molecular dynamics simulations of silicon etching by chlorine atoms

Here, a modified classical molecular dynamics (MD) force field is presented for the interaction between silicon (Si) and chlorine (Cl). The original version of the force field is shown to significantly overestimate the probability of Si etching by thermal Cl atoms. However, the modified force field corrects this problem and results in generally good agreement with experimental data. Further, it is shown that while the modification of the force field improves the prediction of Si spontaneous etching with Cl atoms, it does not degrade predictions of atomic-layer etching of Si with Cl[Formula: see text] molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗

Remote-Sensing Reflectance and Inherent Optical Properties for Optically Deep Waters: A Revisit

Remote-sensing reflectance (r(rs)) is defined as the ratio of upwelling radiance to downwelling irradiance. Relationships between remote-sensing reflectance and inherent optical properties serve as the basis for ocean-color modeling, as well as for spectral deduction of oceanic constituents through analytical/semi-analytical models of ocean color. A decade ago, a simple and concise formula based on Monte Carlo simulations was developed by relating rrs to a property u, the ratio of backscattering (b(b)) to the sum of absorption (a) and backscattering (u = b(b)/(a+b(b))). This relationship generally ignored the shape differences in phase functions between molecular scattering and particle scattering. In this study, the relationship is updated with separate parameters for molecular and particle scattering, based on the Radiative Transfer Equation through use of Hydrolight numerical solutions. The new approach fits r(rs) better than an earlier traditional formula, for both clear and turbid waters.

Lee, Zhong-Ping↗

Spinodal enhancement of fluctuations in nucleus-nucleus collisions

Subensemble Acceptance Method (SAM) [1, 2] is an essential link between measured event-by-event fluctuations and their grand canonical theoretical predictions such as lattice QCD. The method allows quantifying the global conservation law effects in fluctuations. In its basic formulation, SAM requires a sufficiently large system such as created in central nucleus-nucleus collisions and sufficient space-momentum correlations. Directly in the spinodal region of the First Order Phase Transition (FOPT) different approximations should be used that account for finite size effects. Thus, we present the generalization of SAM applicable in both the pure phases, metastable and unstable regions of the phase diagram [3]. Obtained analytic formulas indicate the enhancement of fluctuations due to crossing the spinodal region of FOPT and are tested using molecular dynamics simulations. A rather good agreement is observed. Using transport model calculations with interaction potential we show that the spinodal enhancement of fluctuations survives till the later stages of collision via the memory effect [4]. However, at low collision energies the space-momentum correlation is not strong enough for this signal to be transferred to second and third order cumulants measured in momentum subspace. This result agrees well with recent HADES data on proton number fluctuations at $\sqrt{S_{NN}}$ = 2.4 GeV which are found to be consistent with the binomial momentum space acceptance [5].

Poberezhnyuk, Roman↗

General contamination criteria for optical surfaces

Physical models are developed for establishing criteria to decide on the acceptable contamination level of optical devices in space-borne conditions. Optical systems can be degraded in terms of decreased throughput, i.e., transmissivity or reflectivity, or increases in the total integrated scatter (TIS). Performance losses can be caused by particulate accretion, molecular film accretion, and impact cratering. A quantitative relationship is defined for film thickness and loss of throughput. Formulas are also developed for cases where induced surface defects are larger than the desired viewing wavelengths, or smaller or of the same order of the observed wavelengths. The techniques are used to quantify the degradation of a VUV solar coronagraph, a VUV stellar telescope, and a solar cell due to TIS. Applications are projected for estimating the contamination sensitivity of specific instruments, assessing the contamination hazard from known particulates, or to define clean room standards.

Bremer, J. C.↗

Polysilaketals: High‐Performance Polyether‐Based Electrolytes with Tunable Disubstituted Silane Linkers

Polymer electrolytes exhibit higher energy density and improved safety in lithium-ion batteries relative to traditionally used liquid electrolytes but are currently limited by their lower electrochemical performance. Aiming to access polymer electrolytes with competitive electrochemical properties, we developed the anionic ring-opening polymerization (AROP) of cyclic silaketals to synthesize amorphous silicon-containing polyether-based electrolytes with varying substituent bulk of the general formula [OSi(R)2(CH2CH2O)2]n (R=alkyl, phenyl). As opposed to previously reported uncontrolled polycondensation routes toward low molecular weight polysilaketals, AROP allows access to targeted molecular weights above the entanglement threshold of the polymers. The polysilaketal with the lowest steric bulk (P(OSiMe,Me-2EO)) exceeds the conductivity of poly(ethylene oxide) (PEO), a leading polymer electrolyte. To the best of our knowledge, this is the first solid polymer electrolyte to achieve this benchmark. Steric bulk in polysilaketals was found to impart stability and two bulkier polysilaketals, P(OSiEt,Et-2EO) and P(OSiMe,Ph-2EO), exhibited higher current fractions than PEO over a wide range of salt loadings. Moreover, the efficacy of P(OSiEt,Et-2EO) was competitive with that of PEO. Taken together, the tunable and competitive electrochemical properties of polysilaketals validate the systematic incorporation of silyl groups as a strategy to access high performance polymer electrolytes.

Rugh, Haley J↗

Franck-Condon factor formulae for astrophysical and other molecules

Simple closed-form, approximate, analytic expressions for Franck-Condon factors are given. They provide reliable estimates for Franck-Condon factor arrays for molecular band systems for which only vibrational-frequency, equilibrium internuclear separation and reduced mass values are known, as is often the case for astrophysically interesting molecules such as CeO, CoH, CrH, CrO, CuH, GeH, LaO, NiH, SnH, and ZnH for band systems of which Franck-Condon arrays have been calculated.

Nicholls, R. W.↗