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DOE OSTI2022

Supramolecular assemblies of polybenzimidazole and aromatic polycarboxylic acids with superior mechanical and H 2 /CO 2 separation properties

Aromatic polycarboxylic acids complex with imidazoles, forming supramolecular assemblies. Herein, we demonstrate that polybenzimidazole (PBI) can be augmented by aromatic polycarboxylic acids, including phthalic acid (PA), trimesic acid (TMA), and pyromellitic acid (PMA), and the resulting supramolecular assemblies exhibit attractive H 2 /CO 2 separation performance for precombustion carbon capture. The acid doping decreases the free volume and gas permeability but increases H 2 /CO 2 selectivity, which can be correlated with the molar ratio of the protons to PBI repeating units in the assemblies. Increasing the temperature decreases the H 2 /CO 2 selectivity because of weakened interactions. When challenged with model gas mixtures, a supramolecular assembly based on TMA shows H 2 /CO 2 separation properties superior to state-of-the-art materials and above Robeson's upper bound. Furthermore, this study elucidates the fruitful harnessing of dynamic non-covalent bonds to design robust and highly selective membranes for industrial gas separations.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Analyzing photovoltaic module mechanics using composite plate theories and finite element solutions

Deflection and stress calculated from an experimentally validated, high-fidelity finite element model (FEM) of a photovoltaic module experiencing mechanical load was compared to results from a simplified FEM treating the module laminate as a homogenized composite using a rule of mixtures approach, and further compared to analytical calculations treating the module as a Kirchoff-Love flat plate. The goal of this study was to determine the error incurred by analyzing module mechanics with varying levels of simplification, since resolving the aspect ratios of a module is computationally expensive. Homogenized FEMs were found to underpredict peak deflection under a 1.0 kPa load by between 13 and 19% for lower and upper bound application of the rule of mixtures. However, module shape was captured, implying that a useful replication of a resolved model could be achieved with a reduced, calibrated material stiffness. Homogenized stress results captured glass layer tensile stress components to within 46 to 52% at a sample location of interest, though agreement was poor through the remainder of the laminate due to the lack of material resolution. For plate theory, deflection was overpredicted by 45 to 67% for upper and lower bound homogenizations, and frame-adjacent module shapes were not adequately replicated. Stress results mirrored FEM trends but magnitudes were not well correlated to resolved model values. These results support the use of homogenized laminate models for module shape derivation, though resolved models remain necessary for stress analyses. The accuracy of plate theory was found to be inadequate for most applications.

14 SOLAR ENERGY↗

NASA NTRS1987

Reliability of voting in fault-tolerant software systems for small output spaces

Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting strategy is proposed and its performance is analyzed and compared with other voting strategies. Consensus majority strategy automatically adapts the voting to different component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and 2-of-n voting strategy an upper bound. If r is the cardinality of the output space it is proved the 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.

Mcallister, David F.↗

DOE OSTI2020

Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters: Preprint

This work revisits the theoretical limits of one-degree of freedom wave energy converters (WECs). This paper considers the floating sphere used in the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling and verification effort for analysis. Analytical equations are derived to determine bounds on the motion amplitude, time-averaged power, and power take-off (PTO) force. A unique result was found that shows the time-averaged power absorbed by a WEC can be defined solely by the inertial properties and the radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force amplitude was derived which has provided upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression can only provide a lower bound as there is theoretically no upper bound. These bounds are used to compare the performance of a floating sphere if it were to extract energy using surge or heave motion. The analysis shows that because of the differences in hydrodynamic coefficients of each oscillating mode there will be different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on power absorption while also utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate the time-averaged power with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. These were separated in the expression which allows for limits to be set on the possible values of PTO coefficients to ensure a net flow of power to the grid.

50 EE - Wind and Water Power Program - Water (EE-4↗

DOE OSTI2021

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S 2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves k ℓ (s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves f ℓ (s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters

This work revisits the theoretical limits of one-degree-of-freedom wave energy converters. This paper considers the floating sphere used in the Ocean Energy Systems Task 10 Wave Energy Converter modeling and verification effort for analysis. Analytical equations are derived to determine bounds on the motion amplitude, time-averaged power, and power-take-off (PTO) force. A unique result was found that shows the time-averaged power absorbed by a wave energy converter can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force amplitude was derived that has provided upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression can only provide a lower bound, as there is theoretically no upper bound. These bounds are used to compare the performance of a floating sphere if it were to extract energy using surge or heave motion. The analysis shows that because of the differences in hydrodynamic coefficients of each oscillating mode, there will be different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on power absorption while also utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate the time-averaged power with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. The PTO spring and damping coefficients were separated in the expression, which allows for limits to be set on the possible values of PTO coefficients to ensure a net flow of power to the grid.

50 EE - Wind and Water Power Program - Water (EE-4↗

NASA NTRS1962

Axisymmetric Snap Buckling of Conical Shells

The authors give a brief account of some of their recent analytical and numerical studies of cone buckling. limiting the discussion to axisymmetric deformations. Pertinent numerical results for the relaxation buckling of full cones subjected to uniform external pressure and Belleville springs deformed by axial edge loads are presented. In addition. bifurcation buckling problems are discussed. For a specific case. the existence of Friedrichs' intermediate buckling load, P(m). as applied to cones. is established. Upper and lower bounds for its value are given.

LOADING↗

NASA NTRS1990

Reliability of voting in fault-tolerant software systems for small output spaces

Under a voting strategy in a fault-tolerant software system there is a difference between correctness and agreement. An independent N-version programming reliability model is proposed for treating small output spaces which distinguishes between correctness and agreement. System reliability is investigated using analytical relationships and simulation. A consensus majority voting stratey is proposed and its performance is analyzed and compared with other voting strategies. A consensus voting strategy automatically adapts the voting to diffeerent component reliability and output space cardinality characteristics. It is shown that absolute majority voting strategy provides a lower bound on the reliability provided by the consensus majority, and the 2-of-n voting strategy an upper bound. If r is the cardinality of output space it is proved that 1/r is a lower bound on the average reliability of fault-tolerant system components below which the system reliability begins to deteriorate as more versions are added.

Mcallister, David F.↗

NASA NTRS1977

Analytic studies of local-severe-storm observables by satellites

Attention is concentrated on the exceptionally violet whirlwind, often characterized by a fairly vertical axis of rotation. For a cylindrical polar coordinate system with axis coincident with the axis of rotation, the secondary flow involves the radial and axial velocity components. The thesis advanced is, first, that a violent whirlwind is characterized by swirl speeds relative to the axis of rotation on the order of 90 m/s, with 100 m/s being close to an upper bound. This estimate is based on interpretation of funnel-cloud shape (which also suggests properties of the radial profile of swirl, as well as the maximum magnitude); an error assessment of the funnel-cloud interpretation procedure is developed. Second, computation of ground-level pressure deficits achievable from typical tornado-spawning ambients by idealized thermohydrostatic processes suggests that a two-cell structure is required to sustain such large speeds.

Dergarabedian, P.↗

NASA NTRS1976

Convolutional code performance in the Rician fading channel

The performance of short constraint length convolutional codes in conjunction with binary phase-shift keyed (BPSK) modulation and Viterbi maximum likelihood decoding on the classical Rician fading channel is examined in detail. Primary interest is in the bit error probability performance as a function of E sub b/N sub 0 parameterized by the fading channel parameters. Fairly general upper bounds on bit error probability performance in the presence of fading are obtained and compared with simulation results in the two extremes of zero channel memory and infinite channel memory. The efficacy of simple block interleaving in combating the memory of the channel is thoroughly explored. Results include the effects of fading on tracking loop performance and the subsequent impact on overall coded system performance. The approach is analytical where possible; otherwise resort is made to digital computer simulation.

Modestino, J. W.↗

DOE OSTI2026

Constraints on the normal branch of DGP gravity from SPT galaxy clusters with DES and HST weak-lensing mass calibration and from P l a n c k PR4 CMB anisotropies

We present constraints on the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld gravity model from the abundance of massive galaxy clusters. On scales below the nDGP crossover scale r c , the nDGP model features an effective gravitylike fifth force that alters the growth of structure, leading to an enhancement of the halo mass function (HMF) on cluster scales. The enhanced cluster abundance allows for constraints on the nDGP model using cluster samples. We employ the South Pole Telescope (SPT) cluster sample, selected through the thermal Sunyaev-Zel’dovich effect with the SPT and with mass calibration using weak-lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample contains 1,005 clusters with redshifts 0.25 < z < 1.78 , which are confirmed with the multicomponent matched filter algorithm using optical and near-infrared data. Weak-lensing data from DES and HST enable a robust mass measurement of the cluster sample. We use DES Year 3 data for 688 clusters with redshifts z < 0.95 , and HST data for 39 clusters with redshifts 0.6 < z < 1.7 . We account for the enhancement in the HMF through a semi-analytic correction factor to the standard cosmology HMF derived from the spherical collapse model in the nDGP model. We then further calibrate this model using N -body simulations. In addition, for the first time, we analyze the primary CMB temperature and polarization anisotropy measurements from Planck PR4 within the nDGP model. We obtain a competitive constraint from the joint analysis of the SPT cluster abundance with the Planck PR4 data, and report an upper bound of 1 / H 0 r c < 1.41 at 95% when assuming a cosmology with massive neutrinos.

Vogt, S. M.L. [Munich U. Observ.; LMU Munich (main↗

DOE OSTI2021

Substituted polynorbornene membranes: a modular template for targeted gas separations

Polynorbornenes are ideal materials for systematic structure–property investigations designed to correlate gas-transport properties to polymer structure. The modular nature of norbornene-based systems provides a facile route towards the synthesis of diverse polymeric materials. Though many valuable correlations between gas-permeability and polynorbornene structure have been summarized in a prior review (2017), many of these efforts focused heavily on the design of materials with high permeabilities. More recently, the design of next-generation polynorbornene membranes has shifted toward the development of materials that are highly selective for multiple targeted gas separations. Since 2017, tremendous progress has been realized in the preparation of stable and highly selective polynorbornenes for membrane-based gas separations. Examples include polynorbornene derivatives that exhibit very high selectivity for CO 2 /N 2 and light hydrocarbon (e.g., C 3 +/C 1 ) separations, some of which exhibit gas separation performances that approach or exceed the 2008 upper bound. In this work, we summarize prior findings, present recent developments in the field of advanced polynorbornene membrane materials for targeted gas separations, and provide an outlook for the future of this field of research.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1983

The threshold laws for electron-atom and positron-atom impact ionization

The Coulomb-dipole theory is employed to derive a threshold law for the lowest energy needed for the separation of three particles from one another. The study focuses on an electron impinging on a neutral atom, and the dipole is formed between an inner electron and the nucleus. The analytical dependence of the transition matrix element on energy is reduced to lowest order to obtain the threshold law, with the inner electron providing a shield for the nucleus. Experimental results using the LAMPF accelerator to produce a high energy beam of H- ions, which are then exposed to an optical laser beam to detach the negative H- ion, are discussed. The threshold level is found to be confined to the region defined by the upper bound of the inverse square of the Coulomb-dipole region. Difficulties in exact experimental confirmation of the threshold are considered.

Temkin, A.↗

NASA NTRS1997

Current Collection in a Magnetic Field

It is found that the upper-bound limit for current collection in the case of strong magnetic field from the current is close to that given by the Parker-Murphy formula. This conclusion is consistent with the results obtained in laboratory experiments. This limit weakly depends on the shape of the wire. The adiabatic limit in this case will be easily surpassed due to strong magnetic field gradients near the separatrix. The calculations can be done using the kinetic equation in the drift approximation. Analytical results are obtained for the region where the Earth's magnetic field is dominant. The current collection can be calculated (neglecting scattering) using a particle simulation code. Dr. Singh has agreed to collaborate, allowing the use of his particle code. The code can be adapted for the case when the current magnetic field is strong. The needed dm for these modifications is 3-4 months. The analytical description and essential part of the program is prepared for the calculation of the current in the region where the adiabatic description can be used. This was completed with the collaboration of Drs. Khazanov and Liemohn. A scheme of measuring the end body position is also proposed. The scheme was discussed in the laboratory (with Dr. Stone) and it was concluded that it can be proposed for engineering analysis.

Krivorutsky, E. N.↗

DOE OSTI2021

Stiff and strong, lightweight bi-material sandwich plate-lattices with enhanced energy absorption

Plate-based lattices are predicted to reach theoretical Hashin–Shtrikman and Suquet upper bounds on stiffness and strength. However, simultaneously attaining high energy absorption in these plate-lattices still remains elusive, which is critical for many structural applications such as shock wave absorber and protective devices. In this article, we present bi-material isotropic cubic + octet sandwich plate-lattices composed of carbon fiber-reinforced polymer (stiff) skins and elastomeric (soft) core. This bi-material configuration enhances their energy absorption capability while retaining stretching-dominated behavior. We investigate their mechanical properties through an analytical model and finite element simulations. Our results show that they achieve enhanced energy absorption approximately 2–2.8 times higher than their homogeneous counterparts while marginally compromising their stiffness and strength. When compared to previously reported materials, these materials achieve superior strength-energy absorption characteristics, making them an excellent candidate for stiff and strong, lightweight energy absorbing applications.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Beurling-Selberg extremization and modular bootstrap at high energies

We consider previously derived upper and lower bounds on the number of operators in a window of scaling dimensions [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] at asymptotically large \Delta Δ in 2d unitary modular invariant CFTs. These bounds depend on a choice of functions that majorize and minorize the characteristic function of the interval [\Delta - \delta,\Delta + \delta] [ Δ − δ , Δ + δ ] and have Fourier transforms of finite support. The optimization of the bounds over this choice turns out to be exactly the Beurling-Selberg extremization problem, widely known in analytic number theory. We review solutions of this problem and present the corresponding bounds on the number of operators for any \delta \geq 0 δ ≥ 0 . When 2\delta \in \mathbb Z_{\geq 0} 2 δ ∈ ℤ ≥ 0 the bounds are saturated by known partition functions with integer-spaced spectra. Similar results apply to operators of fixed spin and Virasoro primaries in c>1 c > 1 theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Crosslinked Matrimid®-like polyimide membranes with unimodal network structure for enhanced stability and gas separation performance

Gas separation membranes have attracted academic and industrial attention, and crosslinking has been identified to be one of the most effective ways to enhance membrane stability. In this paper, a series of crosslinked Matrimid®-like films with unimodal network structures are prepared via thermally end-linking phenylethnyl-terminated BTDA-DAPI oligomers with well-controlled molecular weight (i.e., 3000–15,000 g/mol), wherein the crosslink density (the inter-crosslink chain length) of resulting unimodal networks is systematically varied by using oligomers with various molecular weight. Comprehensive characterizations of chemical structure, thermal properties, microstructures are performed. Pure-gas permeation measurements are performed focusing on H 2 /CH 4 and CO 2 /CH 4 separations as a function of crosslink density. In sharp contrast to the commonly observed permeability reduction in randomly crosslinked networks, all the crosslinked unimodal films, even when densely crosslinked, present markedly enhanced permeability and well-maintained ideal selectivity relative to the uncrosslinked linear counterpart, leading to almost horizontal movements towards upper bounds along with expectedly enhanced membrane stability. In conclusion, it is concluded that introducing bulky groups at the crosslink sites provide a practical means to counteract the densification effect induced by crosslinking and the construction of unimodal networks exemplifies a fundamentally new strategy to regulate the microstructure and property of crosslinked membranes for gas separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Matrimid substrates with bicontinuous surface and macrovoids in the bulk: A nearly ideal substrate for composite membranes in CO 2 capture

Scalable fabrication of thin-film composite (TFC) membrane for post-combustion carbon capture is often limited by the availability of high-performance nanoporous substrate. Ideally, the substrate should allow for fast gas transport at the selective layer/substrate interface as well as in the bulk of the substrate. In this study, highly permeable Matrimid substrates were prepared via vapor- and nonsolvent-induced phase separations. The phase separation mechanism of the Matrimid®/N-methyl-2-pyrrolidone casting solution was modulated by the addition of LiCl to control the solution thermodynamic stability, and nanoporous Matrimid substrates were formed with a bicontinuous surface and macrovoids in the bulk. This hierarchically optimized structure resulted in a CO 2 permeance of 2.60 × 10 5 GPU (1 GPU = 1 × 10 –6 cm 3 (STP) cm –2 s –1 cmHg –1 = 3.349 × 10 –10 mol m –2 s –1 Pa –1 ), which was ca. 11 times more permeable than a benchmark polyethersulfone substrate with cellular pores. The benefit of using this new substrate was demonstrated by coating a 170-nm amine-containing polymer to form a TFC facilitated transport membrane. The membrane exhibited a CO 2 permeance of 932 GPU at 57°C, which was 72 GPU higher than the counterpart coated on the benchmark substrate. Meanwhile, the CO 2 /N 2 selectivity was remained at 158. This permeance improvement could be well explained by the resistance-in-series model, where the improved permeance was attributed to the reductions in substrate and lateral diffusion mass transfer resistances. The upper bound (UB) analysis indicates that the Matrimid substrate is nearly ideal for the state-of-the-art polymers for CO 2 /N 2 separation. Here, the substrate improvement could also reduce the parasitic energy associated with the membrane process due to the reduced membrane cost and flue gas compression requirement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗