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At least 37 records · Page 2

Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians

Here, we classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard “phases” and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

97 MATHEMATICS AND COMPUTING↗

CO 2 -selective membranes containing amino acid salts for CO 2 /N 2 separation

In this paper, facilitated transport membranes comprising polyvinylamine (PVAm) as fixed carrier and different amino acid salts (AAS) as mobile carriers were synthesized for post-combustion capture. The AAS carriers were prepared by deprotonating alanine (Ala), lysine (Lys), and proline (Pro) with 2-(1-piperazinyl)ethylamine (PZEA). CO 2 separation performances of the membranes with these AAS carriers were compared, and the AAS effectiveness to facilitate transport of CO 2 was in the order of PZEA-Pro > PZEA-Lys > PZEA-Ala. Here, the membrane comprising 35 wt.% PVAm and 65 wt.% PZEA-Pro at 57 °C rendered a promising CO 2 permeance of 936 GPU and a CO 2 /N 2 mixed gas selectivity of 193. When the PVAm was reduced to 15 wt.%, i.e., its 20 wt.% was replaced by the mobile carrier of PZEA-Sar (sarcosinate), the permeance further improved to 947 GPU with a remarkable CO 2 /N 2 selectivity of 210. Moreover, thermal gravimetric analysis showed a good thermal stability of the membrane, and membrane stability testing also gave stable transport performance. Furthermore, spectroscopic ellipsometry analysis exhibited a uniform membrane selective layer and an excellent agreement on the membrane thickness of ca. 170 nm measured independently by SEM. In addition, the membranes presented in this paper surpassed both the Robeson upper bound and the modified upper bound, indicating a great potential for CO 2 capture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Newton-Okounkov bodies of chemical reaction systems

Despite their noted potential in polynomial-system solving, there are few concrete examples of Newton-Okounkov bodies arising from applications. Accordingly, in this paper, we introduce a new application of Newton-Okounkov body theory to the study of chemical reaction networks and compute several examples. An important invariant of a chemical reaction network is its maximum number of positive steady states Here, we introduce a new upper bound on this number, namely the ‘Newton-Okounkov body bound’ of a chemical reaction network. Further, through explicit examples, we show that the Newton-Okounkov body bound of a network gives a good upper bound on its maximum number of positive steady states. We also compare this Newton-Okounkov body bound to a related upper bound, namely the mixed volume of a chemical reaction network, and find that it often achieves better bounds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantifying Uncertainty in HPC Job Queue Time Predictions

High Performance Computing (HPC) has developed at an unprecedented pace in recent decades. This growth has demanded corresponding development in the area of HPC Operational Data Analytics (ODA), which encompasses a wide range of data analysis techniques, ML/AI efforts, tools, and visualizations. Published studies in ODA offer a variety of practical ways to inform HPC users, administrators, procurement managers, and other stakeholders. Uncertainty analysis, however, is rare in the related published literature. For instance, we identify only 1 out of 14 existing studies focused on job queue time prediction that investigates the uncertainty aspect of their proposed predictions. We recognize the utmost importance uncertainty quantification can have in such predictive analytics solutions, with consequences in how users interpret information they receive, and attempt to bridge this gap. With the goal of improving access to such insights, we develop a process for determining upper and lower bounds of the predicted queue times of a regression model at a specified confidence level. Our current research is focused on the uncertainty in predicting job queue times, yet our approach may be employed in predicting other metrics.

HPC↗

Additive manufacturing of two-phase lightweight, stiff and high damping carbon fiber reinforced polymer microlattices

Carbon fiber reinforced polymer (CFRP) composite is known for its high stiffness-to-weight ratio and hence is of great interest in several engineering fields such as aerospace, automotive, defense, etc. However, such a composite is not suitable for energy dissipation as failure occurs with very little or no plastic deformation. Herein, we present an extendable multi-material projection microstereolithography process capable of producing carbon-fiber-reinforced cellular materials that achieve simultaneously high specific stiffness and damping coefficient. Inspired by the upper bounds of stiffness-loss coefficient in a two-phase composite, we designed and additively manufactured CFRP microlattices with soft phases architected into selected stiff-phase struts. Our results, confirmed by experimental and analytical calculations, revealed that the damping performance can be significantly enhanced by the addition of only a small fraction of the soft phase. The presented design and additive manufacturing strategy allow for optimizing mutually exclusive properties. As a result, these CFRP microlattices achieved high specific stiffness comparable to commercial CFRP, technical ceramics, and composites, while being dissipative like elastomers.

36 MATERIALS SCIENCE↗

Offering of Variable Resources in Regulation Markets with Performance Targets: An Analysis

To date, wind and solar power plants have mainly provided energy. Going forward, with the application of appropriate controls, they can offer additional grid services, such as regulating reserves. Additional grid services can present an opportunity for additional value streams to wind and solar power plants. However, the additional value might not be realized when operator-determined performance targets and settlement adjustments for the delivery of regulation capacity are disregarded. Additionally, this article studies the participation of variable resources in centralized regulation markets. We derive analytical results for regulation offers in terms of quantity and price considering that a variable resource does not want to risk being disqualified as a regulation provider, incurring losses, or foregoing more profitable opportunities. Our analysis suggests that U.S. operator-determined performance targets impose an upper bound on the quantity of a variable resource’s regulation offer; and settlement adjustments for the delivery of regulation affect the price at which variable resources offer and the calculations of opportunity costs in case of imperfect regulation delivery.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Characterizing the Reproducibility of Noisy Quantum Circuits

The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from ill-characterized fluctuations in device noise may lead to computational errors and irreproducible results. While device characterization offers a direct assessment of noise, an outstanding concern is how such metrics bound the reproducibility of a given quantum circuit. Here, we first directly assess the reproducibility of a noisy quantum circuit, in terms of the Hellinger distance between the computational results, and then we show that device characterization offers an analytic bound on the observed variability. We validate the method using an ensemble of single qubit test circuits, executed on a superconducting transmon processor with well-characterized readout and gate error rates. The resulting description for circuit reproducibility, in terms of a composite device parameter, is confirmed to define an upper bound on the observed Hellinger distance, across the variable test circuits. This predictive correlation between circuit outcomes and device characterization offers an efficient method for assessing the reproducibility of noisy quantum circuits.

97 MATHEMATICS AND COMPUTING↗

Benchmark CO 2 separation achieved by highly fluorinated nanoporous molecular sieve membranes from nonporous precursor via in situ cross-linking

Molecular sieve membranes with rigid micropores and CO 2 -philic functionalities within the architectures are promising candidates in CO 2 separation. However, the development of ctieve approaches for their fabrication still remains a significant challenge. In this study, an in situ cross-linking strategy is developed for the preparation of nanoporous fluorinated moleffecular sieve membranes using commercially available dense and non-porous polystyrene (M PS ) as a precursor template. Based on the dehydrative Friedel-Crafts reactions with highly fluorinated benzylic alcohols, M PS membranes are cross-linked in situ upon exposure to Brønsted acid (CF 3 SO 3 H), affording fluorinated microporous polymeric membranes with surface areas up to 523 m 2 g –1 and the presence of micropores centered at 1.1–1.3 nm as well as ultra-micropores (~0.6 nm). The obtained modified membranes exhibit good ideal CO 2 permeability of 797 barrer and CO 2 /N 2 selectivity of 28.5. In addition, high fluorine content (up to 28.5 wt%) and good thermal stability made the cross-linked membranes promising candidates to produce fluorinated carbon molecular sieve membranes with improved textural properties, exhibiting surface areas up to 1020 m 2 g –1 and ultra-micropores of ~0.4 nm. These membranes achieve superior CO 2 /N 2 separation performances exceeding the Robeson upper bound limit (2008).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon molecular-sieve membranes developed from a Tröger’s base polymer and possessing superior gas-separation performance

Carbon molecular-sieve membranes possess tremendous practical advantages over unary polymer membranes by providing high gas-separation performance levels, coupled with excellent mechanical and chemical stability. Improving their overall effectiveness greatly expands the competitiveness of this class of membranes. In the present study, carbon membranes are fabricated from a Tröger’s base polymer as the precursor. Further, by optimizing the carbonization conditions, the gas-separation performance of the resultant membranes are significantly enhanced. Under optimized conditions, a H 2 permeability of up to 1135 Barrer is achieved, with a corresponding H 2 /CH 4 selectivity of 1170 and a CO 2 /CH 4 selectivity of 238. While increasing the operating temperature slightly reduces the selectivity, it still remains in the high-separation region. Overall, the measured separation performance levels for H 2 -related separations, i.e., H 2 /CH 4 , H 2 /N 2 and H 2 /CO 2 , all substantially exceed the Robeson upper bound. Moreover, the CO 2 /CH 4 separation efficacy also lies above the 2019 upper bound, indicating that the carbon membranes developed in the present work are versatile and promising for many different gas-separation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Superior CO 2 /N 2 separation performance of highly branched Poly(1,3 dioxolane) plasticized by polyethylene glycol

With its high content of CO 2 -philic ether oxygen groups, poly(1,3-dioxolane) (PDXLA) has emerged as an attractive platform to achieve excellent CO 2 /N 2 separation properties for post-combustion carbon capture. Herein we demonstrate that the separation properties of PDXLA can be further enhanced by plasticizing with miscible polyethylene glycol (PEG)-based additives using an integrated experimentation and modeling approach. The effects of the chain end groups and loading level of the additives on the physical properties of the blends are thoroughly investigated, including glass transition temperature (T g ), fractional free volume, and gas transport properties, and the effects can be satisfactorily described using models available for homogeneous blends. Notably, a T g -integrated free volume model is adapted to successfully interpret the unified effect of the blend composition and temperature on gas diffusivity and permeability. A sample containing 45 mass% PEG dimethyl ether (PEGDME with a molecular mass of 240 g/mol) displays stable mixed-gas CO 2 permeability of 1540 Barrer and CO 2 /N 2 selectivity of 40 when challenged with a model flue gas at 60 °C, outperforming Robeson's 2008 upper bound. Elucidating how small plasticizers impact gas transport in homogeneous blends may unravel a facile way to design high-performance membranes for gas separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Complexity growth in integrable and chaotic models

We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($\sqrt{N}$), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(e N ), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 (WECs). This work considers the floating sphere used in the OES Task 10 WEC modeling and verification effort for analysis. Analytical equations are derived to determine bounds on displacement amplitude, time-averaged power (TAP), and power-take-off (PTO) force. A unique result found shows that the TAP absorbed by a WEC can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force was derived that provides lower and upper bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression only provides a lower bound, as there is theoretically no upper bound. These bounds assist in comparing the performance of the floating sphere if it were to extract energy using surge or heave motion. The analysis shows because of differences in hydrodynamic coefficients for each oscillating mode, there are different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on TAP while utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate TAP with a nonideal PTO is modified by the electrical conversion efficiency and the ratio of the PTO spring and damping coefficients. Furthermore, the PTO spring and damping coefficients were separated in the expression, allowing for limits to be set on the PTO coefficients to ensure net power generation.

16 TIDAL AND WAVE POWER↗

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↗

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↗

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↗

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↗

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↗

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↗