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Conformal duality of the nonlinear Schrödinger equation: Theory and applications to parameter estimation

The nonlinear Schrödinger equation (NLSE) in one spatial dimension has stationary solutions similar to those of the linear Schrödinger equation (LSE) as well as more exotic solutions such as solitary waves and quantum droplets. Here, we present a newly discovered conformal duality which unifies the stationary and time-dependent traveling-wave solutions of the one-dimensional cubic-quintic NLSE, the cubic NLSE and LSE. Any two systems that are classified by the same single number called the cross ratio are related by this symmetry. Notably, the conformal duality can also be adapted in Newtonian mechanics and serves as a powerful tool for investigating physical systems that otherwise cannot be directly accessed in experiments. Further, we show that the conformal symmetry is a valuable resource to substantially improve NLSE parameter estimation from noisy empirical data by introducing an optimization afterburner. The new method therefore has far reaching practical applications for nonlinear physical systems. Published by the American Physical Society 2025

Reinhardt, David B. (ORCID:0009000409812838)

Conformational ensembles reveal the origins of serine protease catalysis

Enzymes exist in ensembles of states that encode the energetics underlying their catalysis. Conformational ensembles built from 1231 structures of 17 serine proteases revealed atomic-level changes across their reaction states. By comparing the enzymatic and solution reaction, we identified molecular features that provide catalysis and quantified their energetic contributions to catalysis. Serine proteases precisely position their reactants in destabilized conformers, creating a downhill energetic gradient that selectively favors the motions required for reaction while limiting off-pathway conformational states. The same catalytic features have repeatedly evolved in proteases and additional enzymes across multiple distinct structural folds. In conclusion, our ensemble-function analyses revealed previously unknown catalytic features, provided quantitative models based on simple physical and chemical principles, and identified motifs recurrent in nature that may inspire enzyme design.

Du, Siyuan [Stanford Univ., CA (United States)] (O

Multiscale Molecular Dynamics Simulations: Accelerating Conformational Sampling of Biomolecular Systems by Iterating All-Atom and Coarse-Grained Simulations

We developed the atomistic-coarse-grained multiscale MD simulation method in the OpenMM simulation package by iterating between the all-atom (AA) and coarse-grained (CG) MD simulations to enhance the sampling of biomolecular conformations. As the free energy surfaces are flattened during CG MD simulations, we can accelerate the transitions between different low-energy conformations. The AA-CG-AA cycles are repeated, facilitating the accelerated sampling of biomolecular conformations at a CG level, while the finer atomistic interactions are refined with AA simulators.

Do, Hung Nguyen

Conformational heterogeneity in the dGsw purine riboswitch: role of Mg²⁺ and 2’-dG in aptamer folding

Recent advancements in RNA structural biology have focused on unraveling the complexities of non-coding mRNA elements like riboswitches. These cis-acting regulatory regions undergo structural changes in response to specific cellular metabolites, leading to up or downregulation of downstream genes. The purine riboswitch family regulates many prokaryotic genes involved in purine degradation and biosynthesis. They feature an aptamer domain organized around a 3-way helical junction, where ligand encapsulation occurs at the junctional core. In our study, we chemically probed the aptamer domain of the 2’-dG-sensing purine riboswitch from Mesoplasma florum (dGsw) under various solution conditions to understand how Mg²⁺ and 2’-dG influence riboswitch folding. Here, we find that efficient 2’-dG binding strongly depends on Mg²⁺, indicating that Mg²⁺ is essential for priming dGsw for ligand interactions. We identified a previously undescribed sequence in the 5’ tail of dGsw that is complementary to a conserved helix. The inclusion of this region in a construct led to intramolecular competition between the alternate helix, Palt, and P1. Mutational analysis confirmed that 5’ flanking end of the aptamer domain forms an alternate helix in the absence of ligand. Molecular dynamics simulations revealed that this alternative conformation is stable. This helix may, therefore, facilitate the formation of an anti-terminator helix by opening the 3-way junction surrounding the 2’-dG binding site. Our study further establishes the importance of a closed terminal P1 helix conformation for metabolite binding and suggests that the delicate interplay between P1 and Palt may fine-tune downstream gene regulation. These insights offer a new perspective on riboswitch structure and enhance our understanding of the role that a conformational ensemble plays in riboswitch activity and regulation.

Biochemistry & Molecular Biology

A conformal head-up display for the visual approach

The degree of conformity used in matching a superimposed display to its visual background is considered in relation to the information available for vertical guidance and control during a purely visual approach. The information may be represented by individual symbols or combined in a single symbol, and the relative merits of these methods are discussed. A fully conformal display format is developed for the purpose of showing both the position and direction of the flight path, with provision for the effects of disturbances, ILS compatibility, and control needs. The field of view needed for all conditions and phases of the visual approach with a fully conformal display is studied in relation to the limitations of conventional collimator systems. Methods are discussed which depend on deviation of the sight line, and on windshield reflection of the uncollimated image of a simple pointer. Limited flight tests show some promise for the uncollimated method.

Naish, J. M.

Monte Carlo lattice models for adsorbed polymer conformation

The adhesion between a polymer film and a metal surface is of great technological interest. However, the prediction of adhesion and wear properties of polymer coated metals is quite difficult because a fundamental understanding of the polymer surface interaction does not yet exist. A computer model for the conformation of a polymer molecule adsorbed on a surface is discussed. The chain conformation is assumed to be described by a partially directed random walk on a three dimensional simple cubic lattice. An attractive surface potential is incorporated into the model through the use of a random walk step probability distribution that is anisotropic in the direction normal to the attractive surface. The effects of variations in potential characteristics are qualitatively included by varying both the degree of anisotropy of the step distribution and the range of the anisotropy. Polymer conformation is characterized by the average end to end distance, average radius of gyration, and average number of chain segments adsorbed on the surface.

Good, B. S.

A comparison of two conformal mapping techniques applied to an aerobrake body

Conformal mapping is a classical technique which has been utilized for solving problems in aerodynamics and hydrodynamics. Conformal mapping has been successfully applied in the construction of grids around airfoils, engine inlets and other aircraft configurations. Conformal mapping techniques were applied to an aerobrake body having an axis of symmetry. Two different approaches were utilized: (1) Karman-Trefftz transformation; and (2) Point Wise Schwarz Christoffel transformation. In both cases, the aerobrake body was mapped onto a near circle, and a grid was generated in the mapped plane. The mapped body and grid were then mapped back into physical space and the properties of the associated grids were examined. Advantages and disadvantages of both approaches are discussed.

Hommel, Mark J.

Quasi-conformal remapping for compensation of human visual field defects - Advances in image remapping for human field defects

Image coordinate transformations are investigated for possible use in a low vision aid for human patients. These patients typically have field defects with localized retinal dysfunction predominately central (age related maculopathy) or peripheral (retinitis pigmentosa). Previously simple eccentricity-only remappings which do not maintain conformality were shown. Initial attempts on developing images which hold quasi-conformality after remapping are presented. Although the quasi-conformal images may have less local distortion, there are discontinuities in the image which may counterindicate this type of transformation for the low vision application.

Juday, Richard D.

Pilot Non-Conformance to Alerting System Commands

This research project examined the effects of consonance between cockpit displays and alerting system as a technique to encourage pilots to conform to alerting system commands. An experiment used the task of collision avoidance during closely spaced parallel approaches as a case study, building upon previous experiments which identified instances of non-conformance and conflicts between the alerting criteria preferred by pilots, compared to that used by alerting systems. Using a workstation based, part-task simulator, each of 45 subjects completed 45 experiment runs. In each run, the subjects were told they were flying an approach. Their primary task was to keep their wings level despite turbulence through the use of a sidestick. The sidestick commands did not affect the path of the aircraft, however, so that consistent approach paths were be followed. Their secondary task was to indicate when an aircraft on a parallel approach is blundering towards them, as evidenced by the traffic display. Subjects were asked to press different buttons indicating whether they feel an avoidance maneuver is required by the traffic situation or not. At the completion of each run, subjects were asked to rate their confidence in their decision and, if appropriate, to rate the timeliness of automatic alerts when had been given. Three different automatic alert conditions were tested. The "No Automatic Alerts Given" condition is self-explanatory. In the "Automatic Alerts Based on NTZ Criteria" condition, an automatic alert was given when the NTZ criteria was triggered; this criteria is consistent with subject reactions in other studies, in which subjects were found to react, on average, when the other aircraft was 1350 min to the side of the own aircraft. In the "Automatic Alerts Based on MIT Criteria" condition, an automatic alert was given when the MIT criteria was triggered; this criteria was developed by Carpenter and Kuchar for parallel approaches to have better performance, at the cost of increased complexity and higher sensitivity to pilot non-conformance. Three displays were tested. The "Baseline Display" is based on a moving map display, with a top-down view, track-up orientation, iconic presentation of the other aircraft's positions and a text presentation of the other aircraft's altitude. The "NTZ Alert Criteria Shown" display added to the Baseline Display an explicit presentation on the display of the boundary delineating the NTZ criteria, allowing for quick comparison of the other aircraft's position relative to this alert criteria. Likewise, the "MIT Alert Criteria Shown" display added to the Baseline Display an explicit presentation on the display of the boundary delineating the MIT criteria, allowing for quick comparison of the other aircraft's position relative to this alert criteria The test matrix for this experiment was three dimensional, varying displays, alerts and traffic conflict scenarios.

Pritchett, Amy

Comparison of Chain Conformation of Poly(vinyl alcohol) in Solutions and Melts from Quantum Chemistry Based Molecular Dynamics Simulations

Confirmations of 2,4-dihydroxypentane (DHP), a model molecule for poly(vinyl alcohol), have been studied by quantum chemistry (QC) calculations and molecular dynamics (MD) simulations. QC calculations at the 6-311G MP2 level show the meso tt conformer to be lowest in energy followed by the racemic tg, due to intramolecular hydrogen bond between the hydroxy groups. The Dreiding force field has been modified to reproduce the QC conformer energies for DHP. MD simulations using this force field have been carried out for DHP molecules in the gas phase, melt, and CHCl3 and water solutions. Extensive intramolecular hydrogen bonding is observed for the gas phase and CHCl3 solution, but not for the melt or aqueous solution, Such a condensed phase effect due to intermolecular interactions results in a drastic change in chain conformations, in agreement with experiments.

Jaffe, Richard

Plan-graph Based Heuristics for Conformant Probabilistic Planning

In this paper, we introduce plan-graph based heuristics to solve a variation of the conformant probabilistic planning (CPP) problem. In many real-world problems, it is the case that the sensors are unreliable or take too many resources to provide knowledge about the environment. These domains are better modeled as conformant planning problems. POMDP based techniques are currently the most successful approach for solving CPP but have the limitation of state- space explosion. Recent advances in deterministic and conformant planning have shown that plan-graphs can be used to enhance the performance significantly. We show that this enhancement can also be translated to CPP. We describe our process for developing the plan-graph heuristics and estimating the probability of a partial plan. We compare the performance of our planner PVHPOP when used with different heuristics. We also perform a comparison with a POMDP solver to show over a order of magnitude improvement in performance.

Ramakrishnan, Salesh

Structure, Intent and Conformance Monitoring in ATC

Infield studies of current Air Traffic Control operations it is found that controllers rely on underlying airspace structure to reduce the complexity of the planning and conformance monitoring tasks. The structure appears to influence the controller's working mental model through abstractions that reduce the apparent cognitive complexity. These structure-based abstractions are useful for the controller's key tasks of planning, implementing, monitoring, and evaluating tactical situations. In addition, the structure-based abstractions appear to be important in the maintenance of Situation Awareness. The process of conformance monitoring is analyzed in more detail and an approach to conformance monitoring which utilizes both the structure-based abstractions and intent is presented.

Reynolds, Tom G.

Characteristics of a Linearly Tapered Slot Antenna (LTSA) Conformed Longitudinally Around a Cylinder

The family of tapered slot antennas (TSA s) is suitable for numerous applications. Their ease of fabrication, wide bandwidth, and high gain make them desirable for military and commercial systems. Fabrication on thin, flexible substrates allows the TSA to be conformed over a given body, such as an aircraft wing or a piece of clothing for wearable networks. Previously, a Double Exponentially Tapered Slot Antenna (DETSA) was conformed around an exponential curvature, which showed that the main beam skewed towards the direction of curvature. This paper presents a Linearly Tapered Slot Antenna (LTSA) conformed longitudinally around a cylinder. Measured and simulated radiation patterns and the direction of maximum H co-polarization (Hco) as a function of the cylinder radius are presented.

Jordan, Jennifer L.

Reexamination of Ball-Race Conformity Effects on Ball Bearing Life

The analysis in this report considers the life of the ball set as well as the respective lives of the races to reassess the effect of ball-race conformity on ball bearing life. The related changes in ball bearing life are incorporated in life factors that can be used to modify the bearing predicted life using the Lundberg-Palmgren equations and the ANSI/ABMA and ISO Standards. Two simple algebraic relationships were established to calculate life factors LF(sub c) to determine the effect of inner- and outer-race conformity combinations on bearing L(sub 10) life for deepgroove and angular-contact ball bearings, respectively. Depending on the bearing type and series as well as conformity combinations, the calculated life for deep-groove ball bearings can be over 40 percent less than that calculated by the Lundberg-Palmgren equations. For angular-contact ball bearings, the life can vary between +16 and -39 percent from that calculated by the Lundberg-Palmgren equations. Comparing the two ball bearing types, the life factors LF(sub c) for the deep-groove bearings can be as much as 40 percent lower than that for angular-contact ball bearings.

Zaretsky, Erwin V.

Conformance Testing: Measurement Decision Rules

The goal of a Quality Management System (QMS) as specified in ISO 9001 and AS9100 is to provide assurance to the customer that end products meet specifications. Measuring devices, often called measuring and test equipment (MTE), are used to provide the evidence of product conformity to specified requirements. Unfortunately, processes that employ MTE can become a weak link to the overall QMS if proper attention is not given to the measurement process design, capability, and implementation. Documented "decision rules" establish the requirements to ensure measurement processes provide the measurement data that supports the needs of the QMS. Measurement data are used to make the decisions that impact all areas of technology. Whether measurements support research, design, production, or maintenance, ensuring the data supports the decision is crucial. Measurement data quality can be critical to the resulting consequences of measurement-based decisions. Historically, most industries required simplistic, one-size-fits-all decision rules for measurements. One-size-fits-all rules in some cases are not rigorous enough to provide adequate measurement results, while in other cases are overly conservative and too costly to implement. Ideally, decision rules should be rigorous enough to match the criticality of the parameter being measured, while being flexible enough to be cost effective. The goal of a decision rule is to ensure that measurement processes provide data with a sufficient level of quality to support the decisions being made - no more, no less. This paper discusses the basic concepts of providing measurement-based evidence that end products meet specifications. Although relevant to all measurement-based conformance tests, the target audience is the MTE end-user, which is anyone using MTE other than calibration service providers. Topics include measurement fundamentals, the associated decision risks, verifying conformance to specifications, and basic measurement decisions rules.

Mimbs, Scott M.

Conformal Thin Film Packaging for SiC Sensor Circuits in Harsh Environments

In this investigation sputtered silicon carbide annealed at 300 C for one hour is used as a conformal thin film package. A RF magnetron sputterer was used to deposit 500 nm silicon carbide films on gold metal structures on alumina wafers. To determine the reliability and resistance to immersion in harsh environments, samples were submerged in gold etchant for 24 hours, in BOE for 24 hours, and in an O2 plasma etch for one hour. The adhesion strength of the thin film was measured by a pull test before and after the chemical immersion, which indicated that the film has an adhesion strength better than 10(exp 8) N/m2; this is similar to the adhesion of the gold layer to the alumina wafer. MIM capacitors are used to determine the dielectric constant, which is dependent on the SiC anneal temperature. Finally, to demonstrate that the SiC, conformal, thin film may be used to package RF circuits and sensors, an LC resonator circuit was fabricated and tested with and without the conformal SiC thin film packaging. The results indicate that the SiC coating adds no appreciable degradation to the circuits RF performance. Index Terms Sputter, silicon carbide, MIM capacitors, LC resonators, gold etchants, BOE, O2 plasma

Scardelletti, Maximilian C.

Evaluation of High Density Air Traffic Operations with Automation for Separation Assurance, Weather Avoidance and Schedule Conformance

In this paper we discuss the development and evaluation of our prototype technologies and procedures for far-term air traffic control operations with automation for separation assurance, weather avoidance and schedule conformance. Controller-in-the-loop simulations in the Airspace Operations Laboratory at the NASA Ames Research Center in 2010 have shown very promising results. We found the operations to provide high airspace throughput, excellent efficiency and schedule conformance. The simulation also highlighted areas for improvements: Short-term conflict situations sometimes resulted in separation violations, particularly for transitioning aircraft in complex traffic flows. The combination of heavy metering and growing weather resulted in an increased number of aircraft penetrating convective weather cells. To address these shortcomings technologies and procedures have been improved and the operations are being re-evaluated with the same scenarios. In this paper we will first describe the concept and technologies for automating separation assurance, weather avoidance, and schedule conformance. Second, the results from the 2010 simulation will be reviewed. We report human-systems integration aspects, safety and efficiency results as well as airspace throughput, workload, and operational acceptability. Next, improvements will be discussed that were made to address identified shortcomings. We conclude that, with further refinements, air traffic control operations with ground-based automated separation assurance can routinely provide currently unachievable levels of traffic throughput in the en route airspace.

Prevot, Thomas

Vacuum Infusion Process Development for Conformal Ablative Thermal Protection System Materials

Conformal ablators are low density composite materials comprised of a flexible carbon felt based fibrous substrate and a high surface area phenolic matrix. These materials are fabricated to near net shape by molding the substrate, placing in a rigid matched mold and infusing with liquid resin through a vacuum assisted process. The open mold process, originally developed for older rigid substrate ablators, such as PICA, wastes a substantial amount of resin. In this work, a vacuum infusion process a type of liquid composite molding where resin is directly injected into a closed mold under vacuum is advanced for conformal ablators. The process reduces waste over the state-of-the-art technique. Small, flat samples of Conformal Phenolic Impregnated Carbon Ablator are infused using the new approach and subjected to a range of curing configurations and conditions. Resulting materials are inspected for quality and compared to material produced using the standard process. Lessons learned inform subsequent plans for process scale up.

TPS