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At least 559 records · Page 31

Investigations of Clouds and Aerosols on Mars, Venus and Titan

For Titan our interest during the past few years was to explain the observed asymmetry in the albedo. We suggested earlier, from one-dimensional modeling studies, that vertical transport rates were comparable to particle fall speeds. Since heating of the upper atmosphere, which drives dynamical motions, is largely due to the aerosols, a non- linear interaction between dynamics, radiative heating and particle microphysics is possible. We pursued this interaction in a two-dimensional model. We showed that the observed variations in the albedo between the two hemispheres and over an orbital cycle, could be due to dynamical motions suspending particles so that particle sizes and optical depths vary across the planet. In the Cassini time frame, future studies of this interaction between dynamics, radiation and microphysics may be worthwhile using the strong modeling base that others, and we have developed. In our recently approved proposal, however, we plan to extend our modeling to hydrocarbon clouds that lie at lower levels. We know very little about such clouds, and numerical models for their properties are non-existent. These clouds may be observed by the Huygen's Probe, and by the Cassini orbiter, so predictions of their properties should help in the analysis of Cassini data. We have also developed a sophisticated model for the lower, condensational, clouds on Venus. In this model we explored the water vapor budget on Venus, and the properties of the clouds such as particle size distribution. Most researchers have investigated the upper clouds on Venus, which are essentially a photochemical aerosol with a long lifetime. The lower clouds, however, are similar to stratus clouds on Earth. These clouds have short lifetimes, and are tightly coupled to the dynamics at the base of the Venus cloud deck. We believe that the holes in these clouds seen at near infrared wavelengths by Galileo are related to some interaction between dynamics and cloud physics. One goal of our recently approved proposed work is to better understand this interaction, and to better understand how these clouds may vary if the climate of Venus were to vary. During the past few years we have applied our model of the water ice clouds on Mars to new data sets from Pathfinder, and Mars Global Surveyor. We have compared our predictions of cloud properties with those seen by Pathfinder, and found reasonable agreement. More recently we have improved our model by including a radiative transfer algorithm and a boundary layer transport scheme . The goal of this work is to understand the thermal inversions seen in Mars Global Surveyor data. We find that the inversions are created by clouds radiatively cooling the atmospheric layers in which the clouds form. We have also initiated laboratory work on the physics of carbon dioxide particle formation. In our recently approved work we propose to use these laboratory data, and to extend our modeling to carbon dioxide clouds in the Martian atmosphere.

Toon, Owen B.↗

Grid-Aware Charging and Operational Optimization for Mixed-Fleet Public Transit

The rapid growth of urban populations and the increasing need for sustainable transportation solutions have prompted a shift towards electric buses in public transit systems. However, the effective management of mixed fleets consisting of both electric and diesel buses poses significant operational challenges. One major challenge is coping with dynamic electricity pricing, where charging costs vary throughout the day. Transit agencies must optimize charging assignments in response to such dynamism while accounting for secondary considerations such as seating constraints. This paper presents a comprehensive mixed-integer linear programming (MILP) model to address these challenges by jointly optimizing charging schedules and trip assignments for mixed (electric and diesel bus) fleets while considering factors such as dynamic electricity pricing, vehicle capacity, and route constraints. We address the potential computational intractability of the MILP formulation, which can arise even with relatively small fleets, by employing a hierarchical approach tailored to the fleet composition. By using real-world data from the city of Chattanooga, Tennessee, USA, we show that our approach can result in significant savings in the operating costs of the mixed transit fleets.

Sen, Rishav↗

MoorDyn V2: New Capabilities in Mooring System Components and Load Cases

MoorDyn, an open-source mooring dynamics model, is being expanded with capabilities for additional mooring system features and load cases. As floating wind turbine technology matures, mooring systems are becoming more sophisticated and more complex scenarios need to be considered in the design process. Mooring systems may have synthetic line materials, ballast/buoyancy bodies along the lines, or interconnections between platforms. Failure modes may involve multiple cascading line failures that depend on mooring system dynamics. Features recently added to MoorDyn aim to address these emerging needs. MoorDyn’s linear elasticity model has been supplemented to support user-defined stress-strain curves, which can be adjusted to represent synthetic mooring materials. Rigid six-degree-of-freedom bodies in the mooring system can now be modeled using two new model objects. “Rod” objects provide an option for rigid cylindrical bodies. They use the existing Morison equation-based hydrodynamics model and can be connected to mooring lines at either end. “Body” objects provide a generic six-degree-of-freedom rigid-body representation based on a lumped-parameter model of translational and rotational properties. Rod objects can be added to Body objects and mooring lines can be attached at any location, allowing a wide variety of submerged structures to be integrated into the mooring system. Lastly, a means of dynamically simulating mooring line failures has been implemented. These new features, currently in the C++ version of MoorDyn, are described and then demonstrated on a two-turbine shared-mooring array. A qualitative view of the results suggests the new features are functioning as expected.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

MoorDyn V2: New Capabilities in Mooring System Components and Load Cases: Preprint

MoorDyn, an open-source mooring dynamics model, is being expanded with capabilities for additional mooring system features and load cases. As floating wind turbine technology matures, mooring systems are becoming more sophisticated and more complex scenarios need to be considered in the design process. Mooring systems may have synthetic line materials, ballast/buoyancy bodies along the lines, or interconnections between platforms. Failure modes may involve multiple cascading line failures that depend on mooring system dynamics. Features recently added to MoorDyn aim to address these emerging needs. MoorDyn’s linear elasticity model has been supplemented to support user-defined stress-strain curves, which can be adjusted to represent synthetic mooring materials. Rigid six-degree-of-freedom bodies in the mooring system can now be modeled using two new model objects. “Rod” objects provide an option for rigid cylindrical bodies. They use the existing Morison equation-based hydrodynamics model and can be connected to mooring lines at either end. “Body” objects provide a generic six-degree-of-freedom rigid-body representation based on a lumped-parameter model of translational and rotational properties. Rod objects can be added to Body objects and mooring lines can be attached at any location, allowing a wide variety of submerged structures to be integrated into the mooring system. Lastly, a means of dynamically simulating mooring line failures has been implemented. These new features, currently in the C++ version of MoorDyn, are described and then demonstrated on a two-turbine shared-mooring array. A qualitative view of the results suggests the new features are functioning as expected.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. I. Normal responses

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in five squirrel monkeys with intact vestibular function. The VOR evoked by steps of acceleration in darkness (3,000 degrees /s(2) reaching a velocity of 150 degrees /s) began after a latency of 7.3 +/- 1.5 ms (mean +/- SD). Gain of the reflex during the acceleration was 14.2 +/- 5.2% greater than that measured once the plateau head velocity had been reached. A polynomial regression was used to analyze the trajectory of the responses to steps of acceleration. A better representation of the data was obtained from a polynomial that included a cubic term in contrast to an exclusively linear fit. For sinusoidal rotations of 0.5-15 Hz with a peak velocity of 20 degrees /s, the VOR gain measured 0.83 +/- 0.06 and did not vary across frequencies or animals. The phase of these responses was close to compensatory except at 15 Hz where a lag of 5.0 +/- 0.9 degrees was noted. The VOR gain did not vary with head velocity at 0.5 Hz but increased with velocity for rotations at frequencies of >/=4 Hz (0. 85 +/- 0.04 at 4 Hz, 20 degrees /s; 1.01 +/- 0.05 at 100 degrees /s, P < 0.0001). No responses to these rotations were noted in two animals that had undergone bilateral labyrinthectomy indicating that inertia of the eye had a negligible effect for these stimuli. We developed a mathematical model of VOR dynamics to account for these findings. The inputs to the reflex come from linear and nonlinear pathways. The linear pathway is responsible for the constant gain across frequencies at peak head velocity of 20 degrees /s and also for the phase lag at higher frequencies being less than that expected based on the reflex delay. The frequency- and velocity-dependent nonlinearity in VOR gain is accounted for by the dynamics of the nonlinear pathway. A transfer function that increases the gain of this pathway with frequency and a term related to the third power of head velocity are used to represent the dynamics of this pathway. This model accounts for the experimental findings and provides a method for interpreting responses to these stimuli after vestibular lesions.

NASA Program Biomedical Research and Countermeasur↗

Probabilistic measures for biological adaptation and resilience

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed “ecological resilience through adaptation,” specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. Importantly, the resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

60 APPLIED LIFE SCIENCES↗

A structure-preserving machine learning framework for accurate prediction of structural dynamics for systems with isolated nonlinearities

The nonlinearities present in structural systems are often found in isolated regions within the structure, such as those containing joints or interfaces. However, despite the localized nature of these nonlinearities their presence serves to couple together the modes of the underlying linear system and significantly complicate the development of appropriate reduced-order models; the localized nonlinearities have a global effect on the dynamics of the system. Further, in the presence of evolving structural health the nonlinearities can arise from accumulating damage, with dynamics distinct from those observed in the healthy state. The present work develops a data-driven formulation to identify and include the contributions of the isolated nonlinearities on the dynamics of the underlying linear structure. A novel coordinate separation is developed that decomposes those nonlinearities restricted to the isolated subdomain from the known linear system defined over the entire domain, and the influence of the isolated nonlinearities is reintroduced as an appropriately identified traction at the boundary of the isolated subdomain, referred to as the deviatoric force. In the region exterior to the nonlinear subdomain the response of the ideal linear system recovers that of the original nonlinear system. In this work, the deviatoric force component is predicted using a structure-preserving multilayer perceptron, based only on measured responses at the boundary of the isolated subdomain. Therefore introduction of the perceptron is able to bypass the direct numerical simulation of the nonlinearities within the isolated subdomain. This approach is illustrated through a simple structural system in which an interior region contains cubic nonlinearities and hysteretic damping. Once trained, the machine learning system is able to accurately predict the deviatoric force so that the ideal system recovers the response of the original system in the region outside the isolated nonlinear subdomain. Moreover, the data-driven approach is able to accurately predict the response when the system is subject to differing initial conditions and external excitation without the need for retraining, so that the proposed approach provides a robust description of the structural dynamics of the overall system.

Machine learning↗

Bilinear dynamic mode decomposition for quantum control

Abstract Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We develop a data-driven regression procedure, bilinear dynamic mode decomposition (biDMD), that leverages time-series measurements to establish quantum system identification for QOC. The biDMD optimization framework is a physics-informed regression that makes use of the known underlying Hamiltonian structure. Further, the biDMD can be modified to model both fast and slow sampling of control signals, the latter by way of stroboscopic sampling strategies. The biDMD method provides a flexible, interpretable, and adaptive regression framework for real-time, online implementation in quantum systems. Further, the method has strong theoretical connections to Koopman theory, which approximates nonlinear dynamics with linear operators. In comparison with many machine learning paradigms minimal data is needed to construct a biDMD model, and the model is easily updated as new data is collected. We demonstrate the efficacy and performance of the approach on a number of representative quantum systems, showing that it also matches experimental results.

97 MATHEMATICS AND COMPUTING↗

Experimentation in Exploring Photovoltaic Inverter Dynamics Under Different Irradiance Levels Through a Data-Driven Approach

As conventional direct connections of synchronous generators are being phased out, inverter-based resources (IBRs) with grid support functions are increasingly being integrated into power systems. This transition requires the development of accurate dynamic models for IBRs to predict how power systems will adapt to varying levels of IBRs penetration, establish grid code requirements, and ensure compliance. Here, this study introduces an active probing signal-based data-driven modeling technique to accurately derive the dynamics model of a smart photovoltaic inverter operating in Volt-Watt and Freq-Watt modes, in compliance with the IEEE 1547–2018 standard. The paper focuses on investigating how the dynamics of the PV inverter model respond to fluctuations in solar irradiance, utilizing real-time digital simulator experimentation. The experimental analysis demonstrates that the amplitude of dynamics fluctuates with changes in irradiance across both operational modes and confirms the active power’s dependence on irradiance levels. Furthermore, the nature of inverter dynamics varies distinctly between the different modes of activation. Critically, our findings indicate that dynamic models require DC-gain adjustments to accommodate contrasting irradiance levels, highlighting a negative gradient linear relationship between the DC-gain of each model and the irradiance.

14 SOLAR ENERGY↗

A modal analysis of flexible aircraft dynamics with handling qualities implications

A multivariable modal analysis technique is presented for evaluating flexible aircraft dynamics, focusing on meaningful vehicle responses to pilot inputs and atmospheric turbulence. Although modal analysis is the tool, vehicle time response is emphasized, and the analysis is performed on the linear, time-domain vehicle model. In evaluating previously obtained experimental pitch tracking data for a family of vehicle dynamic models, it is shown that flexible aeroelastic effects can significantly affect pitch attitude handling qualities. Consideration of the eigenvalues alone, of both rigid-body and aeroelastic modes, does not explain the simulation results. Modal analysis revealed, however, that although the lowest aeroelastic mode frequency was still three times greater than the short-period frequency, the rigid-body attitude response was dominated by this aeroelastic mode. This dominance was defined in terms of the relative magnitudes of the modal residues in selected vehicle responses.

Schmidt, D. K.↗

A Piecewise Linear State Variable Technique for Real Time Propulsion System Simulation

The emphasis on increased aircraft and propulsion control system integration and piloted simulation has created a need for higher fidelity real time dynamic propulsion models. A real time propulsion system modeling technique which satisfies this need and which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators was developed and demonstrated using flight simulator facilities at NASA Ames. A piecewise linear state variable technique is used. This technique provides the system accuracy, stability and transient response required for integrated aircraft and propulsion control system studies. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model contains approximately 7.0 K bytes of in-line computational code and 14.7 K of block data. It has an 8.9 ms cycle time on a Xerox Sigma 9 computer. A Pegasus-Harrier propulsion system was used as a baseline for developing the mathematical modeling and simulation technique. A hydromechanical and water injection control system was also simulated. The model was programmed for interfacing with a Harrier aircraft simulation at NASA Ames. Descriptions of the real time methodology and model capabilities are presented.

Mihaloew, J. R.↗

A piecewise linear state variable technique for real time propulsion system simulation

The emphasis on increased aircraft and propulsion control system integration and piloted simulation has created a need for higher fidelity real time dynamic propulsion models. A real time propulsion system modeling technique which satisfies this need and which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators was developed and demonstrated using flight simulator facilities at NASA Ames. A piecewise linear state variable technique is used. This technique provides the system accuracy, stability and transient response required for integrated aircraft and propulsion control system studies. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model contains approximately 7.0 K bytes of in-line computational code and 14.7 K of block data. It has an 8.9 ms cycle time on a Xerox Sigma 9 computer. A Pegasus-Harrier propulsion system was used as a baseline for developing the mathematical modeling and simulation technique. A hydromechanical and water injection control system was also simulated. The model was programmed for interfacing with a Harrier aircraft simulation at NASA Ames. Descriptions of the real time methodology and model capabilities are presented.

Mihaloew, J. R.↗

Rolling Maneuver Load Alleviation using active controls

Rolling Maneuver Load Alleviation (RMLA) has been demonstrated on the Active Flexible Wing (AFW) wind tunnel model in the NASA Langley Transonic Dynamics Tunnel. The design objective was to develop a systematic approach for developing active control laws to alleviate wing incremental loads during roll maneuvers. Using linear load models for the AFW wind-tunnel model which were based on experimental measurements, two RMLA control laws were developed based on a single-degree-of-freedom roll model. The RMLA control laws utilized actuation of outboard control surface pairs to counteract incremental loads generated during rolling maneuvers and actuation of the trailing edge inboard control surface pairs to maintain roll performance. To evaluate the RMLA control laws, roll maneuvers were performed in the wind tunnel at dynamic pressures of 150, 200, and 250 psf and Mach numbers of 0.33, .38 and .44, respectively. Loads obtained during these maneuvers were compared to baseline maneuver loads. For both RMLA controllers, the incremental torsion moments were reduced by up to 60 percent at all dynamic pressures and performance times. Results for bending moment load reductions during roll maneuvers varied. In addition, in a multiple function test, RMLA and flutter suppression system control laws were operated simultaneously during roll maneuvers at dynamic pressures 11 percent above the open-loop flutter dynamic pressure.

Woods-Vedeler, Jessica A.↗

Computed and Experimental Flutter/LCO Onset for the Boeing Truss-Braced Wing Wind-Tunnel Model

This paper presents high fidelity Navier-Stokes simulations of the Boeing Subsonic Ultra Green Aircraft Research truss-braced wing wind-tunnel model and compares the results to linear MSC. Nastran flutter analysis and preliminary data from a recent wind-tunnel test of that model at the NASA Langley Research Center Transonic Dynamics Tunnel. The simulated conditions under consideration are zero angle of attack, so that structural nonlinearity can be neglected. It is found that, for Mach number greater than 0.78, the linear flutter analysis predicts flutter onset dynamic pressure below the wind-tunnel test and that predicted by the Navier-Stokes analysis. Furthermore, the wind-tunnel test revealed that the majority of the high structural dynamics cases were wing limit cycle oscillation (LCO) rather than flutter. Most Navier-Stokes simulated cases were also LCO rather than hard flutter. There is dip in the wind-tunnel test flutter/LCO onset in the Mach 0.76-0.80 range. Conditions tested above that Mach number exhibited no aeroelastic instability at the dynamic pressures reached in the tunnel. The linear flutter analyses do not show a flutter/LCO dip. The Navier-Stokes simulations also do not reveal a dip; however, the flutter/LCO onset is at a significantly higher dynamic pressure at Mach 0.90 than at lower Mach numbers. The Navier-Stokes simulations indicate a mild LCO onset at Mach 0.82, then a more rapidly growing instability at Mach 0.86 and 0.90. Finally, the modeling issues and their solution related to the use of a beam and pod finite element model to generate the Navier-Stokes structure mode shapes are discussed.

Bartels, Robert E.↗

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗

Spatially Quasi-Periodic Water Waves of Infinite Depth

Abstract We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Wilkening, Jon (ORCID:0000000327827596)↗

Photon counting with intensified charge coupled device (ICCD) – II. Laser induced breakdown spectroscopy (LIBS) spectral measurement

This study explores the application of photon counting (PC) to enhance the resolution of spectra acquired by an intensified charge-coupled device (ICCD) detector, with a focus on analytical atomic emission spectrometry using laser-induced breakdown spectroscopy (LIBS) as a use-case example. It demonstrates that, for spectra obtained with the same spectrometer–ICCD system, PC provides higher spectral resolution compared to conventional analog detector readout. This enhancement is particularly evident in the line wings of spectral peaks, facilitating better discrimination of isotopic peaks in the measured spectra. Although PC does not improve the resolution of an optical spectrometer directly, it rectifies the resolution lost caused by signal spreading in conventional ICCD analog measurement. However, similar to other counting techniques, excessive photons compromise detector linearity due to signal pileup. A correction model is proposed to mitigate the pileup effect, resulting in improved linearity and dynamic range in PC measurements. Additionally, the study reveals unexpected periodic structures in the flatfield image of the ICCD, which cause non-uniform detector gain in conventional analog as well as PC measurement modes and must be addressed for high-precision measurements.

47 OTHER INSTRUMENTATION↗

How Cooperatively Folding Are Homopolymer Molecular Knots?

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work, we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models, which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies. Populations of different knotted states as a function of temperature can also be manipulated by tuning the backbone torsion stiffness or by adding side-chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition rather than a cooperative knotting step. Furthermore, in some cases, the cooperativity of globule-to-knot and coil-to-globule transitions is comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.

36 MATERIALS SCIENCE↗