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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Understanding Strain and Failure of a Knot in Polyethylene Using Molecular Dynamics with Machine-Learned Potentials

A neural network potential (NNP) has been developed by fitting to ab initio electronic structure data on hydrocarbons and is used to study failure of linear and knotted polyethylene (PE) chains. A linear PE chain must be highly strained before breaking as the stress is equally distributed across the chain. In contrast, the stress in a PE chain with a 31 or overhand knot, accumulates at the knot’s entrance/exit. We find the strain energy is greatest when the bond length and angle are strained simultaneously, and that the knot weakens the chain by increasing the variance of the C–C–C angle, thereby allowing rupture at lower bond strains. Here, we extend our analysis to both 51 and 52 knots and find that both break at the entrance/exit of a loop. Notably, molecular scale PE knots exhibit many of the same characteristics as knots in a macroscopic rope, with stick–slip phenomena upon tightening and similar points of failure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Review: knots and other new topological effects in liquid crystals and colloids

Abstract Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Physics↗
DOE OSTI2022

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↗
DOE OSTI2025

Fusion and fission of particle-like chiral nematic vortex knots

Vortex knots have been seen decaying in many physical systems. Here we describe topologically protected vortex knots, which remain stable and undergo fusion and fission and conserve a topological invariant. The host medium, a chiral nematic liquid crystal, exhibits intrinsic chirality of molecular alignment, whereas cores of the vortex lines are structurally achiral regions in which a molecular twist cannot be defined. We can reversibly switch between fusion and fission of these vortex knots by applying electric pulses. This reveals the physical embodiments of concepts in knot theory, such as connected sums of knots and band surgeries. Our findings demonstrate the interplay of chirality effects at hierarchical levels from constituent molecules to the host medium and the energetically stable chiral vortex knots. This emergent physical behaviour may enable applications in electro-optics and photonics in which such fusion and fission processes of vortex knots can be used for controlling light.

Applied mathematics↗
DOE OSTI2024

Molecular dynamics studies of knotted polymers

Molecular dynamics calculations have been used to explore the influence of knots on the strength of a polymer strand. In particular, the mechanism of breaking 31, 41, 51, and 52 prime knots has been studied using two very different models to represent the polymer: (1) the generic coarse-grained (CG) bead model of polymer physics and (2) a state-of-the-art machine learned atomistic neural network (NN) potential for polyethylene derived from electronic structure calculations. While there is a broad overall agreement between the results on the influence of the pulling rate on chain rupture based on the CG and atomistic NN models, for the simple 31 and 41 knots, significant differences are found for the more complex 51 and 52 knots. Notably, in the latter case, the NN model more frequently predicts that these knots can break not only at the crossings at the entrance/exit but also at one of the central crossing points. The relative smoothness of the CG potential energy surface also leads to stabilization of tighter knots compared to the more realistic NN model.

DelloStritto, Mark (ORCID:0000000206785860)↗
DOE OSTI2022

Vernier template synthesis of molecular knots

Molecular knots are often prepared using metal helicates to cross the strands. Here we found that coordinatively mismatching oligodentate ligands and metal ions provides a more effective way to synthesize larger knots using Vernier templating. Strands composed of different numbers of tridentate 2,6-pyridinedicarboxamide groups fold around nine-coordinate lanthanide (III) ions to generate strand-entangled complexes with the lowest common multiple of coordination sites for the ligand strands and metal ions. Ring-closing olefin metathesis then completes the knots. A 3:2 (ditopic strand:metal) Vernier assembly produces +3 1 #+3 1 and –3 1 #–3 1 granny knots. Vernier complexes of 3:4 (tetratopic strand:metal) stoichiometry selectively form a 378-atom-long trefoil-of-trefoils triskelion knot with 12 alternating strand crossings or, by using opposing stereochemistry at the terminus of the strand, an inverted-core triskelion knot with six alternating and six nonalternating strand crossings.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Knots and entanglement

We extend the entanglement bootstrap program to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions [Ann. Phys. 418, 168164 (2020), Phys. Rev. B 103, 115150 (2021)], we define a variety of superselection sectors and fusion spaces from two axioms on the ground state entanglement entropy. In particular, we identify fusion spaces associated with knots. We generalize the information convex set to a new class of regions called immersed regions, promoting various theorems to this new context. Examples from solvable models are provided; for instance, a concrete calculation of knot multiplicity shows that the knot complement of a trefoil knot can store quantum information. We define spiral maps that allow us to understand consistency relations for torus knots as well as spiral fusions of fluxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Fast Automatic Knot Placement Method for Accurate B-spline Curve Fitting

The choice of knot vector has immense influence on the resulting accuracy of a B-spline approximation of a curve. However, despite the significance of this problem and the various solutions that were proposed in the literature, optimizing the number and placement of knots remains a difficult task. This paper presents a novel method for the approximation of a curve by a B-spline of arbitrary order, which automatically determines a knot vector that achieves high approximation quality. Additionally, at the core of our approach is a feature function that characterizes the amount and spatial distribution of geometric details in the input curve by estimating its derivatives. Knots are then selected in such a way as to evenly distribute the feature contents across their intervals. A comparison to the state of the art for a wide variety of curves shows that our method is faster and achieves more accurate reconstruction results, while typically reducing the number of necessary knots.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Branches, quivers, and ideals for knot complements

We generalize the F K invariant, i.e. Z^ for the complement of a knot K in the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an F K invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these F K invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N = 2 theory T[M 3 ] and to the data of the associated modular tensor category MTC[M 3 ].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

De novo design of knotted tandem repeat proteins

De novo protein design methods can create proteins with folds not yet seen in nature. These methods largely focus on optimizing the compatibility between the designed sequence and the intended conformation, without explicit consideration of protein folding pathways. Deeply knotted proteins, whose topologies may introduce substantial barriers to folding, thus represent an interesting test case for protein design. Here we report our attempts to design proteins with trefoil (3 1 ) and pentafoil (5 1 ) knotted topologies. We extended previously described algorithms for tandem repeat protein design in order to construct deeply knotted backbones and matching designed repeat sequences (N = 3 repeats for the trefoil and N = 5 for the pentafoil). We confirmed the intended conformation for the trefoil design by X ray crystallography, and we report here on this protein’s structure, stability, and folding behaviour. The pentafoil design misfolded into an asymmetric structure (despite a 5-fold symmetric sequence); two of the four repeat-repeat units matched the designed backbone while the other two diverged to form local contacts, leading to a trefoil rather than pentafoil knotted topology. Our results also provide insights into the folding of knotted proteins.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Random Knotting in Fractal Ring Polymers

Many ring polymer systems of physical and biological interest exhibit both pronounced topological effects and nontrivial self-similarity, but the relationship between these two phenomena has not yet been clearly established. Here, we use theory and simulation to formulate such a connection by studying a fundamental topological property—the random knotting probability—for ring polymers with varying fractal dimension, d f . Using straightforward scaling arguments, we generalize a classic mathematical result, showing that the probability of a trivial knot decays exponentially with chain size, N, for all fractal dimensions: P 0 (N) ∝ exp(–N/N 0 ). However, no such simple considerations can account for the dependence of the knotting length, N 0 , on d f , necessitating a more involved analytical calculation. This analysis reveals a complicated double-exponential dependence, which is well supported by numerical data. By contrast, functional forms typical of simple scaling theories fail to adequately describe the observations. These findings are equally valid for two-dimensional ring polymer systems, where “knotting” is defined as the intersection of any two segments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Maximizing ion accessibility in MXene-knotted carbon nanotube composite electrodes for high-rate electrochemical energy storage

Improving the accessibility of ions in the electrodes of electrochemical energy storage devices is vital for charge storage and rate performance. In particular, the kinetics of ion transport in organic electrolytes is slow, especially at low operating temperatures. Herein, we report a new type of MXene-carbon nanotube (CNT) composite electrode that maximizes ion accessibility resulting in exceptional rate performance at low temperatures. The improved ion transport at low temperatures is made possible by breaking the conventional horizontal alignment of the two-dimensional layers of the MXene Ti 3 C 2 by using specially designed knotted CNTs. The large, knot-like structures in the knotted CNTs prevent the usual restacking of the Ti 3 C 2 flakes and create fast ion transport pathways. The MXene-knotted CNT composite electrodes achieve high capacitance (up to 130 F g -1 (276 F cm -3 )) in organic electrolytes with high capacitance retention over a wide scan rate range of 10 mV s -1 to 10 V s -1 . This study is also the first report utilizing MXene-based supercapacitors at low temperatures (down to -60 °C).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Knots are not for naught: Design, properties, and topology of hierarchical intertwined microarchitected materials

Lightweight and tough engineered materials are often designed with three-dimensional hierarchy and interconnected structural members whose junctions are detrimental to their performance because they serve as stress concentrations for damage accumulation and lower mechanical resilience. We introduce a previously unexplored class of architected materials, whose components are interwoven and contain no junctions, and incorporate micro-knots as building blocks within these hierarchical networks. Tensile experiments, which show close quantitative agreements with an analytical model for overhand knots, reveal that knot topology allows a new regime of deformation capable of shape retention, leading to a ~92% increase in absorbed energy and an up to ~107% increase in failure strain compared to woven structures, along with an up to ~11% increase in specific energy density compared to topologically similar monolithic lattices. Our exploration unlocks knotting and frictional contact to create highly extensible low-density materials with tunable shape reconfiguration and energy absorption capabilities.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fourier-informed knot placement schemes for B-spline approximation

Fitting B-splines to scientific data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Further, these quantities are then combined to choose knots that capture the qualitative features of the data, leading to accurate B-spline approximations with few knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot distribution. Aside from fast Fourier transforms to transfer to and from Fourier space, the method runs in linear time with very little communication. We assess performance on several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show the method fits discontinuous data without spurious oscillations and remains effective in the presence of noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants

By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. Furthermore, this opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Observation of a Knotted Electron Diffusion Region in Earth's Magnetotail Reconnection

Magnetic reconnection is a fundamental plasma process that alters the magnetic field topology and releases magnetic energy. Most numerical simulations and spacecraft observations assume a two‐dimensional diffusion region, with the electron diffusion region (EDR) embedded in the same plane as the ion diffusion region (IDR) and a uniform guide field throughout. Using observations from Magnetospheric Multiscale mission, we report a non‐coplanar, knotted EDR in Earth's magnetotail current sheet. The reconnection plane of the knotted EDR deviates by approximately 38° from that of the IDR, with the guide field exhibiting both a 38° directional shift and a twofold increase in amplitude. Moreover, the Hall magnetic field is bipolar in the EDR but quadrupolar in the IDR, indicating different Hall current structures at electron and ion scales. These observations highlight the importance of three‐dimensional effects and illustrate the complexity of multiscale coupling between the EDR and IDR during reconnection studies.

diffusion region↗
DOE OSTI2021

First report of Seville root-knot nematode, Meloidogyne hispanica (Nematoda: Meloidogynidae) in the USA and North America

A high number of second stage juveniles of the root-knot nematode were recovered from soil samples collected from a corn field, located in Pickens County, South Carolina, USA in 2019. Extracted nematodes were examined morphologically and molecularly for species identification which indicated that the specimens of root knot juveniles were Meloidogyne hispanica. The morphological examination and morphometric details from second-stage juveniles were consistent with the original description and redescriptions of this species. The ITS rRNA, D2-D3 expansion segments of 28S rRNA, intergenic COII-16S region, nad5 and COI gene sequences were obtained from the South Carolina population of M. hispanica. Phylogenetic analysis of the intergenic COII-16S region of mtDNA gene sequence alignment using statistical parsimony showed that the South Carolina population clustered with Meloidogyne hispanica from Portugal and Australia. To our best knowledge, this finding represents the first report of Meloidogyne hispanica in the USA and North America.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

3d gravity from Virasoro TQFT: Holography, wormholes and knots

We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.

Collier, Scott (ORCID:0000000286476653)↗