Search NASA⌕ Search

SEARCH · Search NASA

Results for “multifractality”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

26 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Thermal shock resistance of additively manufactured alumina

The mechanical behavior and cracking patterns of thermally-shocked additively manufactured alumina were investigated. The flexural strength of test specimens that had been heated to temperatures ranging from 200°C to 1000°C and then rapidly quenched in water was determined at ambient temperature by four-point bending. Results indicated that the surface cracking patterns had a multifractal structure and that an increase in the thermal shock temperature led to an increase in the density and uniformity of the crack network. Further, the flexural strength results were analyzed with Weibull statistics, where the Weibull moduli for most of the thermal shock conditions tested were found to be statistically indistinguishable. It was also found that a significant decrease (~50%) in flexural strength occurred for heating temperatures ≥300°C. The effect of the manufacturing method on cracking patterns is discussed, as well as the implication of the material behavior for practical applications of these materials.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Microscopic Theory of Long-Time Center-of-Mass Self-Diffusion and Anomalous Transport in Ring Polymer Liquids

We construct a microscopic theory at the level of segment-scale correlated space–time intermolecular forces for the long-time center-of-mass (CM) diffusion constant and intermediate-time non-Fickian transport in dense solutions and melts of ring polymers. The approach combines ideas of polymer, colloid, and liquid-state statistical mechanics to quantify how the multifractal intra-ring conformational structure and inter-ring packing correlations determine dynamic caging constraints and time-dependent friction. Breakdown of Rouse theory is predicted to occur due to length scale-dependent temporal correlation of forces exerted on pairs of tagged ring segments from surrounding polymers. At large enough degrees of polymerization (N), a stronger scaling of the CM diffusion constant (D ∝ N –2 ) is predicted, with a crossover N D proportional to the product of the system-specific macromolecular volume fraction and dimensionless compressibility. In analogy with caging effects in glass-forming fluids, the theory does appear to begin to fail at sufficiently high N/N D for the center-of-mass diffusivity, likely due to another crossover to an even slower activated transport regime. However, use of N/N D with the theoretically predicted N D , in conjunction with dynamic blob scaling ideas for local Rouse friction, collapses semidilute and concentrated solution simulation data onto a master curve. Based on the same physical ideas employed to predict the diffusion constant, a generalized Langevin equation description is formulated for intermediate-time CM transport. It predicts two subdiffusive regimes that emerge due to the self-similar nature of internal ring structure. Analytic and numerical predictions for the apparent non-Fickian exponent as a function of time, N/N D and dimensionless compressibility, the evolution of the maximum degree of subdiffusive motion with N/N D , and the time scale for recovering Fickian diffusion are made, all of which are in good accordance with melt simulations. Furthermore, the present work sets the stage to address activated dynamics and glass formation on the macromolecular scale.

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

Magic-angle semimetals

Abstract Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

Materials Science↗
DOE OSTI2020

Magic-angle semimetals with chiral symmetry

Here, we construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states (DOS) and subdiffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique “unfreezing” transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy DOS develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

Here, we study the critical properties of the noninteracting integer quantum Hall to insulator transition (IQHIT) in a “dual” composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality CF states are delocalized at all energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain ν = 2.56 ± 0.02 and η = 0.51 ± 0.01, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Vacancy-Induced Tunable Kondo Effect in Twisted Bilayer Graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wave functions at the magic angle. Finally, we argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains

Quantum systems evolving unitarily and subject to quantum measurements exhibit various types of non-equilibrium phase transitions, arising from the competition between unitary evolution and measurements. Dissipative phase transitions in steady states of time-independent Liouvillians and measurement induced phase transitions at the level of quantum trajectories are two primary examples of such transitions. Investigating a many-body spin system subject to periodic resetting measurements, we argue that many-body dissipative Floquet dynamics provides a natural framework to analyze both types of transitions. We show that a dissipative phase transition between a ferromagnetic ordered phase and a paramagnetic disordered phase emerges for long-range systems as a function of measurement probabilities. A measurement induced transition of the entanglement entropy between volume law scaling and sub-volume law scaling is also present, and is distinct from the ordering transition. The two phases correspond to an error-correcting and a quantum-Zeno regimes, respectively. The ferromagnetic phase is lost for short range interactions, while the volume law phase of the entanglement is enhanced. An analysis of multifractal properties of wave function in Hilbert space provides a common perspective on both types of transitions in the system. Our findings are immediately relevant to trapped ion experiments, for which we detail a blueprint proposal based on currently available platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Scaling and Complexity of Stress Fluctuations Associated with Smooth and Jerky Flow in FeCoNiTiAl High-Entropy Alloy

Recent observations of jerky flow in high-entropy alloys (HEA) revealed a high role of self-organization of dislocations in their plasticity. The present work reports the first results of the investigation of stress fluctuations during plastic deformation of an FeCoNiTiAl alloy, examined in a wide temperature range covering both smooth and jerky flow. These fluctuations, which accompany the overall deformation behavior representing an essentially slower stress evolution controlled by the work hardening, were processed using complementary approaches comprising Fourier spectral analysis, refined composite multiscale entropy, and multifractal formalisms. The joint analysis at distinct scales testified that even a macroscopically smooth plastic flow is accompanied by nonrandom fluctuations, disclosing the self-organized dynamics of dislocations. Qualitative changes in such a fine-scale “noise” were found with varying temperature. The observed diversity is significant for understanding the relationships between different scales of plasticity of HEAs and crystal materials in general.

36 MATERIALS SCIENCE↗