SEARCH · Engineering Papers

Results for “Diffusion & random walks”

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.

SourceResearch connectionFrom yearThrough year

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

29 records · Page 2

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗

DOE OSTI2022

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient $\hat{q}$ and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Microstructural and rheological training and memory of nanocolloidal soft glasses under cyclic shear

An intrinsic feature of disordered and out-of-equilibrium materials, such as glasses, is the dependence of their properties on their history. An important example is rheological memory, in which disordered solids obtain properties based on their deformation history. Here, in this study, we employ x-ray photon correlation spectroscopy with in situ rheometry to characterize memory formation in a nanocolloidal soft glass due to cyclic shear. During a cycle, particles undergo irreversible displacements composed of a combination of shear-induced diffusion and heterogeneous, residual strain fields. At lower shear amplitudes, the displacements resemble a random walk in which the directions in each cycle are independent of those in preceding cycles, while at high amplitude, the irreversible displacements in consecutive cycles become correlated. The magnitudes of the displacements decrease with each cycle before reaching a steady state where the microstructure has been trained to achieve enhanced reversibility even at shear amplitudes well above yielding and despite the presence of thermal fluctuations. At amplitudes below and near yielding, these decreases are monotonic, while well above yielding, they are nonmonotonic, suggesting evidence of shear banding. Accompanying this microstructural training are corresponding decreases in the dissipation during each cycle and the magnitude of the residual stress toward steady-state values. Memory of the training is revealed by measurements in which the amplitude of the shear is changed after steady state is reached. The magnitude of the particle displacements, as well as the dissipation and the change in residual stress, vary nonmonotonically with the new shear amplitude, having minima near the training amplitude, thereby revealing correlated microscopic and macroscopic signatures of memory.

Chen, Yihao [Johns Hopkins Univ., Baltimore, MD (U↗

DOE OSTI2024

Distinct universality classes of diffusive transport from full counting statistics

The hydrodynamic transport of local conserved densities furnishes an effective coarse-grained description of the dynamics of a many-body quantum system. However, the full quantum dynamics contains much more structure beyond the simplified hydrodynamic description. Here we show that systems with the same hydrodynamics can nevertheless belong to distinct dynamical universality classes, as revealed by new classes of experimental observables accessible in synthetic quantum systems, which can, for instance, measure simultaneous site-resolved snapshots of all of the particles in a system. Specifically, we study the full counting statistics of spin transport, whose first moment is related to linear-response transport, but the higher moments go beyond. We present an analytic theory of the full counting statistics of spin transport in various integrable and nonintegrable anisotropic one-dimensional spin models, including the XXZ spin chain. We find that spin transport, while diffusive on average, is governed by a distinct non-Gaussian dynamical universality class in the models considered. We consider a setup in which the left and right half of the chain are initially created at different magnetization densities, and consider the probability distribution of the magnetization transferred between the two half-chains. We derive a closed-form expression for the probability distribution of the magnetization transfer, in terms of random walks on the half-line. We show that this distribution strongly violates the large-deviation form expected for diffusive chaotic systems, and explain the physical origin of this violation. Here, we discuss the crossovers that occur as the initial state is brought closer to global equilibrium. Our predictions can directly be tested in experiments using quantum gas microscopes or superconducting qubit arrays.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Geometric Delocalization in Two Dimensions

We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat two-dimensional space. We first prove that any rotationally symmetric two-dimensional membrane embedded in flat three-dimensional space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric two-dimensional membrane. We use it to explicitly construct a class of transient two-dimensional manifolds with a nontrivial metric and height function but “zero average curvature,” which we dub “tablecloth manifolds.” The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, nonexistence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

Anderson localization↗

DOE OSTI2024

Formation of transfermium elements in reactions with Pb 208

Within the Langevin framework, we investigate the dynamics of the fusion process for production of transfermium elements in reactions of Ca 48 , Ti 50 , Cr 54 , and Fe 58 with Pb 208 . After the reacting nuclei have made contact, the early dynamical stage is dominated by the dissipation of the initial radial kinetic energy, while the subsequent shape evolution is diffusive. The probability for surmounting the inner barrier and forming a compound system is obtained by simulating the evolution as a Metropolis random walk in a five-dimensional potential-energy landscape. Good agreement with the available data is obtained, especially for the maximal formation probability. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Unified understanding of the impact of semiflexibility, concentration, and molecular weight on macromolecular-scale ring diffusion

Conformationally fluctuating, globally compact macromolecules such as polymeric rings, single-chain nanoparticles, microgels, and many-arm stars display complex dynamic behaviors due to their rich topological structure and intermolecular organization. Synthetic rings are hybrid objects with conformations that display both ideal random walk and compact globular features, which can serve as models of genomic DNA. To date, emphasis has been placed on the effect of ring molecular weight on their unusual behaviors. Here, we combine simulations and a microscopic force-level theory to build a unified understanding for how key aspects of ring dynamics depend on different tunable molecular properties including backbone rigidity, monomer concentration, degree of traditional entanglement, and molecular weight. Our large-scale molecular dynamics simulations of ring melts with very different backbone stiffnesses reveal unanticipated behaviors which agree well with our generalized theory. This includes a universal master curve for center-of-mass diffusion constants as a function of molecular weight scaled by a chemistry and thermodynamic state-dependent critical molecular weight that generalizes the concept of an entanglement cross-over for linear chains. The key physics is how backbone rigidity and monomer concentration induced changes of the entanglement length, interring packing, degree of interpenetration, and liquid compressibility slow down space-time dynamic-force correlations on macromolecular scales. A power law decay of the center-of-mass diffusion constant with inverse molecular weight squared is the first consequence, followed by an ultraslow activated hopping transport regime. Our results set the stage to address slow dynamics and kinetic arrest in different families of compact synthetic and biological polymeric systems.

Science & Technology - Other Topics↗

DOE OSTI2024

The persistence of memory in ionic conduction probed by nonlinear optics

Predicting practical rates of transport in condensed phases enables the rational design of materials, devices and processes. This is especially critical to developing low-carbon energy technologies such as rechargeable batteries. For ionic conduction, the collective mechanisms, variation of conductivity with timescales and confinement, and ambiguity in the phononic origin of translation, call for a direct probe of the fundamental steps of ionic diffusion: ion hops. However, such hops are rare-event large-amplitude translations, and are challenging to excite and detect. Here we use single-cycle terahertz pumps to impulsively trigger ionic hopping in battery solid electrolytes. This is visualized by an induced transient birefringence, enabling direct probing of anisotropy in ionic hopping on the picosecond timescale. The relaxation of the transient signal measures the decay of orientational memory, and the production of entropy in diffusion. We extend experimental results using in silico transient birefringence to identify vibrational attempt frequencies for ion hopping. Using nonlinear optical methods, we probe ion transport at its fastest limit, distinguish correlated conduction mechanisms from a true random walk at the atomic scale, and demonstrate the connection between activated transport and the thermodynamics of information.

25 ENERGY STORAGE↗

DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

Here, we use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile. On top of this mean shrinkage, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening. Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events. In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2022

Rotational Dynamics and Transition Mechanisms of Surface-Adsorbed Proteins

Assembly of biomolecules at solid-water interfaces requires molecules to traverse complex orientation-dependent energy landscapes through processes that are poorly understood, largely due to the dearth of in-situ single molecule measurements and statistical analyses of the rotational dynamics that define directional selection. Emerging capabilities in high-speed atomic force microscopy and machine learning have allowed us to directly determine the orientational energy landscape and observe and quantify the rotational dynamics for protein nanorods on the surface of muscovite mica under a variety of conditions. Comparisons with kinetic Monte Carlo simulations show that the transition rates between adjacent orientation-specific energetic minima can largely be understood through traditional models of in-plane Brownian rotation across a biased energy landscape, with resulting transition rates that are exponential in the energy-barriers between states. However, transitions between more distant angular states are decoupled from barrier height, with jump-size distributions showing a power-law decay that is characteristic of a non-classical Levy-flight random walk, indicating that large jumps are enabled by alternative modes of motion via activated states. The findings provide new insights into the dynamics of biomolecules at solid-liquid interfaces that lead to self-assembly, epitaxial matching and other orientationally anisotropic outcomes and define a general procedure for exploring such dynamics with implications for hybrid biomolecular-inorganic materials design.

Orientational energy landscapes, Rotational dynami↗