Subdiffusive Dynamics Research Articles

Subdiffusive dynamics in photonic random walks probed with classical light.

The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the random walk of intense classical light under dephasing dynamics can disentangle quantum and ensemble averaging, making it possible to observe subdiffusive walker dynamics, i.e., a behavior very distinct from both a classical and a quantum walker. These findings are demonstrated through proposing photonic random walk in synthetic temporal lattices, based on pulse dynamics in coupled fiber loops.

Sculpting the Electronic Nano-Terrain on a Perovskite Film for Efficient Charge Transport.

Nanopatterned halide perovskites have emerged to improve the performance of optoelectronic devices by controlling the crystallographic and optical properties via morphological modification. However, the correlation between the photophysical property and morphology transformation in nanopatterned perovskite films remains elusive, which hinders the rational design of nanopatterned halide perovskites for optoelectronic devices. In this study, we employed nanoimprinting lithography on a perovskite film to exert a precise control over grain growth and manipulate electronic structures at the level of individual grains. Surface-selective fluorescence lifetime imaging microscopy (FLIM) analyzes the spatiotemporally disentangled geometrical variations in carrier recombination rate and band structure modulation according to different pattern morphologies. Consequently, the stereoscopic mechanism of confined grain growth was unveiled, highlighting the quantitative grain size-based parameters that are crucial for nanoscale material engineering. Notably, the pattern-induced reduction of effective charge mass enabled exclusive control over the subdiffusive carrier transport dynamics on perovskite surfaces, ultimately realizing the surface-selective perovskite photodetectors. The implications of this study are expected to provide valuable guidelines, inspiring innovative design protocols for advancing the next-generation optoelectronic technologies.

Fundamental Dynamics of Popularity-Similarity Trajectories in Real Networks.

Real networks are complex dynamical systems, evolving over time with the addition and deletion of nodes and links. Currently, there exists no principled mathematical theory for their dynamics-a grand-challenge open problem. Here, we show that the popularity and similarity trajectories of nodes in hyperbolic embeddings of different real networks manifest universal self-similar properties with typical Hurst exponents H≪0.5. This means that the trajectories are predictable, displaying antipersistent or "mean-reverting" behavior, and they can be adequately captured by a fractional Brownian motion process. The observed behavior can be qualitatively reproduced in synthetic networks that possess a latent geometric space, but not in networks that lack such space, suggesting that the observed subdiffusive dynamics are inherently linked to the hidden geometry of real networks. These results set the foundations for rigorous mathematical machinery for describing and predicting real network dynamics.

Super-ballistic diffusion induced by nonlinear interactions in a one-dimensional quasiperiodic lattice

We numerically investigate the spreading dynamics of wave packets in a one-dimensional lattice with quasiperiodic disorders and nonlinear interactions. Under moderate disorder strength, we reveal an intriguing super-ballistic diffusion driven by increasing the interaction strength from the ballistic diffusion in the non- and weakly interacting cases. We obtain a wide parameter region for such a faster-than-ballistic spreading of wave packets in the quasiperiodic lattice, although the nonlinear self-trapping is dominated under strong interactions. The super-ballistic diffusion is further analyzed based on the point source model. We also show the interaction-induced sub-diffusive spreading in the Anderson localized regime. The super-ballistic and sub-diffusive dynamics are exhibited in the spreading that starts from both the single-site and Gaussian wave packets. Our results showcase the interaction-enabled super-ballistic diffusion, which is scarce and experimentally realizable in artificial atomic or photonic lattices.

A wavelet collocation method for fractional Black–Scholes equations by subdiffusive model

AbstractIn this investigation, we propose a numerical method based on the fractional‐order generalized Taylor wavelets (FGTW) for option pricing and the fractional Black–Scholes equations. This model studies option pricing when the underlying asset has subdiffusive dynamics. By applying the regularized beta function, we give an exact formula for the Riemann–Liouville fractional integral operator (RLFIO) of the FGTW. An error analysis of the numerical scheme for estimating solutions is performed. Finally, we conduct a variety of numerical experiments for several standard examples from the literature to assess the efficiency of the proposed method.

Hierarchically Coupled Ornstein–Uhlenbeck Processes for Transient Anomalous Diffusion

The nonlinear dependence of the mean-squared displacement (MSD) on time is a common characteristic of particle transport in complex environments. Frequently, this anomalous behavior only occurs transiently before the particle reaches a terminal Fickian diffusion. This study shows that a system of hierarchically coupled Ornstein–Uhlenbeck equations is able to describe both transient subdiffusion and transient superdiffusion dynamics, as well as their sequential combinations. To validate the model, five distinct experimental, molecular dynamics simulation, and theoretical studies are successfully described by the model. The comparison includes the transport of particles in random optical fields, supercooled liquids, bedrock, soft colloidal suspensions, and phonons in solids. The model’s broad applicability makes it a convenient tool for interpreting the MSD profiles of particles exhibiting transient anomalous diffusion.

Activation energy and molecular weight dependence of cooperative tracer chains diffusion in highly entangled polymer melts

AbstractThe generalized Langevin equation for cooperative dynamics of Guenza predicts the dynamics of chains in entangled polymers is cooperative with anomalous properties, and at variance with the tube‐reptation model. The center‐of‐mass mean‐square displacements at shorter times are subdiffusive with with β < 1, contradicting the common assumption of reptation within the tube. At some longer time the subdiffusive dynamics exhibits the crossover to free diffusion with . Moreover the subdiffusive dynamics is heterogeneous, non‐Gaussian, and cooperative. These predictions have been confirmed by using neutron spin echo spectroscopy in entangled polyethylene melts [M. Zamponi, et al. J. Phys. Chem. B 2008, 112, 16220], and in tracer diffusion of short polyethylene chains in a highly entangled polyethylene melt [M. Zamponi et al. Phys. Rev. Lett. 2021, 126, 187801]. The latter was confirmed in poly(ethylene oxide) tracer diffusion in highly entangled poly(ethylene oxide) melt [M. Kruteva et al. Macromolecules 2021, 54, 11384]. Notwithstanding, there are other important data sets obtained in the NSE experiments but were left unexplained. One set consists of the activation energies of the Arrhenius temperature dependence of D for each tracer. Another is the molecular weight dependence of D of the tracers determined at the same temperature. In this article the predictions of the Coupling Model are applied to these two sets of data. Good quantitative agreements of the CM predictions with experimental data provide additional support to the cooperativity dynamics of entangled polymers as concluded by others. Additionally, all the properties of cooperative diffusion of entangled polymer chains are shown to be isomorphic to those found in cooperative diffusions in totally different systems. Diffusion in all are governed by interaction between the diffusing units, and from which the universal properties originate.

Subdiffusive dynamics and hydrodynamic fluctuations: how the latter affect the former.

The characteristics of subdiffusion are influenced by hydrodynamic fluctuations, not the scaling of the mean square displacement (MSD) at the long time limit, but rather the transition of this property from ballistic behaviour at early times to its final scaling at large times. Additionally, since a significant portion of the normalised velocity autocorrelation function (NVAF), a widely used motion descriptor, no longer adequately describes the antipersistent character that is typical of a subdiffusive motion, it is also impacted by these fluctuations. The combined findings can lead to misleading conclusions if hydrodynamic fluctuations are not taken into account. Diffusing and vorticity time scales are crucial for the way the motion turns into the final subdiffusion dynamics, whose exponent is determined by the scaling of the friction.

Nanoparticle transport in biomimetic polymer‐linked emulsions

AbstractThe ability of nanoparticles to penetrate and transport through soft tissues is essential to delivering therapeutics to treat diseases or signaling agents for advanced imaging and sensing. Nanoparticle transport in biological systems, however, is challenging to predict and control due to the physicochemical complexity of tissues and biological fluids. Here, we demonstrate that nanoparticles suspended in a novel class of soft matter—polymer‐linked emulsions (PLEs)—exhibit characteristics essential for mimicking transport in biological systems, including subdiffusive dynamics, non‐Gaussian displacement distributions, and decoupling of dynamics from material viscoelasticity. Using multiple particle tracking, we identify the physical mechanisms underlying this behavior, which we attribute to a coupling of nanoparticle dynamics to fluctuations in the local network of polymer‐linked droplets. Our findings demonstrate the potential of PLEs to serve as fully synthetic mimics of biological transport.

What determines sub-diffusive behavior in crowded protein solutions?

The aqueous environment inside cells is densely packed. A typical cell has a macromolecular concentration in the range 90–450 g/L, with 5%–40% of its volume being occupied by macromolecules, resulting in what is known as macromolecular crowding. The space available for the free diffusion of metabolites and other macromolecules is thus greatly reduced, leading to so-called excluded volume effects. The slow diffusion of macromolecules under crowded conditions has been explained using transient complex formation. However, sub-diffusion noted in earlier works is not well characterized, particularly the role played by transient complex formation and excluded volume effects. We have used Brownian dynamics simulations to characterize the diffusion of chymotrypsin inhibitor 2 in protein solutions of bovine serum albumin and lysozyme at concentrations ranging from 50 to 300 g/L. The predicted changes in diffusion coefficient as a function of crowder concentration are consistent with NMR experiments. The sub-diffusive behavior observed in the sub-microsecond timescale can be explained in terms of a so-called cage effect, arising from rattling motion in a local molecular cage as a consequence of excluded volume effects. By selectively manipulating the nature of interactions between protein molecules, we determined that excluded volume effects induce sub-diffusive dynamics at sub-microsecond timescales. These findings may help to explain the diffusion-mediated effects of protein crowding on cellular processes.

Multilayered noise model for transport in complex environments.

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

Cooperation and Competition Coupled Diffusion of Multi-Feature on Multiplex Networks and Its Control

Cooperation and competition widely exist in various kinds of network diffusions which however are usually studied separately. Recently, a novel network diffusion model, called multi-feature diffusion (MFD), attracts considerable attentions. The existing works usually assume that each feature diffuses independently and neglects the possible complex interplay between different features. In this paper, we introduce the cooperation and competition into the MFD and propose the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ooperation and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ompetition coupled diffusion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> ulti- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> eature on multiplex network (CCMF). An unified framework and mathematical analytic theory regarding CCMF are then presented which are applicable and computationally efficient for any number of features and their own different sub-diffusion dynamics. In addition, an interesting finding is obtained in CCMF: compared with the high intensity competition, performing lower intensity competition under weak competition ability is more easier to result in positive effect. Due to the great importance of controlling network diffusion in many diverse contexts, we also propose an optimal allocation strategy of control resource for CCMF which first realizes the promotion and suppression of network diffusion simultaneously under one optimization framework and is also verified to be very efficient.

Stochastic motion and transcriptional dynamics of pairs of distal DNA loci on a compacted chromosome.

Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional processes, including transcription initiation, the pairwise motion of distal chromosomal elements such as enhancers and promoters is essential and necessitates dynamic fluidity. Here, we used a live-imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and their transcriptional output while systematically varying the genomic separation between these two DNA loci. Our analysis reveals the coexistence of a compact globular organization and fast subdiffusive dynamics. These combined features cause an anomalous scaling of polymer relaxation times with genomic separation leading to long-ranged correlations. Thus, encounter times of DNA loci are much less dependent on genomic distance than predicted by existing polymer models, with potential consequences for eukaryotic gene expression.

Theoretical Analysis of Exciton Wave Packet Dynamics in Polaritonic Wires.

We present a comprehensive study of the exciton wave packet evolution in disordered lossless polaritonic wires. Our simulations reveal signatures of ballistic, diffusive, and subdiffusive exciton dynamics under strong light-matter coupling and identify the typical time scales associated with the transitions between these qualitatively distinct transport phenomena. We determine optimal truncations of the matter and radiation subsystems required for generating reliable time-dependent data from computational simulations at an affordable cost. The time evolution of the photonic part of the wave function reveals that many cavity modes contribute to the dynamics in a nontrivial fashion. Hence, a sizable number of photon modes is needed to describe exciton propagation with a reasonable accuracy. We find and discuss an intriguingly common lack of dominance of the photon mode on resonance with matter in both the presence and absence of disorder. We discuss the implications of our investigations for the development of theoretical models and analysis of experiments where coherent intermolecular energy transport and static disorder play an important role.

Subdiffusive movement of chromosomal loci in bacteria explained by DNA bridging

Chromosomal loci in bacterial cells show a robust subdiffusive scaling of the mean square displacement, $\text{MSD}(\ensuremath{\tau})\ensuremath{\sim}{\ensuremath{\tau}}^{\ensuremath{\alpha}}$, with $\ensuremath{\alpha}&lt;0.5$. On the other hand, recent experiments have also shown that DNA-bridging nucleoid associated proteins (NAPs) play an important role in chromosome organization and compaction. Here, using polymer simulations we investigate the role of DNA bridging in determining the dynamics of chromosomal loci. We find that bridging compacts the polymer and reproduces the subdiffusive elastic dynamics of monomers at timescales shorter than the bridge lifetime. Consistent with this prediction, we measure a higher exponent in a NAP mutant compared to the wild type. Furthermore, bridging can reproduce the rare but ubiquitous rapid movements of chromosomal loci that have been observed in experiments. In our model the scaling exponent defines a relationship between the abundance of bridges and their lifetime. Using this and the observed mobility of chromosomal loci, we predict a lower bound on the average bridge lifetime of around five seconds.

Long-Wavelength Fluctuations in Quasi-2D Supercooled Liquids.

We use molecular simulation to characterize the dynamics of supercooled liquids confined in quasi-2D slit geometries. Similar to bulk supercooled liquids, the confined systems exhibit subdiffusive dynamics on intermediate time scales arising from particle localization inside their neighbor cages, followed by an eventual crossover to diffusive behavior as cage rearrangement occurs. The quasi-2D confined liquids also exhibit signatures of long-wavelength fluctuations (LWFs) in the lateral directions parallel to the confining walls, reminiscent of the collective displacements observed in 2D but not 3D systems. The magnitude of the LWFs increases with the lateral dimensions of systems with the same particle volume fraction and confinement length scale, consistent with the logarithmic scaling predicted for 2D Mermin-Wagner fluctuations. The amplitude of the fluctuations is a nonmonotonic function of the confinement length scale because of a competition between caging and strengthening LWFs upon approaching the 2D limit. Our findings suggest that LWFs may play an important role in understanding the behavior of confined supercooled liquids due to their prevalence over a surprisingly broad range of particle densities and confinement length scales.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin.

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks.

This paper presents the development and analysis of artificial neural network (ANN) models for the nonlinear fractional-order (FO) point reactor kinetics model, FO Nordheim-Fuchs model, inverse FO point reactor kinetics model and FO constant delayed neutron production rate approximation model. These models represent the dynamics of a nuclear reactor with neutron transport modeled as subdiffusion. These FO models are nonlinear in nature, are comprised of a system of coupled fractional differential equations and integral equations, and are considered to be difficult for solving both analytically and numerically. The ANN models were developed using the data generated from these models. The work involves the iterative process of ANN learning with different combinations of layers and neurons. It is shown through extensive simulation studies that the developed ANN models faithfully capture the transient and steady-state dynamics of these FO models, thereby providing a satisfactory representation for the nonlinear subdiffusive process of neutron transport in a nuclear reactor.

Subdiffusive High-Pressure Hydrogen Gas Dynamics in Elastomers

Elastomeric rubber materials serve a vital role as sealing materials in the hydrogen storage and transport infrastructure. With applications including O-rings and hose liners, these components are exposed to pressurized hydrogen at a range of temperatures, cycling rates, and pressure extremes. High-pressure exposure and subsequent rapid decompression often lead to cavitation and stress-induced damage of the elastomer due to localization of the hydrogen gas. Here, we use all-atom classical molecular dynamics simulations to assess the impact of compositional variations on gas diffusion within the commonly used elastomer ethylene–propylene–diene monomer (EPDM). With the aim to build a predictive understanding of precursors to cavitation and to motivate material formulations that are less sensitive to hydrogen-induced failure, we perform systematic simulations of gas dynamics in EPDM as a function of temperature, gas concentration, and cross-link density. Our simulations reveal anomalous, subdiffusive hydrogen motion at pressure and intermediate times. We identify two groups of gas with different mobilities: one group exhibiting high mobility and one group exhibiting low mobility due to their motion being impeded by the polymer. With decreasing temperatures, the low-mobility group shows increased gas localization, the necessary precursor for cavitation damage in these materials. At lower temperatures, increasing cross-link density led to greater hydrogen gas mobility and a lower fraction of caged hydrogen, indicating that increasing cross-link density may reduce precursors to cavitation. Finally, we use a two-state kinetic model to determine the energetics associated with transitions between these two mobility states.

Anomalous Dynamics in Macromolecular Liquids.

Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties.