Article
Mathematics, Interdisciplinary Applications
Nickolay Korabel, Hamed Al Shamsi, Alexey O. Ivanov, Sergei Fedotov
Summary: This paper develops a non-Markovian persistent random walk model to study the characteristics of intracellular transport. The results show that the rest times play an important role in the persistence of random walks in the cell.
FRACTAL AND FRACTIONAL
(2023)
Article
Multidisciplinary Sciences
Gaetano Zimbardo, Francesco Malara, Silvia Perri
Summary: The article introduces a transport equation to describe superdiffusive transport of energetic particles in the solar system and plasma environments, where the time derivative is fractional rather than integer. The authors show that this results in superdiffusion parallel to the magnetic field, and discuss the advantages compared to approaches using transport equations with symmetric spatial fractional derivatives.
Article
Mathematics, Applied
Zhiqiang Li, Yanzhe Fan
Summary: In this paper, we focus on studying the asymptotic behaviors of solutions for the Cauchy problem of time-space fractional superdiffusion and subdiffusion equations with integral initial conditions. The Riemann-Liouville derivative is used in the temporal direction, while the integral fractional Laplacian is applied in the spatial variables. We construct and investigate the fundamental solutions of the considered equations, represented in terms of the Fox H-function, using asymptotic expansions. The asymptotic behaviors of solutions in the sense of Lp(Rd) and Lp,infinity(Rd) norms are obtained with the help of Young's inequality for convolution. Gradient estimates and large time behaviors of solutions are also provided, including the optimal L2 decay estimate for the subdiffusion equation.
Article
Materials Science, Multidisciplinary
I. N. Volovichev, D. V. Kadygrob
Summary: The quantum diffusion in a one-dimensional lattice under the influence of spatially inhomogeneous Gaussian noise in a tunneling regime is studied, and it is found that the thermopower appears at any value of the tunneling coupling. In the strong tunneling regime, the thermoelectric effect only occurs in the presence of a constant external electric field, when the drift component of charge transport can be neglected.
Article
Engineering, Mechanical
Aloisi Somer, Andressa Novatski, Gerson Kniphoff da Cruz, Claudia Bonardi Kniphoff da Cruz, Francisco Carlos Serbena, Ervin Kaminski Lenzi
Summary: Obtaining thermal parameters based on the analysis of the amplitude or phase of the photoacoustic signal from photothermal measurements is useful. This study investigates the discrepancy between experimentally measured amplitude and phase and the expected theoretical result from the classical model for AISI 316 samples. The results show inconsistent thermal parameters obtained from individual amplitude analysis compared to phase analysis, and this study aims to propose a simultaneous analysis of both amplitude and phase to obtain a unique value for the thermal parameters. Additionally, fractional models were used to improve the fit of experimental data and provide results close to the expected thermal diffusivity value.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Faheem Gilani, Dimitrios Giannakis, John Harlim
Summary: This study develops a nonparametric method to predict non-Markovian time series of partially observed dynamics, using delay embedding theory and regression functions. The proposed approach utilizes kernel-based linear estimators and Markovian kernel smoothing for effective prediction in high-dimensional covariate spaces, with a nonparametric smoother introduced for denoising noisy training data. Overall, the method shows promising results for skillful prediction in complex scenarios.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Multidisciplinary Sciences
David Wei, Antonio Rubio-Abadal, Bingtian Ye, Francisco Machado, Jack Kemp, Kritsana Srakaew, Simon Hollerith, Jun Rui, Sarang Gopalakrishnan, Norman Y. Yao, Immanuel Bloch, Johannes Zeiher
Summary: Researchers experimentally investigated the relaxation of domain walls in spin chains in a cold-atom quantum simulator and found that it is governed by the KPZ dynamical exponent. They also discovered that the occurrence of KPZ scaling requires both integrability and a nonabelian SU(2) symmetry. Additionally, they used a quantum gas microscope to measure an observable based on spin-transport statistics and observed the nonlinearity characteristic of KPZ universality.
Article
Multidisciplinary Sciences
N. Levernier, T. Mendes, O. Benichou, R. Voituriez, T. Guerin
Summary: Persistence plays a crucial role in random processes, but calculating persistence exponents for non-Markovian systems is difficult. This study introduces a theoretical framework that determines the persistence exponents of Gaussian non-Markovian processes with non-stationary dynamics.
NATURE COMMUNICATIONS
(2022)
Article
Mathematics, Applied
Huibiao Yan, Jin Zhou, Weiqiang Li, Jun-an Lu, Ruguo Fan
Summary: Studies have shown that superdiffusion in multiplex networks may emerge when the interlayer diffusion coefficient is large enough. This paper proposes superdiffusion criteria and a construction mechanism for generating superdiffusible two-layered networks. The method provided can guide the discovery and construction of superdiffusible multiplex networks without the need to calculate the second smallest Laplacian eigenvalues.
Article
Radiology, Nuclear Medicine & Medical Imaging
David A. Reiter, Fatemeh Adelnia, Donnie Cameron, Richard G. Spencer, Luigi Ferrucci
Summary: An anomalous diffusion model was developed to characterize skeletal muscle perfusion, using stretched exponential signal decay to describe superdiffusion. The model showed low errors and stable parameter estimates in numerical simulations.
MAGNETIC RESONANCE IN MEDICINE
(2021)
Article
Physics, Multidisciplinary
S. Vitali, P. Paradisi, G. Pagnini
Summary: Through intensive simulations, it has been shown that the characteristic features of anomalous diffusion can be explained by a random walk driven by two different Markovian hopping-trap mechanisms. By studying ensemble and single-particle observables, it is found that this model matches the main characteristics of anomalous diffusion commonly observed in living systems. The transition of the walker's distribution from exponential to stretched-exponential and finally to Gaussian distribution can be observed by considering the inclusion of non-Gaussian intervals.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mechanics
Vir B. Bulchandani, Sarang Gopalakrishnan, Enej Ilievski
Summary: This review summarizes recent advances in understanding anomalous transport in spin chains, particularly through the lens of integrability. Numerical methods based on tensor-network techniques have revealed anomalous transport in many canonical integrable spin chains, such as the Heisenberg model. The framework of generalized hydrodynamics has been extended to explain some of the underlying mechanisms of anomalous transport, with discussions on similarities and differences with other contexts. Further, potential transport anomalies in systems with emergent or approximate integrability are briefly reviewed, with ongoing research on anomalous transport and dynamics.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Physics, Multidisciplinary
Pieter W. Claeys, Austen Lamacraft, Jonah Herzog-Arbeitman
Summary: Recent studies have found that the dynamics of spin in the spin-1/2 Heisenberg chain at finite temperature exhibits superdiffusion. This study examines spin transport in a spin-1/2 chain with fluctuating exchange couplings and finds that regular diffusion persists at long times with an enhanced diffusion constant.
PHYSICAL REVIEW LETTERS
(2022)
Article
Mathematics
Jingting Yao, Muhammad Ali Raza Anjum, Anshuman Swain, David A. Reiter
Summary: This study introduces the IVIM and FFD models based on DWI for skeletal muscle perfusion and provides a mathematical framework for direct transformation of parameters between the two models. In vivo DWI measurements in skeletal muscle are analyzed using both models, demonstrating the difficulty of model selection based on goodness of fit to experimental data. This analysis offers a framework for interpreting and harmonizing perfusion parameters using IVIM and FFD models.
Article
Mathematics, Applied
Philipp Harms
Summary: Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. Numerical discretizations of these representations have strong convergence rates of arbitrarily high polynomial order, which explains the potential and limitations of using them as a basis for Monte Carlo schemes in fractional volatility models like the rough Bergomi model.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
Article
Quantum Science & Technology
Noah Van Horne, Dahyun Yum, Tarun Dutta, Peter Haenggi, Jiangbin Gong, Dario Poletti, Manas Mukherjee
NPJ QUANTUM INFORMATION
(2020)
Review
Physics, Multidisciplinary
Peter Talkner, Peter Haenggi
REVIEWS OF MODERN PHYSICS
(2020)
Article
Mathematics, Applied
Sergey Denisov, Olga Vershinina, Juzar Thingna, Peter Haenggi, Mikhail Ivanchenko
Article
Physics, Multidisciplinary
Igor Goychuk, Thorsten Poeschel
NEW JOURNAL OF PHYSICS
(2020)
Editorial Material
Physics, Multidisciplinary
Igor Goychuk, Thorsten Poeschel
Article
Physics, Multidisciplinary
Igor Goychuk, Thorsten Poeschel
Summary: Research shows that superdiffusion and supertransport emerge as a critical phenomenon when a Brownian motion is driven out of thermal equilibrium by a constant force. At the edge of a phase transition, velocity fluctuations diverge asymptotically and diffusion becomes superballistic. The autocorrelation function of velocity fluctuations in this nonergodic regime exhibits a striking aging behavior.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Jakub Spiechowicz, Peter Haenggi, Jerzy Luczka
Summary: This study investigates the phenomenon of multistability in the velocity dynamics of a Brownian particle. It finds that the multistability is robust with respect to the choice of the starting position and velocity of the particle for moderate and high temperatures, but is affected by initial conditions in the low temperature regime.
Article
Physics, Multidisciplinary
Igor Goychuk
Summary: We describe a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion. The model features a nonlinear velocity friction and corresponding multiplicative thermal noise. The key nonlinearity in this study comes from the friction instead of a periodic external potential as in previous studies. The phenomenon of giant enhancement of diffusion is closely related to the increased kinetic temperature of particles at and beyond the critical point.
NEW JOURNAL OF PHYSICS
(2022)
Review
Physics, Multidisciplinary
Jakub Spiechowicz, Ivan G. Marchenko, Peter Haenggi, Jerzy Luczka
Summary: The diffusion of small particles is widely studied and applied in various scientific fields. This article focuses on the temperature dependence of the diffusion coefficient for a Brownian particle, exploring different physical systems and their diffusion characteristics.
Article
Multidisciplinary Sciences
Igor Goychuk
Summary: This study investigates a basic model of driven Brownian motion with a velocity-dependent friction coefficient in nonlinear viscoelastic media. The research shows that under constant force driving, microparticles can exhibit nonlinear oscillations of velocity and position by a Hopf bifurcation. These oscillations can exceed the size of the particles and span several time decades, primarily determined by the memory time of the medium.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Physics, Fluids & Plasmas
Igor Goychuk, Thorsten Poschel
Summary: Experimental studies have shown subdiffusion of nanoparticles in various environments, combining features of both viscoelasticity and non-Markovian diffusional processes. The viscoelastic subdiffusion approach in random environments based on Langevin dynamics provides a more rational explanation for these findings compared to earlier proposed theories.
Article
Physics, Fluids & Plasmas
K. Bialas, J. Luczka, P. Haenggi, J. Spiechowicz
Article
Physics, Fluids & Plasmas
Igor Goychuk, Thorsten Poeschel
Article
Physics, Multidisciplinary
P. Haenggi, J. Luczka, J. Spiechowicz
ACTA PHYSICA POLONICA B
(2020)
Article
Physics, Fluids & Plasmas
Igor Goychuk
