Refine
Has Fulltext
- no (242) (remove)
Year of publication
Language
- English (242)
Is part of the Bibliography
- yes (242)
Keywords
- anomalous diffusion (35)
- diffusion (28)
- stochastic processes (10)
- ageing (5)
- first passage (5)
- geometric Brownian motion (5)
- Brownian motion (4)
- Levy flights (4)
- first passage time (4)
- fractional Brownian motion (4)
- living cells (4)
- nonergodicity (4)
- Fokker-Planck equation (3)
- Mittag-Leffler functions (3)
- dynamics (3)
- first-passage (3)
- first-passage time (3)
- models (3)
- polymers (3)
- scaled Brownian motion (3)
- stochastic resetting (3)
- subdiffusion (3)
- superstatistics (3)
- weak ergodicity breaking (3)
- Anomalous diffusion (2)
- Boltzmann distribution (2)
- Debye screening (2)
- Fractional moments (2)
- Langevin equation (2)
- Levy walks (2)
- Sinai diffusion (2)
- active transport (2)
- aspect ratio (2)
- continuous time random walk (CTRW) (2)
- critical phenomena (2)
- crowded fluids (2)
- cylindrical geometry (2)
- diffusing diffusivity (2)
- electrostatic interactions (2)
- financial time series (2)
- first-hitting time (2)
- fluctuation-dissipation theorem (2)
- infection pathway (2)
- nanoparticles (2)
- physiological consequences (2)
- polyelectrolyte adsorption (2)
- power spectral analysis (2)
- probability density function (2)
- protein search (2)
- random diffusivity (2)
- random-walks (2)
- single-particle tracking (2)
- stochastic processes (theory) (2)
- time averaging (2)
- transport (2)
- 15 (1)
- 4 (1)
- Absorption (1)
- Adam-Delbruck scenario (1)
- Ageing (1)
- Antibiotics (1)
- Asymptotic expansions (1)
- Bacterial biofilms (1)
- Bayesian inference (1)
- Biofilms (1)
- Biological Physics (1)
- Biological defense mechanisms (1)
- Black– Scholes model (1)
- Brownian diffusion (1)
- Brownian yet non-Gaussian diffusion (1)
- Bulk-mediated diffusion (1)
- Cattaneo equation (1)
- Characteristic function (1)
- Chebyshev inequality (1)
- Complete Bernstein function (1)
- Completely monotone function (1)
- Composite fractional derivative (1)
- Cystic fibrosis (1)
- Distributed order diffusion-wave equations (1)
- Econophysics (1)
- Fokker-Planck equations (1)
- Fokker-Planck-Smoluchowski equation (1)
- Fokker– Planck equation (1)
- Fox H-function (1)
- Fox H-functions (1)
- Fractional calculus (primary) (1)
- Fractional diffusion equation (1)
- Grunwald-Letnikov approximation (1)
- Interdisciplinary Physics (1)
- Levy flight (1)
- Levy foraging hypothesis (1)
- Levy walk (1)
- Lipid bilayer (1)
- Lévy flights (1)
- Lévy walks (1)
- Markov additive processes (1)
- Mellin transform (1)
- Mittag-Leffler (1)
- Non-Gaussian (1)
- Ornstein–Uhlenbeck process (1)
- Pareto analysis (1)
- Pareto law (1)
- Protein crowding (1)
- Pseudomonas aeruginosa (1)
- Riesz-Feller fractional derivative (1)
- Scaling exponents (1)
- Scher-Montroll transport (1)
- Simulations (1)
- Sputum (1)
- Statistical Physics (1)
- Statistical and Nonlinear Physics (1)
- Stochastic modelling (1)
- Stochastic optimization (1)
- Wealth and income distribution (1)
- adenoassociated virus (1)
- and surface diffusion (1)
- anomalous (or non-Fickian) diffusion (1)
- anomalous heat conduction (1)
- approximate methods (1)
- asymmetric Levy flights (1)
- asymptotic analysis (1)
- autocorrelation function (1)
- autoregressive models (1)
- barrier escape (1)
- behavior (1)
- biological physics (1)
- brownian-motion (1)
- bulk (1)
- cambridge cb4 0wf (1)
- cambs (1)
- cellular signalling (1)
- channel (1)
- chemical relaxation (1)
- clustering (1)
- codifference (1)
- coefficient (1)
- coefficients (1)
- coloured (1)
- comb-like model (1)
- complex (1)
- confinement (1)
- conformational properties (1)
- conservative random walks (1)
- continuous time random (1)
- continuous time random walk (1)
- continuous time random walks (1)
- correlated noise (1)
- coupled initial boundary value problem (1)
- critical adsorption (1)
- crossover anomalous diffusion dynamics (1)
- crossover dynamics (1)
- crowding (1)
- cytoplasm (1)
- density (1)
- dimensional reduction (1)
- dimerization kinetics (1)
- dna coiling (1)
- driven diffusive systems (theory) (1)
- dynamical systems (1)
- dynamics simulation (1)
- ecological (1)
- econophysics (1)
- electrostatics (1)
- endosomal escape (1)
- england (1)
- ensemble and time averaged mean squared displacement (1)
- equation approach (1)
- escherichia-coli (1)
- exact results (1)
- excluded volume (1)
- exclusion process (1)
- exclusion processes (1)
- expanding medium (1)
- extremal values (1)
- fastest first-passage time of N walkers (1)
- first arrival (1)
- first passage process (1)
- first-arrival density (1)
- first-passage time distribution (1)
- first-passage times (1)
- first-reaction time (1)
- flight search patterns (1)
- fluctuations (theory) (1)
- fluorescence correlation spectroscopy (1)
- fluorescence photobleaching recovery (1)
- folding kinetics (1)
- fractional dynamic equations (1)
- fractional dynamics (1)
- fractional dynamics approach (1)
- fractional generalized Langevin equation (1)
- frictional memory kernel (1)
- function (1)
- gel network (1)
- gene regulatory networks (1)
- gene-regulation kinetics (1)
- generalised Langevin equation (1)
- generalised langevin equation (1)
- generalized diffusion equation (1)
- heterogeneous diffusion (1)
- heterogeneous diffusion process (1)
- in-vitro (1)
- income inequality (1)
- income mobility (1)
- intermittent chaotic systems (1)
- intracellular-transport (1)
- kinetic-theory (1)
- langevin equation (1)
- large deviation function (1)
- large-deviation statistic (1)
- lattice gas (1)
- levy flights (1)
- linear response theory (1)
- lipid bilayer membrane dynamics (1)
- local equilibrium (1)
- maximum and range (1)
- mean square displacement (1)
- mean squared displacement (1)
- mean versus most probable reaction times (1)
- membrane (1)
- membrane channel (1)
- memory kernel (1)
- milton rd (1)
- mixed boundary conditions (1)
- mixtures (1)
- mobile-immobile model (1)
- molecular overcrowding (1)
- monte-carlo (1)
- motion (1)
- movement data (1)
- multi-scaling (1)
- multidimensional fractional diffusion equation (1)
- narrow escape problem (1)
- noise (1)
- noise in biochemical signalling (1)
- non-Gaussian (1)
- non-Gaussian diffusion (1)
- non-Gaussian distribution (1)
- non-Gaussian probability (1)
- non-Gaussianity (1)
- non-ergodicity (1)
- non-exponential relaxation (1)
- non-extensive statistics (1)
- nonequilibrium stationary state (1)
- nonstationary diffusivity (1)
- option pricing (1)
- osmotic-pressure (1)
- path integration (1)
- persistence (1)
- phase-transition boundary (1)
- photon-counting statistics (1)
- polyelectrolytes (1)
- polymer translocation (1)
- posttranslational protein translocation (1)
- potential landscape (1)
- power spectral density (1)
- power spectrum (1)
- predator-prey model (1)
- probability distribution function (1)
- quenched energy landscape (1)
- random search process (1)
- random search processes (1)
- random walks (1)
- random-walk (1)
- reaction cascade (1)
- reaction kinetics theory (1)
- reaction rate constants (1)
- recurrence (1)
- reflecting boundary conditions (1)
- resetting (1)
- rotational diffusion (1)
- royal soc chemistry (1)
- science park (1)
- search dynamics (1)
- search efficiency (1)
- search optimization (1)
- sensitivity analysis (1)
- shell-like geometries (1)
- single particle tracking (1)
- single trajectories (1)
- single trajectory analysis (1)
- single-file diffusion (1)
- single-stranded-dna (1)
- single-trajectory analysis (1)
- solid-state nanopores (1)
- space-dependent diffusivity (1)
- spatial-organization (1)
- stationary stochastic process (1)
- statistics (1)
- stochastic dynamics (1)
- stochastic simulation algorithm (1)
- stochastic time series (1)
- structured polynucleotides (1)
- superdiffusion and (1)
- susceptibility (1)
- tau proteins (1)
- telegrapher's equation (1)
- thomas graham house (1)
- time random-walks (1)
- time series analysis (1)
- time-averaged mean squared displacement (1)
- time-series analysis (1)
- trafficking (1)
- truncated power-law correlated noise (1)
- van Hove correlation (1)
- variances (1)
- walks (1)
- water diffusion in the brain (1)
Institute
In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.
Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.
The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories
(2012)
Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.
This paper introduces and analyses a general statistical model, termed the RAndom RElaxations (RARE) model, of random relaxation processes in disordered systems. The model considers excitations that are randomly scattered around a reaction center in a general embedding space. The model's input quantities are the spatial scattering statistics of the excitations around the reaction center, and the chemical reaction rates between the excitations and the reaction center as a function of their mutual distance. The framework of the RARE model is versatile and a detailed stochastic analysis of the random relaxation processes is established. Analytic results regarding the duration and the range of the random relaxation processes, as well as the model's thermodynamic limit, are obtained in closed form. In particular, the case of power-law inputs, which turn out to yield stretched exponential relaxation patterns and asymptotically Paretian relaxation ranges, is addressed in detail.
Macromolecular crowding in living biological cells effects subdiffusion of larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion in terms of random walks on a critical percolation cluster, we here present a case study of EcoRV restriction enzymes involved in vital cellular defence. We show that due to its so far elusive propensity to an inactive state the enzyme avoids non-specific binding and remains well-distributed in the bulk cytoplasm of the cell. Despite the reduced volume exploration capability of subdiffusion processes, this mechanism guarantees a high efficiency of the enzyme. By variation of the non-specific binding constant and the bond occupation probability on the percolation network, we demonstrate that reduced nonspecific binding are beneficial for efficient subdiffusive enzyme activity even in relatively small bacteria cells. Our results corroborate a more local picture of cellular regulation.
Velocity and displacement correlation functions for fractional generalized Langevin equations
(2012)
We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.
Generalized space-time fractional diffusion equation with composite fractional time derivative
(2012)
We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.
We comprehensively analyze the emergence of anomalous statistics in the context of the random relaxation ( RARE) model [Eliazar and Metzler, J. Chem. Phys. 137, 234106 ( 2012)], a recently introduced versatile model of random relaxations in random environments. The RARE model considers excitations scattered randomly across a metric space around a reaction center. The excitations react randomly with the center, the reaction rates depending on the excitations' distances from this center. Relaxation occurs upon the first reaction between an excitation and the center. Addressing both the relaxation time and the relaxation range, we explore when these random variables display anomalous statistics, namely, heavy tails at zero and at infinity that manifest, respectively, exceptionally high occurrence probabilities of very small and very large outliers. A cohesive set of closed-form analytic results is established, determining precisely when such anomalous statistics emerge.
Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin-equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin-equation motion under external confinement are transiently nonergodic-time and ensemble averages behave differently-from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient aging, that is, physical observables such as the time-averaged mean-squared displacement depend on the time lag between the initiation of the system at time t = 0 and the start of the measurement at the aging time t(a). In particular, it turns out that for fractional Langevin-equation motion the aging dependence on ta is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time-averaged mean-squared displacement and present a numerical analysis of this transient aging phenomenon.