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Register a new userUniversal spectral features of different classes of random diffusivity processes
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.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are differe
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Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the proteins instantaneous diffusivity $D_I$. We find that the radius of gyration $R_g$ of the proteins exhibits $1/f$ fluctuations, that are synchronous with the fluctuations of $D_I$. Our analysis demonstrates the validity of the local Stokes-Einstein type relation $D_Ipropto1/(R_g + R_0)$, where $R_0sim0.3$ nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations the validity of the Stokes-Einstein type relation appears to be a general property.
We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $dot{x}_t=sqrt{2 D_0 V(B_t)},xi_t$, where $xi_t$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, and $V(B_t)$ is a stochastic diffusivity (noise strength), which itself is a functional of independent Brownian motion $B_t$. We derive exact, compact expressions for the probability density functions (PDFs) of the first passage time (FPT) $t$ from a fixed location $x_0$ to the origin for three different realisations of the stochastic diffusivity: a cut-off case $V(B_t) =Theta(B_t)$ (Model I), where $Theta(x)$ is the Heaviside theta function; a Geometric Brownian Motion $V(B_t)=exp(B_t)$ (Model II); and a case with $V(B_t)=B_t^2$ (Model III). We realise that, rather surprisingly, the FPT PDF has exactly the Levy-Smirnov form (specific for standard Brownian motion) for Model II, which concurrently exhibits a strongly anomalous diffusion. For Models I and III either the left or right tails (or both) have a different functional dependence on time as compared to the Levy-Smirnov density. In all cases, the PDFs are broad such that already the first moment does not exist. Similar results are obtained in three dimensions for the FPT PDF to an absorbing spherical target.
By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [I. Dornic, textit{et al.} Phys. Rev. Lett. textbf{87}, 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture up and down spins. In particular we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction $x$ of them) assumes a nontrivial shape. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state $T_N(x)$ has an anomalous nonuniversal dependence on $x$.
We study the universal thermodynamic properties of systems consisting of many coupled oscillators operating in the vicinity of a homogeneous oscillating instability. In the thermodynamic limit, the Hopf bifurcation is a dynamic critical point far from equilibrium described by a statistical field theory. We perform a perturbative renormalization group study, and show that at the critical point a generic relation between correlation and response functions appears. At the same time the fluctuation-dissipation relation is strongly violated.
We investigate statistics of lead changes of the maxima of two discrete-time random walks in one dimension. We show that the average number of lead changes grows as $pi^{-1}ln(t)$ in the long-time limit. We present theoretical and numerical evidence that this asymptotic behavior is universal. Specifically, this behavior is independent of the jump distribution: the same asymptotic underlies standard Brownian motion and symmetric Levy flights. We also show that the probability to have at most n lead changes behaves as $t^{-1/4}[ln t]^n$ for Brownian motion and as $t^{-beta(mu)}[ln t]^n$ for symmetric Levy flights with index $mu$. The decay exponent $beta(mu)$ varies continuously with the Levy index when $0<mu<2$, while $beta=1/4$ for $mu>2$.
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