Optimal escape from metastable states driven by non-Gaussian noise

5 pages, 2 figures5 pages, 2 figures5 pages, 2 figuresWe investigate escape processes from metastable states that are driven by non-Gaussian noise. Using a path integral approach, we define a weak-noise scaling limit that identifies optimal escape paths as minima of a stochastic action, while retaining the infinite hierarchy of noise cumulants. This enables us to investigate the effect of different noise amplitude distributions. We find generically a reduced effective potential barrier but also fundamental differences, particularly for the limit when the non-Gaussian noise pulses are relatively slow. Here we identify a class of amplitude distributions that can induce a single-jump escape from the potential well. Our results highlight that higher-order noise cumulants crucially influence escape behaviour even in the weak-noise limit

Entropy production for velocity-dependent macroscopic forces: the problem of dissipation without fluctuations

In macroscopic systems, velocity-dependent phenomenological forces $F(v)$ are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature $T$, ruled by a microscopic Hamiltonian $H$. The mapping $(H,T) \to F(v)$ - even if effective for many purposes - may lead to applications of stochastic thermodynamics where an $incomplete$ fluctuating entropy production (FEP) is derived. An enlightening example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force $F(v)$. Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the $T$-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.Comment: 6 pages, 3 figure

Structural analysis of disordered dimer packings

Jammed disordered packings of non-spherical particles show significant variation in the packing density as a function of particle shape for a given packing protocol. Rotationally symmetric elongated shapes such as ellipsoids, spherocylinders, and dimers, e.g., pack significantly denser than spheres over a narrow range of aspect ratios, exhibiting a characteristic peak at aspect ratios of αmax ≈ 1.4–1.5. However, the structural features that underlie this non-monotonic behaviour in the packing density are unknown. Here, we study disordered packings of frictionless dimers in three dimensions generated by a gravitational pouring protocol in LAMMPS. Focusing on the characteristics of contacts as well as orientational and translational order metrics, we identify a number of structural features that accompany the formation of maximally dense packings as the dimer aspect ratio α is varied from the spherical limit. Our results highlight that dimer packings undergo significant structural changes as α increases up to αmax manifest in the reorganisation of the contact configurations between neighbouring dimers, increasing nematic order, and decreasing local translational order. Remarkably, for α > αmax our metrics remain largely unchanged, indicating that the peak in the packing density is related to the interplay of structural rearrangements for α αmax

Investigation of a generalized Obukhov Model for Turbulence

We introduce a generalization of Obukhov's model [A.M. Obukhov, Adv. Geophys. 6, 113 (1959)] for the description of the joint position-velocity statistics of a single fluid particle in fully developed turbulence. In the presented model the velocity is assumed to undergo a continuous time random walk. This takes into account long time correlations. As a consequence the evolution equation for the joint position-velocity probability distribution is a Fokker-Planck equation with a fractional time derivative. We determine the solution of this equation in the form of an integral transform and derive a relation for arbitrary single time moments. Analytical solutions for the joint probability distribution and its moments are given.Comment: 10 page

Weak Galilean invariance as a selection principle for coarse-grained diffusive models

Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However, the description of real world systems usually requires coarse-grained models integrating complex microscopic interactions indistinguishably as friction and stochastic forces, which intrinsically violate Galilean invariance. By studying the coarse-graining procedure in different frames, we show that alternative rules -- denoted as "weak Galilean invariance" -- need to be satisfied by these stochastic models. Our results highlight that diffusive models in general can not be chosen arbitrarily based on the agreement with data alone but have to satisfy weak Galilean invariance for physical consistency

Optimal random deposition of interacting particles

Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such processes can be found for arbitrary interaction potentials with finite range. The exact solution allows to rigorously prove characteristic features of the deposition kinetics, which have previously only been accessible by simulations. We show in particular that a unique interaction potential exists that leads to a maximally dense line coverage for a given interaction range. Remarkably, this distribution is singular and can only be expressed as a mathematical limit. The relevance of these results for models of nucleosome packing on DNA is discussed. The results highlight how the generation of an optimally dense packing requires a highly coordinated packing dynamics, which can be effectively tuned by the interaction potential even in the presence of intrinsic randomness