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  • 1. Aurell, Erik
    et al.
    Bo, Stefano
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Dias, Marcelo
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Aalto University, Finland.
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Marino, Raffaele
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Diffusion of a Brownian ellipsoid in a force field2016In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 114, no 3, article id 30005Article in journal (Refereed)
    Abstract [en]

    We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a net average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

  • 2.
    Marino, Raffaele
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Aurell, Erik
    Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry2016In: Physical Review E, ISSN 2470-0045, Vol. 93, no 6, article id 062147Article in journal (Refereed)
    Abstract [en]

    We consider coupled diffusions in n-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multiscale analysis. As an example, we consider coupled diffusions in three-dimensional space and on the group manifold SO(3) of proper rotations, generalizing results obtained by H. Brenner [J. Colloid Interface Sci. 80, 548 (1981)]. We show in detail how the analysis can be conveniently carried out using local charts and invariance arguments. As a further example, we consider coupled diffusions in two-dimensional complex space and on the group manifold SU(2). We show that although the local operators may be the same as for SO(3), due to the global nature of the solvability conditions the resulting diffusion will differ and generally be more isotropic.

  • 3.
    Marino, Raffaele
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Aurell, Erik
    Entropy production of a Brownian ellipsoid in the overdamped limit2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 93, no 1, article id 012132Article in journal (Refereed)
    Abstract [en]

    We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called anomalous contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the anomalous entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the anomalous entropy for prolate and oblate spheroids and for near-spherical Brownian particles.

  • 4.
    Marino, Raffaele
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Parisi, Giorgio
    Ricci-Tersenghi, Federico
    The backtracking survey propagation algorithm for solving random K-SAT problems2016In: Nature Communications, ISSN 2041-1723, E-ISSN 2041-1723, Vol. 7, article id 12996Article in journal (Refereed)
    Abstract [en]

    Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with K = 3,4, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.

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