1,721,123 research outputs found
Cooperative dynamics in two-component out-of-equilibrium systems: molecular ‘spinning tops’
No full textWe study the two-dimensional Langevin dynamics of a mixture of two types of particles that live respectively at two different temperatures. Dynamics is constrained by an optical trap and the dissimilar species interact via a quadratic potential. We realize that the system evolves toward a peculiar non-equilibrium steady-state with a non-zero probability current possessing a non-zero curl. This implies that if the particles were to have a finite-size and therefore a rotational degree of freedom, they would experience a torque generated by the non-zero local curl and spin around their geometric centers, like ‘spinning top’ toys. Our analysis shows that the spinning motion is correlated and also reveals an emerging cooperative behavior of the spatial components of the probability currents of dissimilar species
Recognition capabilities of a Hopfield model with auxiliary hidden neurons
Full text linkWe study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly into the regime of complete confusion when memory load exceeds a sharp threshold. This latter circumstance, together with an increase of the storage capacity, renders such a modified Hopfield model a promising candidate for further research, with possible diverse applications
Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components
Full text linkWe consider a model of a two-dimensional molecular machine - called Brownian gyrator - that consists of two coordinates coupled to each other and to separate heat baths at temperatures respectively T x and T y . We consider the limit in which one component is passive, because its bath is 'cold', T x → 0, while the second is in contact with a 'hot' bath, T y > 0, hence it entrains the passive component in a stochastic motion. We derive an asymmetry relation as a function of time, from which time dependent effective temperatures can be obtained for both components. We find that the effective temperature of the passive element tends to a constant value, which is a fraction of T y , while the effective temperature of the driving component grows without bounds, in fact exponentially in time, as the steady-state is approached
Out-of-equilibrium dynamics of two interacting optically-trapped particles
Full text linkWe present a theoretical analysis of a non-equilibrium dynamics in a model system consisting of two particles which move randomly on a plane. The two particles interact via a harmonic potential, experience their own (independent from each other) noises characterized by two different temperatures T1 and T2, and each particle is being held by its own optical tweezer. Such a system with two particles coupled by hydrodynamic interactions was previously realised experimentally in Bérut et al. [EPL 107, 60004 (2014)], and the difference between two temperatures has been achieved by exerting an additional noise on either of the tweezers. Framing the dynamics in terms of two coupled over-damped Langevin equations, we show that the system reaches a non-equilibrium steady-state with non-zero (for T1 ≠ T2) probability currents that possess non-zero curls. As a consequence, in this system the particles are continuously spinning around their centers of mass in a completely synchronized way - the curls of currents at the instantaneous positions of two particles have the same magnitude and sign. Moreover, we demonstrate that the components of currents of two particles are strongly correlated and undergo a rotational motion along closed elliptic orbits
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