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

Singular features in noise-induced transport with dry friction

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric surface vibrations with Poissonian shot noise statistics. We find that the transport of the object exhibits striking non-monotonic and singular features: transport actually improves for increasing dry friction up to a critical dry friction strength $\Delta^*$ and undergoes a transition to a unidirectional mode of motion at $\Delta^*$. This transition is indicated by a cusp singularity in the mean velocity of the object. Moreover, the stationary velocity distribution also contains singular features, such as a discontinuity and a delta peak at zero velocity. Our results highlight that dissipation can in fact enhance transport, which might be exploited in artificial small scale systems.Comment: 6 pages, 2 figure

Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model

We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a piecewise-linear friction force. This models the combined effect of dynamic friction and singular dry friction. We derive an exact solution of the stationary Kolmogorov-Feller (KF) equation in the case of two-sided exponentially distributed amplitudes. The stationary density of the velocity exhibits singular features such as a discontinuity and a delta-peak singularity at zero velocity, and also contains contributions from non-integrable solutions of the KF equation. The mean velocity in our model generally varies non-monotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation.Comment: 9 pages, 5 figure

Langevin formulation of a subdiffusive continuous time random walk in physical time

Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous time random walk (CTRW). Stochastic trajectories of a CTRW can be described mathematically in terms of a subordination of a normal diffusive process by an inverse Levy-stable process. Here, we propose a simpler Langevin formulation of CTRWs without subordination. By introducing a new type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multi-point statistics of this noise and compare it with the noise driving scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive behaviour. Interestingly, these two noises are identical up to the level of the 2nd order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields, and compare our results with those of SBM.Comment: 11 pages, 4 figures - The new version contains corrected figures and new paragraphs in the main tex

Consonanze sinestesiche. Una costante reciprocità traduttiva

La dimensione multimediale e la plasticità dei nuovi media comporta l’intreccio profondo di linguaggi diversi. La digitalizzazione ha consentito sul piano tecnico la massima mescolanza di linguaggi e di tecniche comunicative, rendendo convergente, su piattaforme comuni, l’interazione di forme comunicative storicamente veicolate da di erenti supporti per loro natura tra loro di cilmente dialoganti. Accomunati da una medesima piattaforma, alla base dei sistemi audiovisivi e multimediali convivono tuttavia linguaggi che restano distinti. Si tratta di un processo di avvicinamento senza assimilazione che è poi una particolare forma di traduzione digitale. Le diverse componenti comunicative su base digitale implicano un sistema di reciproche traduzioni mettendo in atto un incessante incrocio interpretativo. Nodi traduttivi sono i punti di massima tangenza che si manifestano nel processotraduttivo. Come il sistema traduttivo della danza con linguaggi e materiali propri crea gure nello spazio interpretando una base musicale, così il sistema audio-visivo mette in gura suoni o traduce immagini in suoni. Sono immagini che danzano e che giocano su coincidenze sincroniche. È così che i sistemi notazionali riferiti al campo multimediale devono necessariamente avvalersi di partiture complesse.The multimedia dimension and the plasticity of new media entails the deep intertwining of di erent languages. Digitalization has allowed, on the technical level, the maximum mix of languages and communication techniques, making converging, on common platforms, the interaction of communicative forms historically conveyed by di erent supports, by their nature di cult to dialogue. Along with the same platform, at the base of the audiovisual and multimedia systems, there are still languages that remain distinct. It is a process of approach without assimilation which is then a particular form of digital translation. The di erent communication components on a digital basis imply a system of reciprocal translations, implementing an incessant interpretive crossover. Translational nodes are the points of maximum tangency that are manifested in the translation process. Just as the translation system of dance, with its own languages and materials, creates gures in space interpreting a musical base, so the audio-visual system puts sounds into shape or translates images into sounds. They are images that dance and play on synchronic coincidences. This is how the notational systems referring to the multimedia eld must necessarily use complex scores

Measuring idiosyncratic risks in leveraged buyout transactions

The authors use a contingent claims analysis model to calculate the idiosyncratic risks in Leveraged Buyout transactions.Idiosyncratic Risk; LBO; Private Equity; Benchmarking; CCA