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Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across…
We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is…
Many-particle simulations of vehicle interactions have been quite successful in the qualitative reproduction of observed traffic patterns. However, the assumed interactions could not be measured, as human interactions are hard to quantify…
In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel, rubber…
A simple method is proposed to estimate the instantaneous correlations between state variables in a hybrid system from the empirical correlations between observable market quantities such as spot rate, stock price and implied volatility.…
Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we…
At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquake-like model which requires numerical studies. We show that this phenomenon can also be described by a master…
In rubber friction studies it is often observed that the kinetic friction coefficient {\mu} depends on the nominal contact pressure p. We discuss several possible origins of the pressure dependency of {\mu}: (a) saturation of the contact…
Frictional motion is harder to initiate than to sustain, as evident when pushing a heavy object. This disparity between static and kinetic friction drives instabilities and stick-slip dynamics in systems ranging from nanodevices and MEMS to…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to…
The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts…
In the context of geometric Impulsive Mechanics of systems with a finite number of degrees of freedom, we model the roughness of a unilateral constraint ${\mathcal S\/}$ by introducing a suitable instantaneous kinetic constraint ${\mathcal…
The noise generated by the friction of two rough surfaces under weak contact pressure is usually called roughness noise. The underlying vibration which produces the noise stems from numerous instantaneous shocks (in the microsecond range)…
Contact mechanics-based models for the friction of nominally flat rough surfaces have not been able to adequately capture certain key experimentally observed phenomenona, such as the transition from a static friction peak to a lower level…
A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the…
Independent of specific local features, global spatio-temporal structures in diverse phenomena around bifurcation points are described by the complex Ginzburg-Landau equation (CGLE) derived using the reductive perturbation method, which…
In this paper, we propose a locomotion training framework where a control policy and a state estimator are trained concurrently. The framework consists of a policy network which outputs the desired joint positions and a state estimation…
The problem of a general, symmetric contact, between elastically similar bodies, and capable of idealisation using half-plane theory, is studied in the presence of interfacial friction. It is subject to a constant set of loads - normal…
The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach…