Gianluca Costagliola

Static and dynamic friction of hierarchical surfaces

Hierarchical structures are very common in nature, but only recently have they been systematically studied in materials science, in order to understand the specific effects they can have on the mechanical properties of various systems. Structural hierarchy provides a way to tune and optimize macroscopic mechanical properties starting from simple base constituents and new materials are nowadays designed exploiting this possibility. This can be true also in the field of tribology. In this paper we study the effect of hierarchical patterned surfaces on the static and dynamic friction coefficients of an elastic material. Our results are obtained by means of numerical simulations using a one-dimensional spring-block model, which has previously been used to investigate various aspects of friction. Despite the simplicity of the model, we highlight some possible mechanisms that explain how hierarchical structures can significantly modify the friction coefficients of a material, providing a means to achieve tunability.

Operator product expansion coefficients of the 3D Ising model with a trapping potential

Recently the operator product expansion coefficients of the 3D Ising model universality class have been calculated by studying via Monte Carlo simulation the two-point functions perturbed from the critical point with a relevant field. We show that this method can be applied also when the perturbation is performed with a relevant field coupled to a nonuniform potential acting as a trap. This setting is described by the trap size scaling ansatz, which can be combined with the general framework of the conformal perturbation in order to write down the correlators

Conformal perturbation of off-critical correlators in the 3D Ising universality class

⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\sigma}(0)⟩

Jarzynski's theorem for lattice gauge theory

,

A 2-D model for friction of complex anisotropic surfaces

⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\epsilon}(0)⟩

Tuning friction with composite hierarchical surfaces

and

Applications of Jarzynski's relation in lattice gauge theories

⟨\ensuremath{\epsilon}(\mathbf{r})\ensuremath{\epsilon}(0)⟩

Evidence of friction reduction in laterally graded materials

, from which the operator product expansion coefficients can be estimated. We find

Modeling and Simulation in Tribology Across Scales : an Overview

{C}_{\ensuremath{\sigma}\ensuremath{\epsilon}}^{\ensuremath{\sigma}}=1.051(3)

Numerical determination of the operator-product-expansion coefficients in the 3D Ising model from off-critical correlators

, in agreement with the results already known in the literature, and