Search

We investigate the persistence of micro-contacts between two elastic random rough surfaces by means of a simple model for quasi-static sliding. Contact clusters are calculated with the Boundary Element Method, then surfaces are repeatedly displaced to study the evolution of the original contact area. While the real contact area remains constant due to the rejuvenation of micro-contacts, the original contact clusters are progressively erased and replaced by new ones. We find an approximate exponential decrease of the original real contact area with a characteristic length that is influenced both by statistics of the contact cluster distribution and physical parameters. This study aims to shine light on the microscopic origins of phenomenological rate-and-state friction laws and the memory effects observed in frictional sliding.

We describe benchmark experiments to evaluate the frictional properties of laser patterned low-density polyethylene as a function of sliding velocity, normal force, and humidity. The pattern is a square lattice of square cavities with sub-mm spacing. We find that dynamic friction decreases compared to nonpatterned surfaces, since stress concentrations lead to early detachment, and that stick-slip behavior is also affected. Friction increases with humidity, and the onset of stick-slip events occurs in the high humidity regime. Experimental results are compared with numerical simulations of a simplified 2D spring-block model. A good qualitative agreement can be obtained by introducing a deviation from the linear behavior of the Amontons-Coulomb law with the load due to a saturation in the effective contact area with pressure. This also leads to the improvement of the quantitative results of the spring-block model by reducing the discrepancy with the experimental results, indicating the robustness of the adopted simplified approach, which could be adopted to design patterned surfaces with controlled friction properties.

In this paper we have considered the 3D Ising model perturbed with the energy operator coupled with a non uniform harmonic potential acting as a trap, showing that this system satisfies the trap-size scaling behavior. Eventually, we have computed the correlators $\langle \sigma (z) \sigma (0)\rangle$, $ \langle \epsilon (z) \epsilon (0)\rangle$ and $\langle \sigma (z) \epsilon (0)\rangle$ near the critical point by means of conformal perturbation theory. Combining this result with Monte Carlo simulations, we have been able to estimate the OPE coefficients $C^{\sigma}_{\sigma\epsilon}$, $C^{\epsilon}_{\sigma\sigma}$ and $C^{\epsilon}_{\epsilon\epsilon}$, finding a good agreement with the values obtained in [1,2]., Comment: 17 pages, 5 figures; minor changes, version to appear on PRD

In many biological structures, optimized mechanical properties are obtained through complex structural organization involving multiple constituents, functional grading and hierarchical organization. In the case of biological surfaces, the possibility to modify the frictional and adhesive behaviour can also be achieved by exploiting a grading of the material properties. In this paper, we investigate this possibility by considering the frictional sliding of elastic surfaces in the presence of a spatial variation of the Young’s modulus and the local friction coefficients. Using finite-element simulations and a two-dimensional spring-block model, we investigate how graded material properties affect the macroscopic frictional behaviour, in particular, static friction values and the transition from static to dynamic friction. The results suggest that the graded material properties can be exploited to reduce static friction with respect to the corresponding non-graded material and to tune it to desired values, opening possibilities for the design of bio-inspired surfaces with tailor-made tribological properties.

New possibilities have emerged in recent years, with the development of high-precision fabrication techniques, to exploit microscale surface patterning to modify tribological properties of polymeric materials. However, the effect of surface topography, together with material mechanical parameters, needs to be fully understood to allow the design of surfaces with the desired characteristics. In this paper, we experimentally assess the effect of various types of micropatterned Polydimethylsiloxane surfaces, including anisotropic ones, on macroscopic substrate friction properties. We find that it is possible, through surface patterning, to modify both static and dynamic friction coefficients of the surfaces, demonstrating the possibility of achieving tunability. Additionally, we compare experimental observations with the numerical predictions of a 2D Spring-Block model, deriving the material parameters from tests on the corresponding flat surfaces. We find a good quantitative agreement between calculated and measured trends for various micropattern geometries, demonstrating that the proposed numerical approach can reliably describe patterned surfaces when appropriate material parameters are used. The presented results can further contribute to the description and understanding of the frictional effects of surface patterning, with the aim of achieving surfaces with extreme tunability of tribological properties. Keywords: Friction, Adhesion, Micro-fabrication, Spring-block model

The friction force observed at macroscale is the result of interactions at various lower length scales that are difficult to model in a combined manner. For this reason, simplified approaches are required, depending on the specific aspect to be investigated. In particular, the dimensionality of the system is often reduced, especially in models designed to provide a qualitative description of frictional properties of elastic materials, e.g. the spring-block model. In this paper, we implement for the first time a two dimensional extension of the spring-block model, applying it to structured surfaces and investigating by means of numerical simulations the frictional behaviour of a surface in the presence of features like cavities, pillars or complex anisotropic structures. We show how friction can be effectively tuned by appropriate design of such surface features., Revised version. Videos related to the paper are attached to the review website

A primary issue in biomaterials science is to design materials with ad hoc properties, depending on the specific application. Among these properties, friction is recognized as a fundamental aspect characterizing materials for many practical purposes. Recently, new and unexpected frictional properties have been obtained by exploiting hierarchical multiscale structures, inspired by those observed in many biological systems. In order to understand the emergent frictional behavior of these materials at the macroscale, it is fundamental to investigate their hierarchical structure, spanning across different length scales. In this article, we introduce a statistical multiscale approach, based on a one-dimensional formulation of the spring-block model, in which friction is modeled at each hierarchical scale through the classical Amontons–Coulomb force with statistical dispersion on the friction coefficients of the microscopic components. By means of numerical simulations, we deduce the global statistical distribu...

Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice gauge theory will be presented, along with numerical results for the $\mathbb{Z}_2$ gauge model in three dimensions and for the equation of state in $\mathrm{SU}(2)$ Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schr\"odinger functional and for the study of QCD in strong magnetic fields., Comment: 7 pages, 2 figures, presented at the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, Southampton, UK

Hierarchical structures are very common in Nature, but only recently have they been systematically studied in materials physics, 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 also true 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 1-D 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., Comment: 11 pages, 13 figures

Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques., Comment: 1+29 pages, 2 pdf figures1+29 pages, 2 pdf figures; v2: 1+34 pages, 2 pdf figures: presentation of the theorem proof in section 2 improved with additional details, discussion in sections 3 and 4 expanded, misprints corrected; matches the journal version

Thanks to the impressive progress of conformal bootstrap methods we have now very precise estimates of both scaling dimensions and OPE coefficients for several 3D universality classes. We show how to use this information to obtain similarly precise estimates for off-critical correlators using conformal perturbation. We discuss in particular the $< \sigma (r) \sigma (0) >$, $< \epsilon (r) \epsilon (0) >$ and $< \sigma (r) \epsilon (0) >$ two point functions in the high and low temperature regimes of the 3D Ising model and evaluate the leading and next to leading terms in the $s = t r^{\Delta_{t}}$ expansion, where $t$ is the reduced temperature. Our results for $< \sigma (r) \sigma (0) >$ agree both with Monte Carlo simulations and with a set of experimental estimates of the critical scattering function., Comment: 4 pages, 2 figures, Expanded the discussion of Conformal Perturbation Theory

We propose a general method for the numerical evaluation of operator product expansion coefficients in three dimensional conformal field theories based on the study of the conformal perturbation of two point functions in the vicinity of the critical point. We test our proposal in the three dimensional Ising model, looking at the magnetic perturbation of the $⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\sigma}(0)⟩$, $⟨\ensuremath{\sigma}(\mathbf{r})\ensuremath{\epsilon}(0)⟩$ and $⟨\ensuremath{\epsilon}(\mathbf{r})\ensuremath{\epsilon}(0)⟩$ correlators from which we extract the values of ${C}_{\ensuremath{\sigma}\ensuremath{\epsilon}}^{\ensuremath{\sigma}}=1.07(3)$ and ${C}_{\ensuremath{\epsilon}\ensuremath{\epsilon}}^{\ensuremath{\epsilon}}=1.45(30)$. Our estimate for ${C}_{\ensuremath{\sigma}\ensuremath{\epsilon}}^{\ensuremath{\sigma}}$ agrees with those recently obtained using conformal bootstrap methods, while ${C}_{\ensuremath{\epsilon}\ensuremath{\epsilon}}^{\ensuremath{\epsilon}}$, as far as we know, is new and could be used to further constrain conformal bootstrap analyses of the 3d Ising universality class.

In large photosynthetic chromophore-protein complexes not all chromophores are coupled strongly, and thus the situation is well described by formation of delocalized states in certain domains of strongly coupled chromophores. In order to describe excitation energy transfer among different domains without performing extensive numerical calculations, one of the most popular techniques is a generalization of Förster theory to multichromophoric aggregates (generalized Förster theory) proposed by Sumi [J. Phys. Chem. B 103, 252 (1999)] and Scholes and Fleming [J. Phys. Chem. B 104, 1854 (2000)]. The aim of this paper is twofold. In the first place, by means of analytic continuation and a time convolutionless quantum master equation approach, a theory of emission lineshape of multichromophoric systems or molecular aggregates is proposed. In the second place, a comprehensive framework that allows for a clear, compact, and effective study of the multichromophoric approach in the full general version proposed by Jang, Newton, and Silbey [Phys. Rev. Lett. 92, 218301 (2004)] is developed. We apply the present theory to simple paradigmatic systems and we show on one hand the effectiveness of time-convolutionless techniques in deriving lineshape operators and on the other hand we show how the multichromophoric approach can give significant improvements in the determination of energy transfer rates in particular when the systems under study are not the purely Förster regime. The presented scheme allows for an effective implementation of the multichromophoric Förster approach which may be of use for simulating energy transfer dynamics in large photosynthetic aggregates, for which massive computational resources are usually required. Furthermore, our method allows for a systematic comparison of multichromophoric Föster and generalized Förster theories and for a clear understanding of their respective limits of validity.

We discuss the effects of a trapping space-dependent potential on the critical dynamics of lattice gas models. Scaling arguments provide a dynamic trap-size scaling framework to describe how critical dynamics develops in the large trap-size limit. We present numerical results for the relaxational dynamics of a two-dimensional lattice gas (Ising) model in the presence of a harmonic trap, which support the dynamic trap-size scaling scenario., Comment: 7 pages

International audience; This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano- and microscales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.

We report experimental measurements of friction between an aluminum alloy sliding over steel with various lubricant densities. Using the topography scans of the surfaces as input, we calculate the real contact area using the boundary element method and the dynamic friction coefficient by means of a simple mechanistic model. Partial lubrication of the surfaces is accounted for by a random deposition model of oil droplets. Our approach reproduces the qualitative trends of a decrease of the macroscopic friction coefficient with applied pressure, due to a larger fraction of the micro-contacts being lubricated for larger loads. This approach relates direct measurements of surface topography to realistic distributions of lubricant, suggesting possible model extensions towards quantitative predictions.