Tomlinson Model Research Articles

Simulations of the kinetic friction due to adsorbed surface layers

Simulations of the kinetic friction due to a layer of adsorbed molecules between two crystalline surfaces are presented. The adsorbed layer naturally produces friction that is consistent with Amontons' laws and insensitive to parameters that are not controlled in experiments. The kinetic friction rises logarithmically with velocity as in many experimental systems. Variations with potential parameters and temperature follow variations in the static friction. This correlation is understood through analogy with the Tomlinson model and the trends are explained with a hard-sphere picture.

Atomic friction studies on well-defined surfaces

Atomic friction studies have been performed by means of a friction force microscope (FFM) in ultrahigh vacuum, where well-defined surfaces can be prepared. A home-built FFM allows us to study lateral forces as low as 0.05 nN using rectangular silicon cantilevers. Furthermore, comparison with dissipation measurements performed in non-contact mode are possible. Recent experimental results are presented and discussed in the framework of a one-dimensional Tomlinson model which includes thermal activation. Atomic-scale stick–slip processes on a metallic surface could be repeatedly measured on Cu(111), while the Cu(100) surface was distorted by the tip during the scanning process. A logarithmic velocity dependence of atomic friction has been measured on Cu(111) and NaCl(100) for low scanning velocities. The dissipation found in stick–slip measurements is compared to the power loss detected in dynamic non-contact measurement.

Velocity dependence of atomic friction

Sliding friction between the tip of a friction force microscope and NaCl(100) was studied to deduce the velocity dependence of friction forces on the atomic scale. A logarithmic dependence of the mean friction force is revealed at low velocities. The experimental data are interpreted in terms of a modified Tomlinson model which is based on reaction rate theory.

Macroscopic versus microscopic description of friction: from Tomlinson model to shearons

In this Letter we investigate the response of an embedded system that is subject to an external drive, which is chosen to be either a constant velocity or a harmonic shear. Two approaches are introduced that cover macroscopic and microscopic aspects of the problem and mimic recent measurements on friction using the surface forces apparatus. The first approach is based on the Tomlinson model and its generalization, and allows for the investigation of the coupled lateral–normal response to a lateral drive. We propose a method for analyzing both linear and nonlinear response of confined systems driven harmonically. The method provides a way to deduce the microscopic parameters responsible for dissipation. The second approach focuses on the microscopic level. The shear is shown to excite “shearons”, which are collective modes of the embedded system with well-defined spatial and temporal patterns that dominate the frictional properties of the driven system. We demonstrate that the slip relaxation in stick–slip motion and memory effects are well described in terms of the creation and/or annihilation of shearons.

Deducing energy dissipation from rheological response

We propose a method for analyzing the nonlinear response regime of confined liquids driven harmonically in measurements using surface force apparatus. The approach is based on calculating the average energy dissipation in the system, and it provides a way to deduce the microscopic parameters which are responsible for the dissipation. We compare the method with the widely used linear fourier analysis in the case of the Tomlinson model and discuss the meaning and applicability of the two approaches.

Extended Tomlinson Model for Rheological Response

AbstractWe investigate the response of a confined harmonic chain to an external harmonic driving force. A model is introduced which extends the one-dimensional Tomlinson model to include motion in the normal direction. This model with lateral-normal coupling mimics recent measurements on friction, using surface forces apparatus (SFA). The model predicts a critical driving amplitude below which the response is linear. For higher amplitudes the system exhibits a nonlinear behavior and an apparent shear thinning. We discuss the effects of shear induced dilatancy, which results from the lateral-normal coupling, on the energy dissipation, and therefore on the frictional properties. It is demonstrated that measurements of response in the normal direction provide additional information on the mechanisms of friction.

Theoretical analysis of atomic-scale friction in frictional-force microscopy

We perform a theoretical analysis of frictional-force microscopy(FFM) images of a cleaved graphite surface. The Tomlinson model with a single-atom tip is powerful for reproducing experimental FFM images. A mapping relation between the tip atom position and the cantilever basal position obtained by a stable equilibrium condition, gives a clear explanation of the physical meaning of FFM image patterns.

Étude de l'architecture aérienne de quelques plantes tropicales à ramification basitone : vers une révision du modèle de Tomlinson

The study of tree architecture initiated in 1970 was followed by that of grasses and liana. Up to now, a larger number of observations were conducted on plants belonging to the Tomlinson's model. Wide variations were perceived at the level of upright part of each “article” or “module”. These observations suggest that the Tomlinson's model should not be considered as a distinct model but rather as a variant with basitone repetition, likely to appear within most of the other known models. Key words: plant architecture, basitone ramification, monocotyledons, dicotyledons. [Journal translation]

Vegetative Growth of Eorhiza arnoldii Robison and Person from the Middle Eocene Princeton Chert Locality of British Columbia

Anatomical studies of several thousand specimens of Eorhiza arnoldii Robison and Person rhizomes and their attached organs have added significantly to our knowledge of these Middle Eocene, semiaquatic dicotyledonous plants from the Princeton chert. Anatomical structure of Eorhiza was studied through serial sections on cellulose acetate peels. In order to establish the growth habit for these plants, individual axes were mapped as to their three-dimensional positions in the chert matrix. Plants grew from an extensive sympodial rhizome system similar to many living monocots and exhibited subopposite branching. Branches gave rise to rhizome sympodia or to branches bearing small scale-leaves. The architecture of Eorhizaconforms to the Tomlinson Model proposed by Halle, Oldeman, and Tomlinson. Leaves are ensiform, equitant, unifacial (isobilateral), and monocot-like with a large central lacuna. Rhizomes show typical dicot stelar anatomy. The presence of an aerenchymatous cortex and the plants' association with ...

Population Structure of the Dominant Palm Species in the Understory of a Mexican Lowland Rain Forest.

Population structure was analyzed for five of the most common species of palms, Astrocaryum mexicanum, Bactris tricophylla, Chamaedorea oblongata, C. tepejilote and Geonoma oxycarpa in a Mexican lowland rain forest. Height and cover of palms with a height> 1.5 m were measured in three 600 m2 plots. The most common species in terms of density were C. tepejilote and A. mexicanum. The highest accumulated cover corresponded to A. mexicanum.Taller palms of C. tepejilote showed higher cover. Almost all palm species had the same architectural model (Comer) and B. tricophylla had the Tomlinson model. Richness of palm species was low compared to other tropical forests although the understory palms in this community represent more than 50 % of all the individuals of the understory vegetation at Los Tuxtlas. The genus Chamaedorea was the most diversified (5 species) while the other genera had only one species.

Advantages and Limitations of "Simple" Fishery Models in Light of Laboratory Experiments

"Simple" fishery models as treated herein are those requiring only catch and effort data for fitting. In the models described, the yield-on-biomass curve is considered equivalent to the growth curve of the population: Schaefer, logistic; Fox, Gompertz; Pella and Tomlinson, generalized. The Fox model is more realistic for fish populations than the Schaefer, eliminating the constraint of a symmetrical yield curve. The Pella–Tomlinson model is general, including the others as special instances. Tests against data from laboratory populations of guppies support the validity of the Fox and Pella–Tomlinson models. The Fox model is the simpler to fit of the two (as it has less parameters) and has been shown to be appropriate for a number of commercial fisheries. Advantages of the models include their minimal requirements for basic data and relative ease of fitting. Limitations include lack of provision for reproductive lag and waste of biological information other than catch and effort.