Largest Lyapunov exponent as a tool for detecting relative changes in the particle positions.

Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent, and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step.

Hysteresis in the underdamped three-layer model.

The hysteretic phenomena were investigated in the three-layer model consisting of a chain of harmonically interacting atoms confined between two rigid periodical substrate potentials, where the top substrate was driven by a external force. The pinning to running and the running-to pinning transitions were examined as the driving force was varied and the influence of the equilibrium spacing and strength of the interaction of the particles in the middle layer on the static and kinetic friction force analyzed in detail. The parameter space in which the friction forces could reach their maxima or minima was determined. These results could be interesting for the selection of lubricant materials and minimization of energy loss in tribology.

Complexity of Shapiro steps.

We demonstrate, using the example of the dc+ac driven overdamped Frenkel-Kontorova model, that an easily calculable measure of complexity can be used for the examination of Shapiro steps in the presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function, we were able to detect Shapiro steps, measure their size with the desired precision, and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, with an unconventional, but practical and easy tool for examination of Shapiro steps in real systems.

Farey sequence in the appearance of subharmonic Shapiro steps.

The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.

Friction phenomena in the overdamped three-layer model.

An overdamped three-layer model consisting of two harmonic chains of interacting particles, representing the upper and the middle layers, which move over the substrate potential, is studied in the present paper. A dc+ac force is applied only on the upper harmonic chain, and dynamics of both layers are investigated. The results show that the dynamical mode locking and Shapiro steps appear not only in the upper layer but also in the middle one. It is noted that the motion of particles in the upper layer corresponds to the standard Frenkel-Kontorova model. The dependence of the Shapiro steps of the middle layer on the system parameters are determined. It is shown that the height of the first Shapiro step of the upper layer is unrelated to the interaction parameters of the particles of both the upper and the middle layers, while the height of the first Shapiro step of the middle layer depend only on the interaction parameters of the particles of the middle layers. Two critical forces which transfer from locked state to the sliding one of both the upper and the middle layers are also studied. They depend on the amplitude and the frequency of the external ac driving force.

[Hard dental tissue minimal-invasive preparation using contemporary polymer rotating instruments and laser].

Goal of contemporary dentistry is to decrease the patient's discomfort during treatment. Dentists aim to achieve maximum with the newly developed dental materials as well as with new cavity preparation techniques in the shortest time span. Since the development of the first constructed borer (drilling machine) for caries removal, the preparation techniques have considerably changed. The progress of dental materials as well as the cavity preparation techniques has led us to contemporary carbide tungsten and diamond borers that are used with obligatory water cooling. The innovation within this field represents newly developed polymer borers that can detect the difference between carious lesions and healthy tooth structure. In this way the cavity preparation may be performed without damaging dental healthy tissue. This is possible owing to their hardness which is lower than the hardness of intact dentin. Polymer borer preparation is painless with less vibration, while the increase in temperature is negligible. Lasers have been used in clinical dentistry since 1980s so it can be said that they represent a new technology. The function of lasers is based on ablation which requires water. Erbium lasers have shown the highest potential with their ability to produce effective ablation of hard dental tissues. Laser application in dentistry requires special training as well as some protective measures. Laser advantages, compared to traditional preparation techniques, involve the absence of vibration, painless preparation, possibility of preparation without anesthetic and easier patient's adjustment to dental intervention which is of importance, especially in pediatric dentistry.

[The application of air abrasion in dentistry].

One of the main objectives of contemporary dentistry is to preserve healthy tooth structure by applying techniques of noninvasive treatment. Air abrasion is a minimally invasive nonmechanical technique of tooth preparation that uses kinetic energy to remove carious tooth structure. A powerful narrow stream of moving aluminum-oxide particles hit the tooth surface and they abrade it without heat, vibration or noise. Variables that affect speed of cutting include air pressure, particle size, powder flow, tip's size, angle and distance from the tooth. It has been proposed that air abrasion can be used to diagnose early occlusal-surface lesions and treat them with minimal tooth preparation using magnifier. Reported advantages of air abrasion include reduced noise, vibration and sensitivity. Air abrasion cavity preparations have more rounded internal contours than those prepared with straight burs. This may increase the longevity of placed restorations because it reduces the incidence of fractures and a consequence of decreased internal stresses. However, air abrasion cannot be used for all patients, i.e. in cases involving severe dust allergy, asthma, chronic obstructive lung disease, recent extraction or other oral surgery, open wounds, advanced periodontal disease, recent placement of orthodontic appliances and oral abrasions, or subgingival caries removal. Many of these conditions increase the risk of air embolism in the oral soft tissues. Dust control is a challenge, and it necessitates the use of rubber dam, high-volume evacuation, protective masks and safety eyewear for both the patient and the therapist.

Ratchet effect and amplitude dependence of phase locking in a two-dimensional Frenkel-Kontorova model.

We demonstrate the ratchet and phase locking effects in a two-dimensional overdamped Frenkel-Kontorova model with a square symmetric periodic substrate when both a longitudinal dc drive and a circular ac drive are applied. Besides the harmonic steps, the large half integer steps can also clearly be seen in the longitudinal (x) direction. These half integer steps are directly correlated to the appearance of positive and negative ratchet effects in the transverse (y) direction due to the symmetry breaking in the combination of the dc and ac drives. The angle between the net displacement and the longitudinal direction is analytically obtained in a single period of the ac drive. In the examination of the amplitude dependence of the ac drive, the maxima decrease monotonically with the amplitude, while the anomalies occur for the critical depinning force and the harmonic steps due to the spatial symmetry breaking of orbits in the presence of the ac drive.

Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps.

Existence and properties of the Shapiro steps in the presence of noise have been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. The results have shown that the influence of noise on interference phenomena is determined by the presence and the size of half-integer steps. Since half-integer steps are more affected by noise, and the properties of harmonic steps are directly correlated with the size of half-integer steps, noise will have completely different effects on the harmonic steps if half-integer steps are present. As temperature increases, in the amplitude dependence of the step width, deviation from the well-known Bessel-like oscillations has been observed, and three different types of behavior have been classified. In the influence of noise on the frequency dependence of the steps, appearance of oscillations and strong influence of half-integer steps on their form have been observed.

Existence and stability of the resonant phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model with the incommensurate structure.

Dynamical mode-locking phenomena in the incommensurate structures of the dc- and ac-driven overdamped Frenkel-Kontorova model are studied by molecular-dynamics simulations. The obtained results have shown that Shapiro steps exhibit significantly different amplitude and frequency dependence from the one observed in the commensurate structures. Due to the incommensurability of the system the special symmetry of the motion of particles is broken, and in the amplitude dependence of Shapiro steps, this will result in the appearance of anomalies and deviation from the well-known Bessel-like behavior. In the frequency or period dependence, oscillations have been observed in the high-amplitude limit; however, they exhibit strong anomalies compared with those in the commensurate structures. The oscillatory behavior and the anomalies have been also be revealed in the (F(ac),F) and the (ν(0),F) phase diagrams where several phases are defined.

Frequency dependence of the subharmonic Shapiro steps.

Frequency dependence of the subharmonic Shapiro steps has been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. As potential gets deformed, in addition to the harmonic steps, subharmonic steps appear in the number and size that increase as the frequency of the external force increases. It was found that size of both harmonic and subharmonic steps strongly depend on the frequency where in the high-amplitude limit oscillatory dependence appears. When expressed as a function of period these oscillations of the step size with frequency have the same form as the oscillations of the step size with amplitude. Deformation of the potential has strong influence on these oscillations, and as in the case of amplitude dependence, with the increase of deformation, the same three distinctive types of behavior have been classified.

Properties of the Shapiro steps in the ac driven Frenkel-Kontorova model with deformable substrate potential.

Properties of the dynamical-mode-locking phenomena are studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. Appearance of very large subharmonic steps due to deformation of the substrate potential significantly influences the stability and existence of harmonic steps. Strong correlation among harmonic and subharmonic steps has been observed in which the larger the width of half-integer steps, the smaller that of harmonic steps. Amplitude dependence of harmonic steps significantly changes with the deformation of the potential where deviation from the well-known Bessel-like oscillations appears. Strong influence of the frequency of the ac driving force on the appearance and size of subharmonic steps has been observed.

Friction phenomena and phase transition in the underdamped two-dimensional Frenkel-Kontorova model.

Locked-to-sliding phase transition has been studied in the driven two-dimensional Frenkel-Kontorova model with the square symmetric substrate potential. It is found that as the driving force increases, the system transfers from the locked state to the sliding state where the motion of particles is in the direction different from that of driving force. With the further increase in driving force, at some critical value, the particles start to move in the direction of driving force. These two critical forces, the static friction or depinning force, and the kinetic friction force for which particles move in the direction of driving force have been analyzed for different system parameters. Different scenarios of phase transitions have been examined and dynamical phases are classified. In the case of zero misfit angle, the analytical expressions for static and kinetic friction force have been obtained.

Noise effects in the ac-driven Frenkel-Kontorova model.

The noise effects on dynamical-mode-locking phenomena in the ac-driven dissipative Frenkel-Kontorova model are studied by molecular-dynamics simulations. It was found that the noise strongly influences the properties of the Shapiro steps and the way they respond to the changing of system parameters. The increase of temperature produces the melting of the Shapiro steps, while the critical depinning force is significantly reduced. The oscillatory form of the amplitude dependence is strongly affected where the Bessel-like form changes as the temperature increases. In the frequency dependence of the Shapiro steps, due to the decrease of the dc threshold value, noise may transfer the system to the high-amplitude regime where oscillations of the step width with frequency or period of the ac force appear. These phenomena will additionally destabilize the steps in real systems and significantly limit the region of parameters where dynamical-mode-locking phenomena could be observed.

Amplitude and frequency dependence of the Shapiro steps in the dc- and ac-driven overdamped Frenkel-Kontorova model.

The amplitude and frequency dependence of dynamical mode locking phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model is studied by molecular-dynamics simulations. It was found that the Shapiro steps and the critical depinning force exhibit very complex behavior. The form of amplitude dependence is determined by the frequency of ac force, where the Bessel-type oscillations appear at the high frequencies. With a changing of frequency, after initial increase, the critical depinning force saturates, while the step width remains strongly frequency dependent even at the high frequencies. The dependence of frequency is strongly influenced by the amplitude of ac force where, in the large amplitude regime, the oscillations of the step width and the critical depinning force have been observed at the low frequencies. In the physical processes that stay behind amplitude and frequency oscillations of the step size, an analogy between the influence of amplitude and the period of the ac force is revealed. These oscillations are directly related to the existence and the stability of the interference phenomena in the real systems.

Dynamical mode locking in commensurate structures with an asymmetric deformable substrate potential.

The overdamped dynamics in the commensurate structures of the one-dimensional Frenkel-Kontorova model subjected to a parametrized deformable periodic substrate potential and driven by a periodic force is examined. It was found that when the shape of the substrate potential starts to deviate from the standard one, new subharmonic steps appear in the response function even in the structures with an integer value of average interparticle distance while the critical depinning force can even decrease for some values of system parameters. These novel phenomena could be particularly relevant for the charge-density wave systems, vortex lattices, and systems of Josephson-junction arrays.

Dynamic phases in the two-dimensional underdamped driven Frenkel-Kontorova model.

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. When driving force increases, the system transfers from a disorder locked state to an ordered sliding state corresponding to a moving crystal. By varying the values of the effective elastic constant, damping, and temperature, we found different scenarios and intermediate phases during the ordering transition. For a soft atomic layer, the system passes through a plastic-channel regime that appears as a steady-state regime at higher values of the damping coefficient. For high values of the effective elastic constant, when the atomic layer is stiff, the intermediate plastic phase corresponds to a traffic-jam regime with immobile islands in the sea of running atoms. At a high driving of the stiff layer, a solitonlike elastic flow of atoms has been observed.