Kink Motion Research Articles

The effect of detachment and attachment to a kink motion in the asymmetric simple exclusion process

We study the dynamics of a kink in a one-lane asymmetric simple exclusion process with detachment and attachment of the particle at arbitrary sites. For a system with one site of detachment and attachment we find that the kink is trapped by the site, and the probability distribution of the kink position is described by the overdumped Fokker-Planck equation with a V-shaped potential. Our results can be applied to the motion of a kink in arbitrary number of sites where detachment and attachment take place. When detachment and attachment take place at every site, we confirm that the kink motion obeys the diffusion in a harmonic potential. We compare our results with the Monte Carlo simulation, and check the quantitative validity of our theoretical prediction of the diffusion constant and the potential form.

Imaging dislocation cores – the way forward

Although the sub-angstrom resolution of the modern transmission electron microscope (TEM) has made major contributions to defect structure analysis in many fields (such as oxides, interfaces, nanoparticles and superconductors) it has yielded little direct information on the core structure of dislocations. We suggest that “forbidden reflection” lattice images recorded in an ultra-high vacuum TEM in projections normal to the dislocation line could provide interpretable images of cores at atomic resolution. These could answer crucial questions, such as the nature of kinks, core reconstruction and periodicity, the nature of obstacles, and help distinguish obstacle theories of kink motion from the secondary Peierls–valley Hirth–Lothe theory. We give experimental forbidden reflection images and a new image obtained from silicon under UHV conditions with atomically smooth surfaces, whose preparation did not anneal out all dislocations. We also show experimental coherent nanodiffraction patterns and scanning transmission electron microscope (STEM) images recorded with the beam parallel to the core, so that core reconstruction can be expected to introduce a “half-order” Laue zone ring. We discuss the contribution that energy-loss spectroscopy from dislocation cores can be expected to make if a nanoprobe beam is used.

The return of the kink

We present a simple theory for the statistics of subsequent passages of kinks at a particular position along a fluctuating step on a crystal surface. Two situations are treated, namely one where the waiting time until the next passage is measured starting from the previous passage of a kink at the observation point, and one where the waiting time is measured starting from a random instant in time. In both cases the waiting time distribution is shown not to obey simple Poisson statistics. Monte Carlo simulations of kink motion show that Poisson statistics emerges for longer waiting times only when the creation and annihilation of kink–antikink pairs are explicitly included. Together, the theory and simulations provide an alternative interpretation of experimental results obtained by Giesen et al. with Scanning Tunneling Microscopy [M. Giesen-Seibert, H. Ibach, Surf. Sci. 316 (1994) 205].

Carbon gets kinky

Putting carbon nanotubes under stress at high temperatures reveals that deformation occurs through the motion of kinks

Kink Formation and Motion in Carbon Nanotubes at High Temperatures

We report that kink motion is a universal plastic deformation mode in all carbon nanotubes when being tensile loaded at high temperatures. The kink motion, observed inside a high-resolution transmission electron microscope, is reminiscent of dislocation motion in crystalline materials: namely, it dissociates and multiplies. The kinks are nucleated from vacancy creation and aggregation, and propagate in either a longitudinal or a spiral path along the nanotube walls. The kink motion is related to dislocation glide and climb influenced by external stress and high temperatures in carbon nanotubes.

Energetics and dynamics of Cu(001)-c(2×2)Cl steps

The energetics of the step faceting transition of Cu(001) [copper (001) surface] upon Cl (chloride) adsorption in contact with HCl (hydrogen chloride) solution is modeled in terms of a solid-on-solid model that incorporates both nearest-neighbor and next-nearest-neighbor interactions. It is shown that faceting of the closed packed [110] Cu(001) steps into step segments oriented along [010] directions of the Cu(001)-c(2×2)Cl can be explained by a strongly repulsive interaction between next-nearest-neighbor Cl atoms in the c(2×2) adlayer. The dynamics of kink motion along the [010]-oriented steps of the Cl-covered Cu(001) surface via attachment/detachment is studied with scanning tunneling microscopy. At some kink sites local dissolution takes place, whereas at other kink sites growth occurs. After correcting for the net local dissolution (or growth) process the kinks perform a one-dimensional random walk along the [010] oriented step segments.

Directed transport in quantum Hall bilayers

The pseudo-spin model for double layer quantum Hall system with total landau level filling factor $\nu=1$ is discussed. Unlike the "traditional" one where interlayer voltage enters as static magnetic field along pseudo- spin hard axis, in our model we consider applied interlayer voltage as a frequency of precessing pseudo-magnetic field lying into the easy plane. It is shown that a Landau-Lifshitz equation for the considered pseudo magnetic system well describes existing experimental data. Besides that, the mentioned model predicts novel directed intra-layer transport phenomenon in the system: unidirectional intra-layer energy transport is realized due to interlayer voltage induced motion of topological kinks. This effect could be observed experimentally detecting counter-propagating intra-layer inhomogeneous charge currents which are proportional to the interlayer voltage and total topological charge of the pseudo-spin system.

Motion of Kink in Hydrogen-Bonded Chain with Asymmetric Double-Well Potential

We discuss the nonlinear excitations and the motion of kink in hydrogen-bonded chain with asymmetric double-well potential, in presence of an external force and damping using a new two-component soliton model. We obtain the kink soliton solution using the phase-plane method, we study soliton velocity and find the expression of the mobility of the kink soliton.

Superplastic carbon nanotubes

The theoretical maximum tensile strain--that is, elongation--of a single-walled carbon nanotube is almost 20%, but in practice only 6% is achieved. Here we show that, at high temperatures, individual single-walled carbon nanotubes can undergo superplastic deformation, becoming nearly 280% longer and 15 times narrower before breaking. This superplastic deformation is the result of the nucleation and motion of kinks in the structure, and could prove useful in helping to strengthen and toughen ceramics and other nanocomposites at high temperatures.

Coronal Mass Ejections as Loss of Confinement of Kinked Magnetic Flux Ropes

We perform MHD simulations in a spherical geometry of the evolution of the three-dimensional coronal magnetic field as a twisted magnetic flux tube emerges slowly into the low-β corona previously occupied by a potential arcade. We study the evolution of the emerged flux rope in the corona as its twist and magnetic energy increases due to flux emergence. We find two distinct stages of the evolution. The earlier evolution is nearly quasi-static, with the flux rope being able to settle into an neighboring equilibrium when the emergence is stopped. When the twist in the emerged flux rope reaches some critical level, the flux rope is found to undergo kink motion and erupt through the arcade field at a localized region, with most of the arcade field remaining closed. The nonlinear evolution of the kink instability facilitates the loss of confinement of the flux rope by changing its orientation at the apex such that it becomes easier for the flux rope to part and erupt through the arcade. The eruption of the writhing flux rope produces prominence field with Λ-shaped and cross-legged morphologies that have been seen in the cores of some CMEs.

Motion of dislocation kinks in a simple model crystal

To investigate the effects of lattice periodicity on kink motion, a molecular-dynamic simulation for a kink in a screw dislocation has been performed in a simple model lattice of diamond type. The Stillinger–Weber potential is assumed to act between atoms. Under applied stresses larger than 0.0027 G, a long distance motion of a kink is possible, where G is the shear modulus. A moving kink emits lattice waves and loses its kinetic energy, which is compensated by the applied stress. The kink attains a terminal velocity after moving a few atomic distances. The kink velocity is not proportional to the applied stress, and exceeds the shear wave velocity when the applied stress is larger than 0.026 G. The energy loss of the moving kink is one order of magnitude smaller than that of a moving straight dislocation and is about the same order of magnitude as the theoretical value of phonon-scattering mechanisms at room temperature.

Dislocation processes in quasicrystals—Kink-pair formation control or jog-pair formation control

A computer simulation of dislocation in a model quasiperiodic lattice indicates that the dislocation feels a large Peierls potential when oriented in particular directions. For a dislocation with a high Peierls potential, the glide velocity and the climb velocity of the dislocation can be described almost in parallel in terms of the kink-pair formation followed by kink motion and the jog-pair formation followed by jog motion, respectively. The activation enthalpy of the kink-pair formation is the sum of the kink-pair formation enthalpy and the atomic jump activation enthalpy, while the activation enthalpy of the jog-pair formation involves the jog-pair enthalpy and the self-diffusion enthalpy. Since the kink-pair energy can be considerably larger than the jog-pair energy, the climb velocity can be faster than the glide velocity, so that the plastic deformation of quasicrystals can be brought not by dislocation glide but by dislocation climb at high temperatures.

Synchronization of kinks in the two-lane totally asymmetric simple exclusion process with open boundary conditions

We study the motion of kinks in a two-lane model of the totally asymmetric simple exclusion process with open boundaries. We analytically study the motion of the kinks by a decoupling approximation. In terms of the decoupling approximation, we find that the positions of the kinks become synchronized, though the difference in the number of particles between lanes remains non-zero when the rate of lane change is asymmetric. The validity of this result is confirmed for small asymmetric cases through the Monte Carlo simulation.

Activated dynamics of semiflexible polymers on structured substrates

We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.

Numerical Simulations of Three‐dimensional Coronal Magnetic Fields Resulting from the Emergence of Twisted Magnetic Flux Tubes

We present the results of MHD simulations in the low-β regime of the evolution of the three-dimensional coronal magnetic field as an arched, twisted magnetic flux tube emerges into a preexisting coronal potential magnetic arcade. We find that the line-tied emerging flux tube becomes kink-unstable when a sufficient amount of twist is transported into the corona. For an emerging flux tube with a left-handed twist (which is the preferred sense of twist for active region flux tubes in the northern hemisphere), the kink motion of the tube and its interaction with the ambient coronal magnetic field lead to the formation of an intense current layer that displays an inverse-S shape, consistent with the X-ray sigmoid morphology preferentially seen in the northern hemisphere. The position of the current layer in relation to the lower boundary magnetic field of the emerging flux tube is also in good agreement with the observed spatial relations between the X-ray sigmoids and their associated photospheric bipolar magnetic regions. We argue that the inverse-S-shaped current layer formed is consistent with being a magnetic tangential discontinuity limited by numerical resolution and thus may result in the magnetic reconnection and significant heating that causes X-ray sigmoid brightenings.

Soliton ratchets induced by excitation of internal modes.

Recently Phys. Rev. Lett. 88, 184101 (2002)]] used a symmetry analysis to predict the appearance of directed energy current in homogeneously spatially extended systems coupled to a heat bath in the presence of an external ac field E (t). Their symmetry analysis allowed them to make the right choice of E (t) so as to obtain symmetry breaking which causes directed energy transport for systems with a nonzero topological charge. Their numerical simulations verified the existence of the directed energy current. They argued that the origin of their strong rectification in the underdamped limit is due to the excitation of internal modes and their interaction with the translational kink motion. The internal mode mechanism as a cause of current rectification was also proposed by Salerno and Zolotaryuk [Phys. Rev. E. 65, 056603 (2002)]]. We use a rigorous collective variable for nonlinear Klein-Gordon equations to prove that the rectification of the current is due to the excitation of an internal mode Gamma (t), which describes the oscillation of the slope of the kink, and due to a dressing of the bare kink by the ac driver. The internal mode Gamma (t) is excited by its interaction with the center of mass of the kink, X (t), which is accelerated by E (t). The external field E (t) also causes the kink to be dressed. We derive the expressions for the dressing and numerically solve the equations of motion for Gamma (t), X (t), and the momentum P (t), which enable us to obtain the explicit expressions for the directed energy current and the ac driven kink profile. We then show that the directed energy current vanishes unless the slope Gamma (t) is a dynamical variable and the kink is dressed by the ac driver.

Ultrasonic absorption in ultra-low carbon steel

The laser-based reverberant technique is used to measure ultrasonic absorption spectra in the 2 to 45 MHz frequency range. This technique, being contactless, allows measurements at high temperature. The absorption spectra of ultra-low carbon steel samples are studied at room temperature in a magnetic field (in order to suppress the magnetoelastic contribution) and in a high temperature furnace (20–1200 °C) without magnetic field. Small steel samples (about 10×10×1 mm3) are used. At room temperature, two main contributions to the ultrasonic absorption are identified: microeddy currents (magnetoelastic contribution) and absorption caused by dislocations (deformation contribution). A typical microeddy current peak is observed and yields a reasonable estimate of the magnetic domain size. Above 10 MHz, the nonmagnetic contribution to the total absorption follows the classical vibrating string model. However, other phenomena also contribute to the absorption spectra. Below 10 MHz, an amplitude-independent damping background is observed. In addition, a small frequency-independent contribution to the absorption is observed at room temperature and is attributed to a thin surface layer. The absorption at high temperature is dominated below the Curie point by the magnetoelastic contribution. Two internal friction peaks are also detected. The first one, at 100 °C, is related to the dislocation kink motion. The second one, measured at 330 °C and 10 MHz, is attributed to the Snoek relaxation of carbon and/or nitrogen in α-iron. The Curie transition as well as the ferrite-austenite transition strongly affect the internal friction spectra.

Interactive Computer Simulation of Dislocation Damping Spectra Associated with the Coupled Motion of Geometric Kinks and Point Defects Subjected to the Bulk Segregation Phenomenon

Interactive Computer Simulation of Dislocation Damping Spectra Associated with the Coupled Motion of Geometric Kinks and Point Defects Subjected to the Bulk Segregation Phenomenon

Multifrequency kinks in multifrequency external fields

Two-dimensional analytical equations for multifrequency kink groups were derived and solved from general principles and without simplifications for any given amplitude of multifrequency forces. Kink motion was analyzed.

Two-dimensional lattice models of the Peierls type

Two-dimensional discrete models are used to describe nonlinear interactions of 'atoms' within interface regions. An evolution algorithm is presented for a distribution of dislocations on a plane. Results of numerical simulations illustrate motion of a dislocation kink. A finite-thickness nonlinear interface is studied in two dimensions; it gives a further extension of the mathematical model to the analysis of contact problems with frictional interfaces.