Number Of Kinks Research Articles

SNAPPING ELASTIC CURVES AS A ONE-DIMENSIONAL ANALOGUE OF TWO-COMPONENT LIPID BILAYERS

In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes, we consider planar curves that are made of a material with two phases. Each phase induces a preferred curvature to the curve, and these curvatures as well as phase boundaries may lead to the development of kinks. We introduce a family of energies for smooth curves and phase fields, and we show that these energies Γ-converge to an energy for curves with a finite number of kinks. The theoretical result is illustrated by some numerical examples.

Platinum Concave Nanocubes with High‐Index Facets and Their Enhanced Activity for Oxygen Reduction Reaction

Platinum nanoparticles are widely used as the primary catalysts in a myriad of industrial processes such as CO/NOx oxidation in catalytic converters, nitric acid production, petroleum cracking, as well as hydrogen (or alcohol) oxidation and oxygen reduction reactions in fuel-cell technology. For most catalytic reactions, it has been shown that high-index planes, which are associated with large numbers of atomic steps, edges, and kinks hold the key to the enhancement of catalytic performance in terms of activity and/or selectivity. A number of protocols have been demonstrated for generating Pt nanoparticles enclosed by high-index facets, including those based on electrochemical reduction and heat treatment. For example, Sun and co-workers have reported the synthesis of tetrahexahedral (THH) Pt nanocrystals with high-index facets, such as {730}, {210}, and {520}, by applying a square-wave potential to polycrystalline Pt microspheres supported on a glassy carbon electrode. Although these Pt nanocrystals have been shown to have high catalytic activity, their sizes are still relatively too large and the method of preparation is rather limited in terms of production volume. It still remains a challenge to produce Pt nanocrystals with high-index facets by using a simple, scalable route based on wet chemical reduction. Over the past several years, kinetic control has been demonstrated as a simple and versatile approach to the shapecontrolled synthesis of noble-metal nanocrystals in the solution phase. In general, kinetic control can be achieved by: 1) substantially slowing down the formation rate of atoms, 2) using a weak reducing agent, 3) introducing an oxidation process, and 4) taking advantage of Ostwald ripening. When the concentration of metal atoms in the solution is low, the atoms tend to add to the edges and corners of a seed rather than the entire surface, thus leading to the formation of nanocrystals with thermodynamically unfavorable morphologies, including rods, plates, multipods, and dendritic structures. In recent years, nanocrystals with concave rather than flat faces have attracted attention because of their high-index facets. To this end, Zheng and co-workers have demonstrated the synthesis of concave Pd polyhedral nanocrystals with high electrocatalytic activity for formic acid oxidation. Mirkin and co-workers have also reported the synthesis of concave cubic Au nanocrystals, and demonstrated higher chemical activity compared to octahedra enclosed by lowindex {111} facets. Herein we report the first synthesis of Pt concave nanocubes enclosed by high-index facets including {510}, {720}, and {830} by slowly adding an aqueous NaBH4 solution and a mixture containing K2PtCl4, KBr, and Na2H2P2O7 into deionized water by using two syringe pumps. In this synthesis, the formation of a Pt pyrophosphato complex (that is formed by mixing K2PtCl4 and Na2H2P2O7) and the slow addition of this precursor by a syringe pump are believed to play a key role in the formation of Pt concave nanocubes. In this case, the seeds selectively overgrow from corners and edges, and the Br ion serves as a capping agent to block the growth of the h100i axis. The Pt concave nanocubes exhibited substantially enhanced specific activity (per unit surface area) relative to those of Pt nanocubes, cuboctahedra, and commercial Pt/C catalysts that are bounded by low-index facets such as {100} and {111} toward the oxygen reduction reaction (ORR), which is the ratedetermining step in a proton-exchangemembrane (PCM) fuel cell. In a typical synthesis, an aqueous NaBH4 solution and a mixture containing K2PtCl4, KBr, and Na2H2P2O7 were prepared separately and then injected simultaneously at an injection rate of 67 mLmin 1 by using two syringe pumps into deionized water maintained at 95 8C. The color of the solution immediately turned from light pink to black upon the addition of the reactant solutions, thus indicating rapid reduction of PtCl4 2 into elemental Pt by NaBH4. Figure 1a shows a typical transmission electron microscopy (TEM) image of the product that contains Pt nanocubes with a concave structure. [*] Dr. T. Yu, D. Y. Kim, Prof. H. Zhang, Prof. Y. Xia Department of Biomedical Engineering Washington University Saint Louis, MO 63130 (USA) E-mail: xia@biomed.wustl.edu D. Y. Kim Department of Chemical and Biomolecular Engineering (BK21 graduate program) Korea Advanced Institute of Science and Technology (KAIST) 335 Gwahangro, Yuseong-gu, Daejeon 305-701 (Korea)

Intrinsic structural variability of DNA allows multiple genomic encoding for nucleosomes: Comment on “Cracking the chromatin code: Precise rule of nucleosome positioning” by E.N. Trifonov

The review by Trifonov [1] gives a fascinating account of the discovery of immense compaction of DNA in eukaryotic chromosomes and the consequent three-decade-long search for a chromatin code, to which the author himself contributed in no small measure. It culminates in the derivation of a sequence motif by the author that possibly represents the code. However, the story is rather one-sided, based as it is primarily on the author’s own results, with no mention of the large number of experimental studies ([2], and several references therein) which indicate that sequence plays little or no role in the formation of nucleosome structure. It leaves no room for the possibility that maybe, just maybe, there is no chromatin code. In this commentary, we would like to play the devil’s advocate and focus on the ambiguities surrounding the existence of a chromatin code. The theoretical postdiction by Trifonov implicitly assumes that dinucleotide steps take up unique structures. However, analysis of high-resolution DNA crystal structures [3] and molecular dynamics studies [4] have shown that several dinucleotide steps not only show large variation in their structures within the same distribution, but also display multimodal distributions. Further, the structure of RR/YY and YR/YR steps is dependent on their immediate neighbors [4]. Large variation in dinucleotide level structure is also seen in an analysis of nucleosome crystal structures [5]. In fact, it has been shown that “DNA overall flexibility increases considerably upon particle formation” [6]. Thus the absence of unique dinucleotide structures is a serious impediment to sequencebased structure prediction algorithms. An added complication is the presence of a large number of kinks in the nucleosome crystal structures [5]. Molecular dynamics studies have shown that kinks, similar to the ones observed in nucleosome structure, can spontaneously form in long, ∼ 90-mer oligonucleotides, and these kinks are stiff [7]. A linear elastic model does not apply to such stiff regions. Can one then really argue about which steps would (energetically) favor kinking into the major or minor grooves? For example, in free and other protein-bound DNA, the GG/CC step bends into the major groove, and almost never into the minor groove. However, in the nucleosome structure, several kinks into minor groove are observed at

An ensemble of B-DNA dinucleotide geometries lead to characteristic nucleosomal DNA structure and provide plasticity required for gene expression.

BackgroundA nucleosome is the fundamental repeating unit of the eukaryotic chromosome. It has been shown that the positioning of a majority of nucleosomes is primarily controlled by factors other than the intrinsic preference of the DNA sequence. One of the key questions in this context is the role, if any, that can be played by the variability of nucleosomal DNA structure.ResultsIn this study, we have addressed this question by analysing the variability at the dinucleotide and trinucleotide as well as longer length scales in a dataset of nucleosome X-ray crystal structures. We observe that the nucleosome structure displays remarkable local level structural versatility within the B-DNA family. The nucleosomal DNA also incorporates a large number of kinks.ConclusionsBased on our results, we propose that the local and global level versatility of B-DNA structure may be a significant factor modulating the formation of nucleosomes in the vicinity of high-plasticity genes, and in varying the probability of binding by regulatory proteins. Hence, these factors should be incorporated in the prediction algorithms and there may not be a unique 'template' for predicting putative nucleosome sequences. In addition, the multimodal distribution of dinucleotide parameters for some steps and the presence of a large number of kinks in the nucleosomal DNA structure indicate that the linear elastic model, used by several algorithms to predict the energetic cost of nucleosome formation, may lead to incorrect results.

Gravitational wave signatures from kink proliferation on cosmic (super-) strings

Junctions on cosmic string loops give rise to the proliferation of sharp kinks. We study the effect of this proliferation on the gravitational wave (GW) signals emitted from string networks with junctions, assuming a scaling solution. We calculate the rate of occurrence and the distribution in amplitude of the GW bursts emitted at cusps and kinks in the frequency bands of LIGO and LISA as a function of the string tension, the number of sharp kinks on loops with junctions and the fraction of loops in the cosmological network which have junctions. Combining our results with current observational constraints, we find that pulsar data rule out a significant number of kinks on loops for strings with tensions G\mu > 10^{-12}. By contrast, for smaller tensions current observations allow for a large number of kinks on loops. If this is the case, the incoherent superposition of small bursts emitted at kink-kink encounters leads to an enhanced GW background that hides the strong individual bursts from kinks and cusps.

Spontaneous nucleation of structural defects in inhomogeneous ion chains

Structural defects in ion crystals can be formed during a linear quench of the transverse trapping frequency across the mechanical instability from a linear chain to a zigzag structure. The density of defects after the sweep can be conveniently described by the Kibble–Zurek mechanism (KZM). In particular, the number of kinks in the zigzag ordering can be derived from a time-dependent Ginzburg–Landau equation for the order parameter, here the zigzag transverse size, under the assumption that the ions are continuously laser cooled. In a linear Paul trap, the transition becomes inhomogeneous, since the charge density is larger in the center and more rarefied at the edges. During the linear quench, the mechanical instability is first crossed in the center of the chain, and a front, at which the mechanical instability is crossed during the quench, is identified that propagates along the chain from the center to the edges. If the velocity of this front is smaller than the sound velocity, the dynamics become adiabatic even in the thermodynamic limit and no defect is produced. Otherwise, the nucleation of kinks is reduced with respect to the case in which the charges are homogeneously distributed, leading to a new scaling of the density of kinks with the quenching rate. The analytical predictions are verified numerically by integrating the Langevin equations of motion of the ions, in the presence of a time-dependent transverse confinement. We argue that the non-equilibrium dynamics of an ion chain in a Paul trap constitutes an ideal scenario to test the inhomogeneous extension of the KZM, which lacks experimental evidence to date.

Generation of optical and matter-wave solitons in binary systems with a periodically modulated coupling

We consider a quasi-one-dimensional two-component systm, described by a pair of Nonlinear Schr\"{o}dinger/Gross-Pitaevskii Equations (NLSEs/GPEs), which are coupled by the linear mixing, with local strength $\Omega $, and by the nonlinear incoherent interaction. We assume the self-repulsive nonlinearity in both components, and include effects of a harmonic trapping potential. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics, and in Bose-Einstein condensates too. Depending on the strengths of the linear and nonlinear couplings between the components, the ground states (GSs) in such binary systems may be symmetric or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $\Omega $ an odd, or even function of the coordinate. The sign flips of $\Omega (x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $\Omega $. Using a systematic numerical analysis, and an analytical approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. Final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd/even modulation function giving rise to the odd/even number of the kinks. The modulation of $\Omega (x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.

Numerical study on effects of surface impedance and external magnetic fields in THz wave emission from intrinsic Josephson junctions

Numerical study on effect of the surface impedance Z in THz wave emission from intrinsic Josephson junctions reveals that there exist dynamical phase transitions between the McCumber-like state (stable for low Z and low bias current J) and π-phase-kink states (stable for most parameter regions and the number of kinks n depends on J), and the dynamical phase diagram in the Z–J plane is evaluated. When external in-plane magnetic fields are further applied, simple scaling relations hold at emission peaks in the McCumber-like state, while nontrivial emission behaviors are observed in the π-phase-kink states. Field dependence of the n=1 emission peak varies significantly as Z changes, which can be used for experimental evaluation of Z.

Wire Bonding UPH and Stitch Bond Improvement using 20 Micron Diameter Insulated Wire with Security Bump

In this study, security bumps are used for strengthening the stitch bonds of two 20 micron diameter insulated Au wire bonding example processes. Bump bonding as a variant of the ball bonding process has been commonly used in the microelectronic industry to make bumps on dies that will later be flip-chip bonded. The optimized stitch bond parameters combined with the security bumps placed upon the stitch bonds substantially improve the second bond strength demonstrated on the two example processes on two different types of wire bonding equipment. A comparison of pull test results shows that security bumps increase stitch pull force up to 100%. The effect of varying the relative position (shift) of the security bump relative to the stitch bond location is investigated for one process. The window with the highest pull force improvement is ranging from 16 to 31 micron shift towards the ball bond. Looping with insulated wire is faster than with bare wire because of less effort to mitigate the risks of wires touching each other and producing a short. If two wire loops touch each other e.g. after molding, the wire insulation prevents shorts. Therefore, the looping requirements of the example processes with security bumps can be relaxed by reducing the number of kinks (reverses) from four to two. Due to the reduced looping complexity, the overall UPH increased with insulated wire by about 3.0 % and 4.9 % for the two processes, respectively. This increase is in spite of the time required for the additional security bumps, and compared to bare wire processes without security bumps but with more complex looping.

Dynamics of a quantum phase transition with decoherence: Quantum Ising chain in a static spin environment

We consider a linear quench from the paramagnetic to ferromagnetic phase in the quantum Ising chain interacting with a static spin environment. Both decoherence from the environment and nonadiabaticity of the evolution near a critical point excite the system from the final ferromagnetic ground state. For weak decoherence and relatively fast quenches the excitation energy, proportional to the number of kinks in the final state, decays like an inverse square root of a quench time, but slow transitions or strong decoherence makes it decay in a much slower logarithmic way. We also find that fidelity between the final ferromagnetic ground state and a final state after a quench decays exponentially with a size of a chain, with a decay rate proportional to average density of excited kinks and a proportionality factor evolving from 1.3 for weak decoherence and fast quenches to approximately 1 for slow transitions or strong decoherence. Simultaneously, correlations between kinks randomly distributed along the chain evolve from a near-crystalline antibunching to a Poissonian distribution of kinks in a number of isolated Anderson localization centers randomly scattered along the chain.

Effect of the experimental parameters on the structure of nitrogen-doped carbon nanotubes produced by aerosol chemical vapour deposition

We describe the systematic study of multi-walled carbon nanotubes with different nitrogen doping produced by aerosol chemical vapor deposition. Benzylamine:toluene mixtures of 0:100, 5:95, 10:90, 25:75, 50:50, 75:25 and 100:0 were thermally decomposed at 800–900 °C under argon at atmospheric pressure, whereby the nitrogen content of the bulk material was varied between 0 and 2.2 at%. We also show how the presence of nitrogen in the precursor changed the nanotube morphology, i.e. nitrogen decreased the number of kinks incorporated into the carbon nanotubes, decreased their length and diameter and increased the proportion of ‘bamboo’ shaped nanotubes. Furthermore, due to the nitrogen doping, the oxidation resistance of the nanotube material was decreased. With concentrations above 10% benzylamine the increase of the reaction temperature had no significant effect on the quality of the nanotubes, however, at higher temperatures the nitrogen content was decreased. We demonstrate the control over the nanotube geometry, the nitrogen content and oxidation resistance of the nanotubes, and show that these properties are interlinked.

Pile-ups in kink-chains

Dislocation segments inclined at small angles to close-packed lattice directions in crystals with high Peierls energy contain a sequence of geometrical kinks. The distribution of these kinks under the action of an applied stress is studied. The segments are assumed to be pinned a distance L apart and the formation of kink-pairs is excluded. For kinks with finite width only numerical solutions are possible by minimizing the enthalpy. For abrupt kinks with nearest-neighbour interactions, analytical solutions are obtained. It turns out of that at a critical stress σcr there is a phase transition in the distribution. For σ < σcr the area A swept out by the kinks is proportional to σL 3 and independent of the number of kinks. For σ > σcr the kinks form a free pile-up, in which their separation distance decreases proportionally to . The changes in the area ΔA upon changes in stress Δσ are then independent of L but depend now on the number of kinks.

The study of parallel pump microwave magnetic field instability threshold in metallic ferromagnetic strip under in-plane confinement

Using the Landau-Lifshitz equation, the propagating of spin wave in metallic magnetic stripe has been investigated, in which the effective boundary condition is applied for the dynamic magnetization of the metallic magnetic strip. The relationship between spin wave spectrum and width of the strip has analytically been derived. Numerical calculations show that in-plane confinement results in the obvious kinks in the threshold curves. And with the increase of strip width, the kink numbers almost rise exponentially, while the threshold jump at the first kink is nearly in inverse proportion to its width.

On the mechanisms behind the ability of CMC to enhance paper strength

The attachment of CMC to pulp is known to have a strong impact on the tensile strength properties. The mechanisms behind the strength-enhancing ability of the CMC have been investigated by studying the effect of surface carboxymethylation on some basic fibre and sheet properties. Standard methods were used for the strength evaluation, and the relative bonded area was determined from both light-scattering measurements and BET-analysis. The effect of CMC on the shear bond strength was calculated using Page's equation. The attachment of CMC was shown to increase the shape factor and reduce the number of kinks per fibre, which is beneficial for the tensile strength. Surface carboxymethylation also increased the relative bonded area, but on a small-scale structural level detectable only using BET-analysis and not by the scattering coefficient. The sheet density was not affected by the treatment. CMC attachment also increased the shear bond strength. In order to use Page's equation for this evaluation, the relative bonded area had to be determined by BET-analysis. The positive effect of CMC on sheet formation also contributed to an increase in tensile strength.

Observation of the One-Dimensional Diffusion of Nanometer-Sized Dislocation Loops

Dislocations are ubiquitous linear defects and are responsible for many of the properties of crystalline materials. Studies on the glide process of dislocations in bulk materials have mostly focused on the response of dislocations with macroscopic lengths to external loading or unloading. Using in situ transmission electron microscopy, we show that nanometer-sized loops with a Burgers vector of (1/2)111 in alpha-Fe can undergo one-dimensional diffusion even in the absence of stresses that are effective in driving the loops. The loop size dependence of the loop diffusivity obtained is explained by the stochastic thermal fluctuation in the numbers of double kinks.

Characterization of the anisotropic etching of silicon in two-component alkaline solution

The characteristics of wet chemical etching processes were compared for crystalline Si in aqueous solutions of pure NaOH and NaOH with added oxidizing agent NaOCl (sodium-hypochlorite). Due to the addition of NaOCl to the reference NaOH solution, the etch rate decreased for the {1 0 0} and {1 1 0} planes and increased for the {1 1 1} plane. The difference between the activation energy of these etching processes for the three different crystallographic directions became rather small due to the combined effect of the oxidation and the subsequent etching sub-processes. This means that the temperature dependence of the number of kinks as chemical oxidation sites is very similar for the different planes. For the {1 1 1} plane the oxidation sub-process has a higher efficiency resulting in an increased etch rate whereas the etch rate decays for the {1 0 0} and {1 1 0} planes due to enhanced passivation, and these two phenomena contribute to the decrease of the anisotropy. Due to the addition of NaOCl, the oxidation sub-process is more isotropic but still site dependent. In the practice, the etched surface remains of good quality without defect development. In the presence of the oxidizing agent, the difference of the etch rates in the ⟨1 0 0⟩ and ⟨1 1 0⟩ directions is reversed to R⟨100⟩ < R⟨110⟩. This fact can be exploited in the formation of novel 3D structures on the (1 0 0) wafers by forming a square-masking pattern aligned precisely to the ⟨1 0 0⟩ directions.

The effects of CMC attachment onto industrial and laboratory-cooked pulps&lt;

The effect of surface carboxymethylation of industrial and laboratory-cooked pulp was studied regarding attached amount, fibre properties and paper sheet strength. The strength development was compared with the effects of PFI beating. Attachment of CMC was shown to be equally effective with industrial pulp as with laboratory-produced pulp. The attachment level was 100% for both pulp types and no difference in paper strength enhancement could be detected. CMC attachment had a small impact on sheet density, especially compared to PFI beating. Moreover, surface carboxymethylation was shown to increase the shape factor, reduce the number of kinks per fibre and to increase the rewetted zero-span index. This straightening effect of CMC was interpreted in terms of an increase in carboxyl group repulsion on the fibre surface and is probably a factor contributing to the increase in paper strength. Differences in fibre curl between industrial and laboratory-cooked pulp decreased when CMC was attached to the fibre surface. This may explain why no differences in CMC efficiency could be detected.

Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model

Quantum Ising model in one dimension is an exactly solvable example of a quantum phase transition. We investigate its behavior during a quench caused by a gradual turning off of the transverse bias field. The system is then driven at a fixed rate characterized by the quench time ${\ensuremath{\tau}}_{Q}$ across the critical point from a paramagnetic to ferromagnetic phase. In agreement with Kibble-Zurek mechanism (which recognizes that evolution is approximately adiabatic far away, but becomes approximately impulse sufficiently near the critical point), quantum state of the system after the transition exhibits a characteristic correlation length $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$ proportional to the square root of the quench time ${\ensuremath{\tau}}_{Q}$: $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}=\sqrt{{\ensuremath{\tau}}_{Q}}$. The inverse of this correlation length is known to determine average density of defects (e.g., kinks) after the transition. In this paper, we show that this same $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$ controls the entropy of entanglement, e.g., entropy of a block of $L$ spins that are entangled with the rest of the system after the transition from the paramagnetic ground state induced by the quench. For large $L$, this entropy saturates at $\frac{1}{6}\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}\phantom{\rule{0.2em}{0ex}}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, as might have been expected from the Kibble-Zurek mechanism. Close to the critical point, the entropy saturates when the block size $L\ensuremath{\approx}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, but---in the subsequent evolution in the ferromagnetic phase---a somewhat larger length scale $l=\sqrt{{\ensuremath{\tau}}_{Q}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{\ensuremath{\tau}}_{Q}$ develops as a result of a dephasing process that can be regarded as a quantum analog of phase ordering, and the entropy saturates when $L\ensuremath{\approx}l$. We also study the spin-spin correlation using both analytic methods and real time simulations with the Vidal algorithm. We find that at an instant when quench is crossing the critical point, ferromagnetic correlations decay exponentially with the dynamical correlation length $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$, but (as for entropy of entanglement) in the following evolution length scale $l$ gradually develops. The correlation function becomes oscillatory at distances less than this scale. However, both the wavelength and the correlation length of these oscillations are still determined by $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\xi}}$. We also derive probability distribution for the number of kinks in a finite spin chain after the transition.

Reducing topological defects in self-organizing maps using multiple scale neighborhood functions

In this paper, we propose a method of reducing topological defects in self-organizing maps (SOMs) using multiple scale neighborhood functions. The multiple scale neighborhood functions are inspired by multiple scale channels in the human visual system. To evaluate the proposed method, we applied it to the traveling salesman problem (TSP), and examined two indexes: the tour length of the solution and the number of kinks in the solution. Consequently, the two indexes are lower for the proposed method. These results indicate that our proposed method has the ability to reduce topological defects.

Modelling the Bordoni peak†

In fcc metals, kink-pair formation in dislocation lines aligned along close-packed lattice directions can give rise to internal friction effects called Bordoni relaxation. The resulting internal friction peak is a superposition of several individual peaks, each with complex features. To study this behaviour, the differential equation describing the movement of dislocation segments by thermally activated kink-pair formation is solved numerically. It is assumed that the kink mobility is high. As a result, the movement is asymmetric, since the backward movement can occur by kink collapse without need of thermal activation. The influence of the external parameters, such as segment length, number of geometrical kinks, internal stress, amplitude and frequency of the applied stress and temperature on the position and shape of the internal friction peaks is studied. When the original configuration is in a bowed out state, the Paré condition is satisfied. Application of an external stress increases the magnitude of internal friction by aligning originally inclined dislocation segments in the direction of the Peierls valleys. †Dedicated to Prof. Frank. R. N. Nabarro on the occasion of his 90th birthday, on 7 March 2006.