Kink Velocity Research Articles

Modified sine-Gordon theory with static multikinks

We construct a modified non-Bogomol’nyi-Prasad-Sommerfield sine-Gordon theory which supports stable static kinks of arbitrary topological degree N. We use this toy model to study problems that are interesting for higher-dimensional soliton theories supporting multisolitons. We construct a 2-kink collective coordinate model and use it to generate scattering trajectories, which are compared to full-field dynamics. We find that the approximation works well, but starts to fail as radiation becomes more important, due to our model becoming less Bogomol’nyi-Prasad-Sommerfield or when the initial kink velocities are large. We also construct the quantum 2-kink using various approximations and consider how these quantum corrections affect the binding energy of the 2-kink. Published by the American Physical Society 2024

When discrete fronts and pulses form a single family: FPU chain with hardening-softening springs

We consider a version of the classical Hamiltonian FPU (Fermi–Pasta–Ulam) problem with nonlinear force-strain relation in which a hardening response is taken over by a softening regime above a critical strain value. We show that in addition to pulses (solitary waves) this discrete system also supports non-topological and dissipation-free fronts (kinks). Moreover, we demonstrate that these two types of supersonic traveling wave solutions belong to the same family. Within this family, solitary waves exist for continuous ranges of velocity that extend up to a limiting speed corresponding to kinks. As the kink velocity limit is approached from above or below, the solitary waves become progressively more broad and acquire the structure of a kink–antikink bundle. Direct numerical simulations and Floquet analysis of linear stability suggest that all of the obtained solutions are effectively stable. To motivate and support our study of the discrete problem we also analyze a quasicontinuum approximation with temporal dispersion. We show that this model captures the main effects observed in the discrete problem both qualitatively and quantitatively.

Relativistic moduli space and critical velocity in kink collisions.

One important tool in the analysis of the collision of kinks and other topological solitons is the reduction of the original field theory to a finite-dimensional system of so-called collective coordinates. Here we study one recent proposal of a collective coordinate model (CCM), the perturbative relativistic moduli space (pRMS), where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyze the possibility to calculate within the pRMS the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multibounce or annihilation collision. We find that for a growing number of Derrick modes the critical velocity of the CCM approaches the full field theory value. In particular, in the case of the ϕ^{4} model we reach a 99% accuracy. We also see this convergence for a wide range of models belonging to the family of the double sine-Gordon and Christ-Lee theories, especially in those cases where the kinks do not reveal a too well-pronounced half-kink inner structure.

Nature, Generation, and Dissipation of Alfvénic Kinks/Switchbacks Observed by Parker Solar Probe and WIND

The discovery of very prominent magnetic kinks/switchbacks in the solar wind within 0.3 au has become a scientific highlight of the Parker Solar Probe (PSP) mission. This discovery points at the promising impact of small-scale solar activity on the inner heliosphere. To address the nature, generation, and dissipation of these kinks, we perform a statistical analysis of the plasma and boundary properties of the kinks using PSP multi-encounter observations and WIND measurements at 1 au. The kinks show strong Alfvénicity and velocity fluctuations of the order of the local Alfvén speed. These findings suggest that the nature of the kinks is consistent with large-amplitude Alfvén pulses, and the steepening of these Alfvén pulses is likely the formation mechanism of these kinks. Based on the angle between the normal direction of the kinks’ boundaries and the background magnetic field vector, PSP kinks and WIND kinks can be divided into two groups: quasi-parallel and quasi-perpendicular kinks. We speculate that quasi-parallel kinks form through the coupling of Alfvén and fast waves as launched from coronal interchange magnetic reconnection. In contrast, quasi-perpendicular kinks may come from the steepening of Alfvén waves launched from both coronal interchange magnetic reconnection and from the more inhomogeneous lower solar atmosphere. We find that the kink velocity perturbation gradually decreases during outward propagation and is much lower than expected from WKB theory, suggesting a progressive dissipation of the kinks. Comparing PSP kinks and WIND kinks, we conjecture that the kinks dissipate through merging with the turbulent energy cascade within 0.25 au.

Electronic stopping power of protons in platinum: Direct valence and inner-shell-electron excitations from first-principles calculations

The electronic energy loss of proton in platinum (Pt) is studied through nonadiabatic electron-ion coupling dynamic simulations within time-dependent density functional formalism. We have clarified the counterintuitive deviation from velocity proportionality due to the existence of kink velocity of the $d$ electron excitation for a slow proton moving in metal Pt, whose valence $d$ band indeed extends up above the Fermi energy. We have also quantitatively investigated the involvement of the host core electron excitation in the ion-target interaction, through monitoring the evolution of the bound electron number on a specific orbital of the host atom during the close encounter with the flying incident ion. It is found that the low-lying $5p$, $5s$, and $4f$ configuration excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum.

Abundant Resonant Behaviors of Soliton Solutions to the (3+1)-dimensional BKP-Boussinesq Equation

Resonant phenomena have been observed and investigated in various situations, such as plasma experiments, the maritime security and the microtubule in cell physiology. In this paper, abundant resonant behaviors are studied for the (3+1)-dimensional BKP-Boussinesq equation. We mainly discuss the resonant two- and three-soliton solutions in the (x, y)-plane and (x, z)-plane. The characteristics are given for the kink soliton waves, including expressions, maximums, minimums and velocities. The kink soliton waves in the (x, y)-plane are parallel, and the fusion or fission may occur. The kink soliton waves in the (x, z)-plane are not parallel and the resonant phenomena among them are more complicated.

ОДНОМЕРНАЯ ДИНАМИКА ДОМЕННОЙ ГРАНИЦЫ В СЕМИСЛОЙНОЙ ФЕРРОМАГНИТНОЙ СТРУКТУРЕ

The dynamics of the domain boundary is considered using the example of a seven-layer ferromagnetic structure with three thin and four wide magnetic layers. The structure of the domain boundary is represented as a kink solution of the sine-Gordon equation. The equation of motion for magnetization was solved numerically using an explicit scheme. The discretization of the equation was carried out according to a standard five-point scheme of the "cross" type. The paper shows the features of the dynamics of the domain boundary in a multilayer magnetic system in the presence of thin magnetic layers with an increased value of the magnetic anisotropy constant. Thin layers with an increased value of the magnetic anisotropy constant compared to the homogeneous state represent potential barriers to the moving domain boundary. Thin layers with an increased magnitude of magnetic anisotropy compared to a homogeneous state represent potential barriers to a moving domain boundary. A diagram of possible scenarios of the dynamics of the domain boundary is constructed depending on the initial velocity of its movement and the distance between three thin magnetic layers. The maximum value of the kink velocity for reflection from all potential barriers, depending on their size, is obtained. With an increase in the height and width of the barrier, the value of such a threshold maximum reflection velocity of the domain boundary increases nonlinearly. With a sufficiently high barrier height, there is already an almost linear dependence on the width of this threshold velocity. With a slight increase in the speed of movement of the domain boundary, the kink can pass through the first barrier, but it is reflected from the second barrier. There is also a case of kink oscillation between the second and third potential barriers. Such fluctuations are clearly inharmonious. The dependence of the threshold velocity on the distance between the barriers is obtained. As the distance between the barriers increases, the threshold speed value tends to a value equal to the threshold speed for one barrier. In the work, the minimum value of the speed of the domain boundary of the passage of all layers, depending on the parameters of potential barriers, is obtained. It is also found that there is a critical distance separating the dynamics of the domain boundary into two regions with qualitatively different behavior of the system.

Kink dynamics of the sine-Gordon equation in a model with three identical attracting or repulsive impurities

Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of the kinks in the sine-Gordon model with “impurities” (or spatial inhomogeneity of the periodic potential). Methods. Using the method of collective variables for the case of three identical point impurities located at the same distance from each other, a system of differential equations is obtained. Resulting system of equations makes it possible to describe the dynamics of the kink taking into account the excitation of localized waves on impurities. To analyze the dynamics of the kink in the case of extended impurities, a numerical finite difference method with an explicit integration scheme was applied. Frequency analysis of kink oscillations and localized waves calculated numerically was performed using a discrete Fourier transform. Results. For the kink dynamics, taking into account the excitation of oscillations in modes, a system of equations for the coordinate of the kink center and the amplitudes of waves localized on impurities is obtained and investigated. Significant differences are observed in the dynamics of the kink when interacting with a repulsive and attractive impurity. The dynamics of the kink in a model with three identical extended impurities, taking into account possible resonant effects, was solved numerically. It is established that the found scenarios of kink dynamics for an extended rectangular impurity are qualitatively similar to the scenarios obtained for a point impurity described using a delta function. All possible scenarios of kink dynamics were determined and described taking into account resonant effects. Conclusion. The analysis of the influence of system parameters and initial conditions on possible scenarios of kink dynamics is carried out. Critical and resonant kink velocities are found as functions of the impurity parameters.

Kink Dynamics in the $\varphi^{4}$ Model with Extended Impurity

The $\varphi^{4}$ theory is widely used in many areas of physics, from cosmology and elementary particle physics to biophysics and condensed matter theory. Topological defects, or kinks, in this theory describe stable, solitary wave excitations. In practice, these excitations, as they propagate, necessarily interact with impurities or imperfections in the on-site potential. In this work, we focus on the effect of the length and strength of a rectangular impurity on the kink dynamics. It is found that the interaction of a kink with an extended impurity is qualitatively similar to the interaction with a well-studied point impurity described by the delta function, but significant quantitative differences are observed. The interaction of kinks with an extended impurity described by a rectangular function is studied numerically. All possible scenarios of kink dynamics are determined and described, taking into account resonance effects. The inelastic interaction of the kink with the repulsive impurity arises only at high initial kink velocities. The

Kink Migration along 30° Si‐Core Partial Dislocations in 4H‐SiC

Single‐layer Shockley‐type stacking fault (SSF) expansion in 4H‐SiC due to irradiation by a focused e‐beam in the scan mode with a different rate and at fixed points has been studied. It is shown that the focused e‐beam enhances the 30° Si‐core partial dislocation glide at room and liquid nitrogen temperatures only at distances smaller than about 10 μm. The dislocations are found to glide as straight lines with a velocity independent of their length even when this length essentially exceeds the size of excitation volume and the diffusion length. The results obtained show that the dislocation velocity under irradiation is mainly determined by the double kink generation rate and allow to conclude that kink migration can occur without any excitation. The kink velocity in 4H‐SiC is estimated for the first time and the lower limit for the kink velocity is of 2 × 10−4 cm s−1 at room temperature and about 2 times smaller at liquid nitrogen temperature that confirming the small activation energy for the kink migration in 4H‐SiC.

First-principles study of the electronic stopping power of indium for protons and He ions

The electronic stopping power of protons and He ions traveling along the channeling and off-channeling trajectories in indium is reported based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the microcosmic excitation mechanism of the semicore $4d$ electrons of In. The velocity-proportional electronic stopping power and the kink velocity which is due to $4d$-electron excitation are reproduced in the low-energy regime. Because the $5s5p$ valence electrons are uniformly distributed in indium, the electronic excitation of valence electrons via Coulomb scattering is independent of the impact parameter in the investigated velocity range. On the contrary, due to the highly localized nature of semicore electrons, the excitation of $4d$ electrons increases significantly with decreasing of the impact parameter, which suggests that it is triggered by direct ion-electron collision. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, we examined the extent to which the linear response theory is applicable to describe the electronic stopping power by quantifying the velocity dependence of the mean steady-state charge of protons and $\ensuremath{\alpha}$ particles and the effective charge state for $\ensuremath{\alpha}$ particles, and it is found that the linear response theory can be used to predict the stopping power in a wider energy range if the mean steady-state charge is used instead of assuming fully ionized charges.

Double energy profile of pBR322 plasmid

A small circular DNA - plasmid pBR322, is considered as a complex dynamic system where nonlinear conformational perturbations which are often named open states or kinks, can arise and propagate. To describe the internal dynamics of the plasmid we use mathematical model consisting of two coupled sine-Gordon equations that in the average field approximation are transformed to two sine-Gordon independent equations with renormalized coefficients. The first equation describes angular oscillations of nitrous bases of the main chain. The second equation describes angular oscillations of nitrous bases in the complementary chain. As a result, two types of kink-like solutions have been obtained. One type kinks were the solutions of the first equation, and the other kinks were the solutions of the second equation. We calculated the main characteristics of the kink motion, including the time dependences of the kink velocity, coordinates, and total energy. These calculations were performed at the initial velocity equal to 1881 m/s which was chosen to avoid reflections from energy barriers corresponding to CDS-1 and CDS-2. The movement of the kinks was investigated by the method of the double energy profile. The maximum complete set of the DNA dynamic parameters was used to calculate the double profile. To calculate the velocity, energy and trajectory of the kinks, the block method was used. The results obtained made it possible to explain in which region of the plasmid the formation of a transcription bubble is most likely, as well to understand in which direction the bubble will move and the transcription process will go.

Plasmid pBR322 and Nonlinear Conformational Distortions (Kinks)

Plasmid pBR322 containing two coding regions in the matrix chain is a convenient object to study the DNA nonlinear dynamics that is known to play an important role in the processes of transcription, replication, denaturation and transmission of structural changes and information along the DNA molecule. The aim of the present work is to study by the methods of mathematical modeling the dynamics of local conformational distortions – kinks, in the plasmid pBR322. To calculate the dynamic characteristics of the kinks, we applied the method of McLaughlin-Scott, complemented by the block method. This permitted us to model kinks as quasi-particles moving in the potential field of the plasmid. We calculated the time dependences of the kink energy, velocity and coordinate. Calculations were made for three different values of the initial kink velocity: 150 m/s, 1650 m/s and 1879 m/s. The results obtained presented in the form of 3D trajectories and their projections, showed that the necessary condition for kink passing the entire plasmid is the enough large value of the initial kink velocity υ not less than 1656.66 m/c which is, however, less than sound velocity (1904.60 m/c).

The solvent effect on the nonlinear dynamics of U-model microtubules

Microtubules are hollow cylindrical protein polymers composed of tubulin dimers and act as executives in cellular dynamics. The solvent effect on the microtubules dynamics of U-model is investigated. The focus of study is the effect of time-dependent damping coefficient on the system dynamics. The model of γ (t) is γ1(t) = γ0 + e−βt2 and γ2(t) = γ0 – e−βt2. The system dynamics is described by kink and anti-kink solutions obtained by using modified extended tanh-function methode (METHF). The decrease of the damping coefficient will increase the kink and anti-kink velocities. The result obtained also shows that the solvent affects the process of disassembly and kinesin motion.

Analytical Approaches to Investigating the Dynamics of Genes with a Single Coding Region

The question of how the heterogeneity of DNA, such as the presence of functionally important sites (promoters, terminators, and coding regions) in its sequence, affects the dynamic properties of the molecule, is one of the core concerns in the biophysics of DNA. Research in this field is expected to provide a deeper understanding of the role of dynamic mechanisms in the functioning of the molecule. In this paper, the dynamics of the interferon alpha 17 gene were studied. In particular, the McLaughlin–Scott analytical method was applied to solve the problem concerning the motion of transcription bubbles, which are commonly termed DNA kinks. The energy profile of the gene was constructed. The time dependencies of the kink velocity, coordinate, and total energy are found. The mechanism by which the coding region influences the kink dynamics was investigated.

Resonant interaction of ϕ4 kink with [formula omitted]-symmetric perturbation with spatially periodic gain/loss coefficient

The resonant interaction of the ϕ4 kink with a PT-symmetric perturbation is observed in the numerical study performed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). The perturbation is in the form of first partial derivative in time term with a spatially periodic gain/loss coefficient. When the kink interacts with the perturbation, the kink’s internal mode is excited with the amplitude varying in time quasiperiodically. The maximal value of the amplitude was found to grow when the kink velocity is such that it travels one period of the gain/loss prefactor in nearly one period of the kink’s internal mode. It is also found that the kink’s translational and vibrational modes are coupled in a way that an increase in the kink’s internal mode amplitude results in a decrease in kink velocity. The results obtained with the collective variable method are in a good qualitative agreement with the numerical simulations for the continuum model. The results of the present study suggest that kink dynamics in open systems with balanced gain and loss can have new features in comparison with the case of conservative systems.

Trajectories of the DNA kinks in the sequences containing CDS regions

Coding regions (CDS) being an integral part of any gene sequence, play an important role in the process of transcription. One of the tasks associated with the CDS regions, consists in the modeling of the passage of transcription bubbles named also open states or DNA kinks through the coding regions. In this paper, we present a simple and convenient approach to the modeling of the passage. It includes the calculation of the energy profile of the sequence and reducing the initial task to the modeling of the movement of a quasi particle in the field with this energy profile. To illustrate the method, we present the results of the calculations of the trajectories of the DNA kinks moving in the sequence of gene coding interferon alpha 17 (IFNA17) that consists of the three regions: the coding region and the two regions with unknown functional properties. To analyze the kink dynamics, we apply approximation where the DNA parameters are being averaged separately over each of the three regions. In the absences of dissipation, the total kink energy is constant. At the same time the kink velocity is constant only inside each of the regions. In the presence of dissipation, the total kink energy decreases. It is shown that the greater the total initial energy of the kink, the faster the energy decrease. It is suggested that the proposed approach could be useful in finding the ways to govern the movement of transcription bubbles at the first stage of the process of transcription.

On the modeling of the motion of a transcription bubble under constant torque

The motion of a transcription bubble under constant torque is investigated. The motion of the bubble was modeled by a modified sine-Gordon equation. Numerical solutions of this equation (kinks) were found. Trajectories of the kink motion in homogeneous and inhomogeneous sequences were calculated for different model values of the torque M τ and the initial velocity v 0. It was shown that a change in the torsion moment M τ has a significant impact on the character of the kink trajectory. At the same time, a change in the initial kink velocity v 0 in a rather wide range of values does not affect the character of the kink trajectory.

О движении кинка ДНК под действием постоянного торсионного момента

The influence of the torsion moment on the DNA kink motion is studied by the methods of mathematical modeling. Time dependence of the kink coordinate, velocity, size, and energy on the different values of the parameters of the external torsion moment have been found. It has been shown that by changing the parameters, by switching on and off of the external action, one could regulate the velocity and the direction of the kink movement. Estimation of the torque value necessary for the kink (open state) movement with the velocity comparable to the transcription velocity, has been made.

Room-temperature solid solution softening in Fe-V binary system

Molecular dynamics simulations of the glide of an edge dislocation in the bcc matrix of Fe-V alloys were performed to investigate the room-temperature solid solution softening by V atoms. For this purpose, the glide velocity of an edge dislocation was calculated as a function of V concentration under the shear stresses of 100-300MPa using the Fe-V cross-potential constructed newly in the present study. Whereas the solid solution hardening occurred as the V concentration is less than 0.13 at% or more than 0.5 at%, the room-temperature solid solution softening was observed in Fe-(0.13-0.5) at% V alloys. The solid solution softening occurring in Fe-(0.13-0.5) at% V alloys was caused by the accelerated growth velocity of kinks by solute V atoms. The increase in kink velocity happened when the interatomic distance between solute V atoms was similar to the length of dislocation kinks.