Double Kink Research Articles

Soliton-based modeling of nano-ionic currents in transmission line

Many nonlinear evolution equations, such as the nano-ionic currents (NIC) equation, are used extensively in many scientific and technological domains particularly in nanoelectronics and bioelectronics. The mathematical modeling of NIC phenomena is vital for understanding their behavior and optimizing device performance. Our research leverages an array of mathematical methods, including multi-wave analysis, periodic wave solutions, lump soliton dynamics, breather wave phenomena, homoclinic breathers, M-shaped waveforms, and rogue wave analysis. Additionally, our investigation encompasses the exploration of single kink and double kink configurations, interactions between periodic and kink waves, interaction between M shaped with kink and rogue, interaction between M shaped with one kink, interaction between M shaped with kink and periodic, interaction between M shaped with two kinks as well as periodic wave interactions with lump waves. To further emphasize the structure of solutions derived from particular parameter choices, we include three-dimensional, two-dimensional, streamplot, and contour graphs.

Numerical modelling of sawteeth and sawtooth-free regime

To better understand the sawteeth physics and the sawtooth-free regime associated with the hybrid scenario in tokamak experiments, numerical calculations up to quasi-steady state have been carried out for realistic middle-size tokamak plasma parameters, including the bootstrap current perturbation and basing on both the single- and two-fluid equations with the large aspect ratio approximation. Two types of the sawtooth crash are found in multiple sawteeth simulations: (1) For a low equilibrium bootstrap current fraction, the crash is caused by the internal kink mode, as expected; (2) When the bootstrap current density fraction is larger than 10% in the core region, however, the crash is caused by the non-ideal double kink mode, in contrary to the conventional understanding. In this case, a non-monotonic radial profile of the safety factor q with two q=1 surfaces emerges before the crash, caused by the bootstrap current density and plasma resistivity perturbations, although the original equilibrium has only single q = 1 surface. In both types of sawtooth crashes, the crash time in two-fluid simulations is tens of microseconds, as observed in experiments. Furthermore, for a relatively low ion density and finite bootstrap current density fraction, a transition from the sawtooth to the sawtooth-free regime is found, in which flat q profiles with the q value being about unity in the central region, similar to that observed in hybrid scenario experiments, are maintained by the dynamo effect. To enter into the sawtooth-free regime in two-fluid simulations, a much larger Alfvén velocity than that in single-fluid simulations is required due to the diamagnetic drift.

Novel nonlinear quantum dust acoustic waves for modified variable coefficients Zakharove–Kusnetsov equation in dusty plasma

In this paper, the direct similarity reduction method is used to reduce the modified variable coefficient Zakharove–Kusnetsov equation (vcmZK), which represents the propagation of quantum dust acoustic waves (QDAWs) in an inhomogeneous magnetized dusty plasma field, into a nonlinear ordinary differential equation (NODE). Moreover, the Jacobi elliptic method is used to solve the NODE, where many novel double periodic, kink, and solitary wave solutions are obtained. Additionally, we have chosen to plot periodic, kink, and soliton QDAWs solutions according to some choices for the variable coefficients. According to the a chieved results, we can conclude that the choices of the functional forms of the variable coefficients can control the QDAWs propagation. Finally, the new discovered results may have many important applications in astrophysics, atmospheric science, nanotechnology, and industrial plasma physics.

Reshaping Covalent Nanowires by Exploiting an Unexpected Plasticity Mediated by Deformation Twinning.

Nanowires (NWs) are among the most studied nanostructures as they have numerous promising applications thanks to their various unique properties. Furthermore, the properties of NWs can be tailored during synthesis by introducing structural defects such as nano-twins, periodic polytypes, and kinks, i.e., abrupt changes in their axial direction. Here, this work reports for the first time the postsynthesis formation of such defects, achieved by exploiting a peculiar plasticity that may occur in nanosized covalent materials. Specifically, in this work the authors found that single-crystal CuO NWs can form double kinks when subjected to external mechanical loading. Both the microscopy and atomistic modeling suggest that deformation-induced twinning along the plane is the mechanism behind this effect. In a single case the authors are able to unkink a NW back to its initial straight profile, indicating the possibility of reversible plasticity in CuO NWs, which is supported by the atomistic simulations. The phenomenon reported here provides novel insights into the mechanisms of plastic deformation in covalent NWs and offers potential avenues for developing techniques to customize the shape of NWs postsynthesis and introduce new functionalities.

Novel rational solitons and generalized breathers for (1+1)-dimensional longitudinal wave equation

This paper deals with the evaluation of multiwave, homoclinic breather, M-shaped rational solitons and interaction of M-shaped rational solitons with single and double kinks for [Formula: see text]-dimensional longitudinal wave equation via the logarithmic transformation and symbolic computation with ansatz functions method. We will obtain two types of M-shaped rational solitons and their dynamics are revealed in figures by choosing the distinct values of involved parameters. In addition, two forms of interaction of M-shaped rational soliton with kink wave will also be evaluated. Furthermore, we will compute kink cross-rational solutions, periodic cross-rational solutions, generalized breathers and Akhmediev breathers for governing model. The solitons behaviors via different values of parameters in the produced solutions will be analyzed.

Some special exact solutions in nonlocal Alice-Bob sine-Gordon systems ∗ ∗ The work was sponsored by the National Natural Science Foundation of China (Nos. 11435005, 11975131, 12235007) and K. C. Wong Magna Fund in Ningbo University.

Three nonlocal Alice-Bob sine-Gordon (ABSG) systems with the parity and time reversal nonlocality and/or space-time exchange nonlocality are investigated. For the common local SG equation, two types of N-soliton solutions and three types of periodic solutions are presented. The multiple solutions, breather solution, double kink solution, and periodic solutions of the ABSG systems are obtained from the symmetry reductions of a coupled local sine-Gordon system.

Dynamic microstructure evolution and mechanical properties of dilute Mg-Al-Ca-Mn alloy during hot rolling

The dynamic microstructure and texture of dilute Mg-0.50Al-0.71Ca-0.33Mn (wt.%) during hot rolling at two slab temperatures were investigated by electron backscattered diffraction (EBSD) and high resolution transmission electron microscopy (HRTEM). The results show that the development of the rolling microstructures is to first form {10–12} extension twins in the original grains, thereby forming the extension-twinned regions, and then to further form {10–11} - {10–12} double twins and kinks in the extension-twinned regions, and finally to form continuous dynamic recrystallized (continuous DRXed) grains in the double twins and the cross parts of the shear-deformed coarse extension-twinned regions. These extension twins, double twins and kinks show a decisive effect on the formation of rolling texture. The number of {10–11} - {10–12} double twins and resultant the continuous DRX process are strongly affected by the rolling slab temperature and the reduction thickness per pass. By optimizing the rolling conditions, texture and microstructures of the multi-pass rolled Mg-Al-Ca-Mn alloy sheets are successfully modified. Although the total alloy content is only 1.5 wt.%, these Mg-Al-Ca-Mn alloy sheets show much higher strength than the commercial Mg-3Al-1 Zn (wt.%) (AZ31B) sheet.

Magnetic Relaxation in Commercial REBCO Tapes With and Without Artificial Pinning Centers

High-temperature superconducting REBCO tapes are expected to be applied to next-generation magnets for their high current density. One of their problems in the magnet application is the magnetic field instability caused by the decay of magnetization due to the shielding current caused by the tape shape. Therefore, it is important to evaluate the magnetization relaxation of REBCO tapes for the magnet design. In this study, we evaluated the magnetization relaxation of commercial REBCO tapes with and without APCs from Fujikura, SuperPower, and SuperOx in a wide temperature and field range. As a result, at low temperatures below 20K, there was negligible change, but at medium and above temperatures, the change due to the introduction of APC was different for each providers. By discussing the temperature dependence based on the flux creep model and the double kink excitation model, we explained why magnetization relaxation occurs, which is necessary for magnet design.

Vortex Dynamics and Critical Current Densities in 90 K-phase and 60 K-phase YBa2Cu3O7−δ with Splayed Columnar Defects

Enhancement of critical current density (J c) was observed in YBa2Cu3O7−δ with splayed columnar defects (CDs). In the case of 90 K-phase YBa2Cu3O7−δ with splayed CDs, the enhanced J c drops suddenly at the depinning temperature of vortices from CDs (T dp), which is interpreted to be caused by the excitation of double kinks traversing neighboring CDs. In addition to the optimal 90 K-phase, where the superconductivity dominates, there is another stable 60 K-phase and other phases with different T c. This study reports temperature dependence of J c and the step-like decrease of J c in YBa2Cu3O7−δ with CDs and with different T c. Results show that the T dp is strongly related to the T c. However, additional entropic reduction of T dp may depend on parameters other than T c.

Heat traveling waves in rigid thermal conductors with phase lag and stability analysis

Recently, a model equation that describes nonlinear heat waves in a rigid thermal conductor has been derived. The system of the governing equations for temperature and heat flux is nonlinear. The objective of the present work is to find a variety of traveling wave solutions of this system of equations in the whole space. This is achieved by implementing the unified method. The obtained solutions are evaluated numerically and represented graphically. The behavior of these solutions is investigated, where it is shown that the temperature and the heat flux attain steady states in space, but increase with time. The effects of the characteristic length, time, heat flux, and reference temperature are studied via some material data. It is shown that the solutions may have the form of solitary wave, soliton, or soliton with double kinks. It is observed that the heat flux in the material is negative, this reflects the fact that heat flux is in the opposite direction of the normal vector to the material surface on which it is evaluated. The steady state solution of the considered model equation is studied. It is found that the stability of the solutions depends significantly on the wave number.

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.

Nonlinear oscillations of topological structures in the sine-Gordon systems

The nonlinear effect of the energy localization on topological inhomogeneities is investigated in the sine-Gordon systems. The regimes of nonlinear oscillations of nonequilibrium configurations of domain walls in the quasi-one-dimensional ferromagnet are described in terms of kink and breather solutions of the sine-Gordon equation. The conditions of the energy localization, i.e., the formation of breather excitations on these topological inhomogeneities, are found for the initial configurations of the dilated double kink structures. The results are obtained in the framework of the Schrödinger-type equation of the direct scattering problem associated with the sine-Gordon equation. It is shown that the final state of the evolution of the nonequilibrium topological spin structure represents the multi-frequency precessing domain wall in the ferromagnet, which radiates the continuous spectrum waves.

Second-harmonic generation via double topological valley-Hall kink modes in all-dielectric photonic crystals

Nonlinear topological photonics, which explores topics common to the fields of topological phases and nonlinear optics, is expected to open up a new paradigm in topological photonics. Here, we demonstrate second-harmonic generation (SHG) via nonlinear interaction of double topological valley-Hall kink modes in all-dielectric photonic crystals (PhCs). We first show that two topological frequency bandgaps can be created around a pair of frequencies, $\omega_0$ and $2\omega_0$, by gapping out the corresponding Dirac points in two-dimensional honeycomb PhCs. Valley-Hall kink modes along a kink-type domain wall interface between two PhCs placed together in a mirror-symmetric manner are generated within the two frequency bandgaps. Importantly, through full-wave simulations and mode dispersion analysis, we demonstrate that tunable, bi-directional phase-matched SHG via nonlinear interaction of the valley-Hall kink modes inside the two bandgaps can be achieved. In particular, by using Stokes parameters associated to the magnetic part of the valley-Hall kink modes, we introduce a new concept, SHG directional dichroism, which is employed to characterize optical probes for sensing chiral molecules. Our work opens up new avenues towards topologically protected nonlinear frequency mixing and active photonic devices implemented in all-dielectric material platforms.

Solid-solution strengthening by Al and Cr in FeCrAl oxide-dispersion-strengthened alloys

FeCrAl oxide-dispersion-strengthened (ODS) alloys are promising materials for accident tolerant fuels for light water reactors (LWRs). In these alloys, Al and Cr are key elements with important synergistic effects: enhancement of the formation of oxidation-resistant Al 2 O 3 phase by Cr addition and suppression of the formation of the embrittling Cr-rich α′ phase by Al addition. The solid-solution strengthening resulting from Al and Cr co-addition was investigated in this study. The Al and Cr contents were systematically varied from 9 to 16 at.% and 10–17 at.%, respectively, and tensile tests were conducted at 298 K, 573 K, and 973 K. The solid-solution strengthening increased linearly, 20 MPa per 1 at.% Al and 5 MPa per 1 at.% Cr, at the typical LWR operational temperature of 573 K. The conventional Fleischer–Friedel and Labusch theories cannot explain this level of solid-solution strengthening. It was originally clarified that the solid-solution strengthening by Al and Cr in the FeCrAl-ODS alloys can be reasonably predicted by modifying shear modulus difference for the Suzuki's double kink theory for screw dislocations. The inverse dependency on the absolute temperature and linear dependency on the Al and Cr content can be successfully realized by this approach.

Cooperative roles of stacking fault energies on dislocation nucleation at bimetal interface through tunable potentials

By tuning consistent potentials for bimetal system, the cooperative roles of stacking fault energies (SFEs) such as intrinsic SFE (ISFE) and unstable SFE (USFE) on the dislocation nucleation are comprehensively explored. It reveals that the dislocation nucleation at semi-coherent interface is determined by the misfit dislocations, but the critical yield stress depends strongly on the values of ISFE and USFE that are function of external loadings. To account for such relationship, a modified analytical model is proposed based on the nucleation and propagation of double kinks at the interface, showing good agreement with the simulation results. These results not only resolve the previous inconsistency in the role of stacking faults on plastic deformation but shed light on evaluating the atomistic mechanism according to the synergistic effect between stacking faults and loading schemes.

Description of Shapiro steps on the potential energy surface of a Frenkel\u2013Kontorova model, Part II: free boundaries of the chain

We explain Shapiro steps in a Frenkel–Kontorova (FK) model for a 1D chain of particles with free boundaries. The action of an external alternating force for the oscillating structure of the chain is important here. The different ’floors’ of the potential energy surface (PES) of this model play an important role. They are regions of kinks, double kinks, and so on. We will find out that the preferable movements are the sliding of kinks or antikinks through the chain. The more kinks / antikinks are included the higher is the ’floor’ through the PES. We find the Shapiro steps moving and oscillating anywhere between the floors. They start with a single jump over the highest SP in the global valley through the PES, like in part I of this series. They finish with complicated oscillations in the PES, for excitations directly over the critical depinning force. We use an FK model with free boundary conditions. In contrast to other results in the past, for this model, we obtain Shapiro steps in an unexpected, inverse sequence. We demonstrate Shapiro steps for a case with soft ’springs’ between an 8-particle FK chain.Graphic abstract

Statistical mechanics of kinks on a gliding screw dislocation

The ability of a body-centered cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a critical temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.

Solid solution softening in dislocation-starved Mg–Al alloys

Here, we report molecular dynamics (MD) calculations of spall strength in pure magnesium and magnesium alloys with 1–8 at.% aluminum in solid solution. The Mg–Al solid solution alloys are found to have a weaker spall strength than pure magnesium, e.g. the spall strength of Mg-8 at.% Al is found to be 12% lower than pure magnesium. Moreover, we find that the spall strength of Mg–Al alloys monotonically decreases with increasing concentration of Al content. We term this phenomena solid solution softening (SSS) of spall strength, which is contrary to the conventional solid solution strengthening observed in most alloys (including Mg–Al alloys) deformed at quasi-static loading rates. We argue that this transition from solid solution strengthening at quasi-static rates to SSS at extreme loading rates is due to a transition from dislocation glide dominated failure at low rates to dislocation nucleation dominated failure at extreme rates. The distortion of the host lattice by solute atoms is found to retard dislocation glide, but aids dislocation nucleation. We thus conclude that SSS may manifest in any dislocation-starved system, regardless of loading rate. To this end, we propose a theoretical model for spall strength in dislocation-starved bulk and nanoporous alloys that exhibits remarkable agreement with our molecular dynamics calculations. Our theory bares some resemblance to the double kink nucleation enhancement theory for low-temperature SSS in some body centered cubic metals, e.g. refractory metals alloyed with group IV-VIII elements.

Dynamic Atomic Displacements and Athermal Dislocation Glide in Crystals

A dislocation glide mechanism at low temperatures is proposed. The mechanism is based on the inclusion of dynamic atomic displacements, i.e., those caused by nonadiabatic transitions of atoms in a crystal with a dislocation under action of an external force. The dynamic displacements initiate the instability of a rectilinear dislocation with respect to low-amplitude displacements during atomic vibrations. The instability development leads to the formation of a double kink and the dislocation displacement by one interatomic distance.

Collision of two kinks with inner structure

In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of two such kinks is simulated by using the Fourier spectral method. We numerically calculate how the critical velocity and the widths of the first three two bounce windows vary with the model parameters. After that, we report some interesting collision results including two-bion escape final states, kink-bion-antikink intermediate states and kink or antikink intertwined final states. These results show that kinks with inner structure in the energy density have similar properties as those of the double kinks.