Weak Kink Research Articles

Bifurcations and exact traveling wave solutions for the regularized Schamel equation

Abstract In the present paper, we focus on studying the bifurcations and the traveling wave solutions (TWSs) for the regularized Schamel equation. Based on the bifurcation method of a dynamical system, a complete phase portrait analysis is given in various parameter conditions and some novel TWSs with the same energy of the Hamiltonian system are discovered. Various significant results on exact expressions of TWSs, including solitary waves, periodic waves, cusp waves, weak kink waves, loop solitons, compactons in different conditions are obtained.

Weak kink wave and peakon solutions with an arbitrary parameter

In this paper, we reconsider the weak-kink and peakon solution of the integrable equation (Alber et al 2001 Commun. Math. Phys. 221, 197)mt=bux+12α1m(u2−ux2)x+12α2(2mux+mxu),m=u−uxx,where b, α1, α2 are three real numbers, through redefining the value of the conventional sign function sgn(x) at x = 0 as sgnθ (0) = θ, where θ is an arbitrary number. Then, our computation generates more generalized peakon and multi-peakon solutions involved in parameter θ, and all of those classical peakon solutions are special cases where we place θ = 0 here in the present paper. Furthermore, we also study a weak kink wave solution and the interactional dynamics of peakons with the weak kink wave if the parameter . All wave profiles are depicted through graphs for different values of parameter θ.

Blow-up scenario for a generalized Camassa–Holm equation with both quadratic and cubic nonlinearity

ABSTRACT In this paper, we mainly devote to study an integrable generalized Camassa–Holm equation with both quadratic and cubic nonlinearity proposed by Xia, Qiao and Li [An integrable system with peakon, complex peakon, weak kink, and kink-peakon interactional solutions. Commun Nonlinear Sci Numer Simul. 2018;63:292–306]. By overcoming the difficulties cased by the complicated mixed nonlinear structure, we present a precise blow-up scenario and some new blow-up results for strong solutions under different initial data.

Colossal magnetoresistance in low-doped EuTi1−xNbxO3 (x = 0.003 and 0.005)

We studied the magnetization (M), magnetostriction (λ||), resistivity (ρ), magnetoresistance (MR), and thermoelectric properties of low-doped EuTi1−xNbxO3 (x = 0.003 and 0.005). In both the samples, Eu2+(4f7) spins order antiferromagnetically at TN≅5.5K, and the paramagnetic to antiferromagnetic transition is accompanied by a spontaneous contraction of the length in the absence of magnetic field and a positive magnetostriction under external magnetic fields. ρ(T) shows non-metallic behavior in the temperature range 400–2.5 K but a weak kink at TN in a zero magnetic field. The application of an external magnetic field induces the semimetal-metal transition and negative MR. The magnitude of negative MR has a maximum value of 82% (57%) under 7 T for x = 0.003 (0.005) at T = 2.5 K, and the MR monotonously decreases with increasing temperature. Thermopower data indicate that the doped carriers are electrons. It is suggested that scattering of 4d1 electrons doped in the impurity band by 4f spin fluctuations is responsible for the colossal magnetoresistance.

Short-range order in the quantum XXZ honeycomb lattice material BaCo2(PO4)2

We present observations of highly frustrated quasi two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the S$_{eff}$ = 1/2 compound $\gamma$-BaCo$_2$(PO$_4$)$_2$ ($\gamma$-BCPO). Specific heat shows a broad peak comprised of two weak kink features at $T_{N1} \sim$ 6 K and $T_{N2} \sim$ 3.5 K, the relative weights of which can be modified by sample annealing. Neutron powder diffraction measurements reveal short range quasi-2D order that is established below $T_{N1}$ and $T_{N2}$, at which two separate, incompatible, short range magnetic orders onset: commensurate antiferromagnetic correlations with correlation length $\xi_c = 60\pm2$ \AA \ ($T_{N1}$) and in quasi-2D helical domains with $\xi_h = 350 \pm 11$ \AA \ ($T_{N2}$). The ac magnetic susceptibility response lacks frequency dependence, ruling out spin freezing. Inelastic neutron scattering data on $\gamma$-BCPO is compared with linear spin wave theory, and two separate parameter regions of the XXZ $J_1$-$J_2$-$J_3$ model with ferromagnetic nearest-neighbor exchange $J_1$ are favored, both near regions of high classical degeneracy. High energy coherent excitations ($\sim 10$ meV) persist up to at least 40 K, suggesting strong in-plane correlations persist above $T_N$. These data show that $\gamma$-BCPO is a rare highly frustrated, quasi-2D S$_{eff}$ = 1/2 honeycomb lattice material which resists long range magnetic order and spin freezing.

An integrable system with peakon, complex peakon, weak kink, and kink-peakon interactional solutions

In this paper, we study an integrable system with both quadratic and cubic nonlinearity: mt=bux+12k1[m(u2−ux2)]x+12k2(2mux+mxu),m=u−uxx, where b, k1 and k2 are arbitrary constants. This model is kind of a cubic generalization of the Camassa–Holm (CH) equation: mt+mxu+2mux=0. The equation is shown integrable with its Lax pair, bi-Hamiltonian structure, and infinitely many conservation laws. In the case b=0, peaked soliton (peakon), complex peakon, and multi-peakon solutions are studied. In particular, the two-peakon dynamical system is explicitly presented and their collisions are investigated in details. In the case b ≠ 0, the weak kink and kink-peakon interactional solutions are found for the first time. Significant difference from the CH equation is analyzed through a comparison. In the paper, we also investigate all possible smooth one-soliton solutions for the system.

On Peakon and Kink-peakon Solutions to a (2+1) Dimensional Generalized Camassa-Holm Equation

In this paper, we study a (2+1)-dimensional generalized Camassa-Holm (2dgCH) equation with both quadratic and cubic nonlinearity. We derive a peaked soliton (peakon) solution, double-peakon solutions, and kink-peakon solutions. In particular, weak kink - peakon solution is the first time to address in the 2 + 1-dimensional integrable system.

ϕ 3 theory with F4 flavor symmetry in 6 − 2ϵ dimensions: 3-loop renormalization and conformal bootstrap

We consider $\phi^3$ theory in $6-2\epsilon$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $\phi$ are also computed. We then employ conformal bootstrap technique to study the fixed point predicted from the perturbative approach. For each putative scaling dimension of $\phi$ ($\Delta_{\phi})$, we obtain the corresponding upper bound on the scaling dimension of the second lowest scalar primary in the ${\mathbf 26}$ representation $(\Delta^{\rm 2nd}_{{\mathbf 26}})$ which appears in the OPE of $\phi\times\phi$. In $D=5.95$, we observe a sharp peak on the upper bound curve located at $\Delta_{\phi}$ equal to the value predicted by the 3-loop computation. In $D=5$, we observe a weak kink on the upper bound curve at $(\Delta_{\phi},\Delta^{\rm 2nd}_{{\mathbf 26}})$=$(1.6,4)$.

Quantization and anomalous structures in the conductance of Si/SiGe quantum point contacts

Quantum point contacts (QPCs) are fabricated on modulation-doped Si/SiGe heterostructures and ballistic transport is studied at low temperatures. We observe quantized conductance with subband separations up to 4 meV and anomalies in the first conductance plateau at 4e2/h. At a temperature of T = 22 mK in the linear transport regime, a weak anomalous kink structure arises close to 0.5(4e2/h), which develops into a distinct plateau-like structure as temperature is raised up to T = 4 K. Under magnetic field parallel to the wire up to B = 14 T, the anomaly evolves into the Zeeman spin-split level at 0.5(4e2/h), resembling the "0.7 anomaly" in GaAs/AlGaAs QPCs. Additionally, a zero-bias anomaly (ZBA) is observed in nonlinear transport spectroscopy. At T = 22 mK, a parallel magnetic field splits the ZBA peak up into two peaks. At B = 0, elevated temperatures lead to similar splitting, which differs from the behavior of ZBAs in GaAs/AlGaAs QPCs. Under finite dc bias, the differential resistance exhibits additional plateaus approximately at 0.8(4e2/h) and 0.2(4e2/h) known as "0.85 anomaly" and "0.25 anomaly" in GaAs/AlGaAs QPCs. Unlike the first regular plateau at 4e2/h, the 0.2(4e2/h) plateau is insensitive to dc bias voltage up to at least VDS = 80 mV, in-plane magnetic fields up to B = 15 T, and to elevated temperatures up to T = 25 K. We interpret this effect as due to pinching off one of the reservoirs close to the QPC. We do not see any indication of lifting of the valley degeneracy in our samples.

Persistence properties and unique continuation for a dispersionless two-component Camassa-Holm system with peakon and weak kink solutions

In this paper, we study the persistence properties and unique continuation for a dispersionless two-component system with peakon and weak kink solutions. These properties guarantee strong solutions of the two-component system decay at infinity in thespatial variable provided that the initial data satisfies the condition of decaying at infinity.Furthermore, we give an optimal decaying index of the momentum for the system and show that the system exhibits unique continuation if the initial momentum $m_0$ and $n_0$ are non-negative.

Modelling toroidal rotation damping in ITER due to external 3D fields

The linear and quasi-linear plasma response to the n = 3 and n = 4 (n is the toroidal mode number) resonant magnetic perturbation (RMP) fields, produced by the in-vessel edge localized mode control coils, is numerically studied for an ITER 15 MA H-mode baseline scenario. Both single fluid and fluid-kinetic hybrid models are used. The inclusion of drift kinetic effects does not strongly alter the plasma response compared to the fluid approximation for this ITER plasma. The full toroidal drift kinetic model is also used to compute the neoclassical toroidal viscous (NTV) torque, yielding results close to that of an analytic model based on geometric simplifications. The computed NTV torque from low-n RMP fields is generally smaller than the resonant electromagnetic torque for this ITER plasma. The linear response computations show a weak core kink response, contrary to a strong kink response often computed for plasmas from present day tokamak devices. Initial value quasi-linear simulations, including various torque models, show a localized damping of the plasma toroidal flow near the edge, as a result of the applied RMP fields. This localized rotation damping can be weak or strong depending on whether a weakly unstable edge localized peeling mode is present. No qualitative difference is found between the n = 3 and n = 4 RMP field configurations, in both the linear and non-linear response results.

Qualitative Analysis for a New Integrable Two-Component Camassa–Holm System with Peakon and Weak Kink Solutions

This paper is devoted to a new integrable two-component Camassa–Holm system with peaked solitons (peakons) and weak-kink solutions. It is the first integrable system that admits weak kink and kink–peakon interactional solutions. In addition, the new system includes both standard (quadratic) and cubic Camassa–Holm equations as two special cases. In the paper, we first establish the local well-posedness for the Cauchy problem of the system, and then derive a precise blow-up scenario and a new blow-up result for strong solutions to the system with both quadratic and cubic nonlinearity. Furthermore, its peakon and weak kink solutions are discussed as well.

Magnetic properties and heat capacity of the three-dimensional frustratedS=12antiferromagnetPbCuTe2O6

We report magnetic susceptibility (chi) and heat capacity Cp measurements along with ab-initio electronic structure calculations on PbCuTe2O6, a compound made up of a three dimensional 3D network of corner-shared triangular units. The presence of antiferromagnetic interactions is inferred from a Curie-Weiss temperature (theta_CW) of about -22 K from the chi(T) data. The magnetic heat capacity (Cm) data show a broad maximum at T^max ~ 1.15 K (i.e. T^max/theta_CW ~ 0.05), which is analogous to the the observed broad maximum in the Cm/T data of a hyper-Kagome system, Na4Ir3O8. In addition, Cm data exhibit a weak kink at T^* ~ 0.87 K. While the T^max is nearly unchanged, the T^* is systematically suppressed in an increasing magnetic field (H) up to 80 kOe. For H > 80 kOe, the Cm data at low temperatures exhibit a characteristic power-law (T^{\alpha}) behavior with an exponent {\alpha} slightly less than 2. Hopping integrals obtained from the electronic structure calculations show the presence of strongly frustrated 3D spin interactions along with non-negligible unfrustrated couplings. Our results suggest that PbCuTe2O6 is a candidate material for realizing a 3D quantum spin liquid state at high magnetic fields.

Integrable peakon systems with weak kink and kink-peakon interactional solutions

We report two integrable peakon systems that have weak kink and kink-peakon interactional solutions. Both peakon systems are guaranteed integrable through providing their Lax pairs. The peakon and multi-peakon solutions of both equations are studied. In particular, the two-peakon dynamic systems are explicitly presented and their collisions are investigated. The weak kink solution is studied, and more interesting, the kink-peakon interactional solutions are proposed for the first time.

Effect of electron-phonon coupling in the ARPES spectra of the tri-layer cuprate Bi2Sr2Ca2Cu3O10+δ

Angle-resolved photoemission spectroscopy using tunable low energy photons allows us to study the quasi-particle (QP) dispersions of the inner and outer CuO2 planes (IP and OP) separately in the tri-layer cuprate Bi2Sr2Ca2Cu3O10+δ (Bi2223). The kink energy of the OP band is ~ 70 meV, as observed in various high-Tc cuprates, while that of the IP band is as large as ~ 100 meV in the superconducting (SC) state. This large kink energy is attributed to the ~35 meV buckling mode plus the large (~ 60 meV) SC gap of IP. The IP band also shows a weak kink feature at ~ 70 meV in the SC state. The latter feature can be explained either by the 70 meV half-breathing mode or by the ~ 35 meV buckling-phonon mode plus the ~ 40 meV SC gap of OP if interlayer scattering of QP is involved.

Spin Hall and spin Nernst effects in graphene with intrinsic and Rashba spin—orbit interactions

The spin Hall and spin Nernst effects in graphene are studied based on Green's function formalism. We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in the Kane—Mele model with various structures. When both intrinsic and Rashba spin—orbit interactions are present, their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level. When the Rashba spin—orbit interaction is smaller than intrinsic spin—orbit coupling, a weak kink in the conductance appears. The kink disappears and a divergence appears when the Rashba spin—orbit interaction enhances. When the Rashba spin—orbit interaction approaches and is stronger than intrinsic spin—orbit coupling, the divergence becomes more obvious.

KOHN ANOMALY ENERGY IN CONVENTIONAL SUPERCONDUCTORS EQUALS TWICE THE ENERGY OF THE SUPERCONDUCTING GAP: HOW AND WHY?

Kohn anomaly occurs in metals as a weak but discernible kink in the phonon spectrum around 2kF arising out of screened Coulombic interaction. Over the years this has been observed in a number of normal metallic systems. As a major surprise however, the recent neutron spin-echo experiments on elemental (conventional) superconductors Pb and Nb reveal a very important and striking relation that Kohn (anomaly) energy equals twice the energy of the superconducting gap. In this paper we explore the microscopic origin of this novel phenomenon and discuss its implication to the standard model BCS Theory.

Non-Collinear Magnetic Structure of TbB4

Non-Collinear Magnetic Structure of TbB₄

AC floating-body effects in submicron fully depleted (FD) SOI nMOSFETs and the impact on analog applications

We report the impact of submicron fully depleted (FD) SOI MOSFET technology on device AC characteristics and the resultant effects on analog circuit issues. The weak DC kink and high frequency AC kink dispersion in FD SOI still degrade circuit performance in terms of distortion and low-frequency noise requirements. These issues raise concerns about FD devices for mixed-mode applications. Therefore, further device optimization such as source/drain engineering is still necessary to solve the aforementioned issues for FD SOI. On the other hand, partially depleted SOI MOSFET with body contact structures provide an alternative technology for RF/baseband analog applications.

Q dependence of the magnetic response in URu2Si2.

We have performed inelastic neutron-scattering experiments with E/sub 0/ = 12.7 meV on the superconducting heavy-fermion system URu/sub 2/Si/sub 2/ in the temperature range 5--50 K. The main feature of the magnetic response is an inelastic excitation at a few meV. The intensity of the magnetic scattering shows a chemically bondQchemically bond dependence which we will discuss for temperatures above and below the Neel temperature T/sub N/ = 17.5 K. From the neutron-scattering data one can extract a local magnetic susceptibility, which shows strong spatial correlations even above T/sub N/. These correlations are mainly visible in the direction. The Van Vleck term of the local susceptibility corresponding to the inelastic excitation shows a clear peak at the Neel temperature, in contrast to a weak kink in the static bulk susceptibility.