Linear Kink Research Articles

A microscopic traffic flow model for explaining nonlinear traffic phenomena: Modeling, stability analysis and validation

As the core of reproducing the real nonlinear phenomena of traffic congestion, the investigation of car-following models, which take into account human factors, has consistently assumed a central role within the domain of transportation science. Nevertheless, it is noteworthy that prior studies have invariably employed a fixed value for driver reaction time to stimuli, whereas it is imperative to recognize the dynamic nature of this parameter, closely associated with the instantaneous vehicle speed. To address this issue, this paper constructs a dynamic sensitivity coefficient (DSC), and further develops a nonlinear human factoring car-following model to reveal the relation between the reaction time and the current speed. Firstly, the linear critical stability condition and the mKdV equation of the model are derived by the linear stability analysis and kink–antikink solution analytic method, respectively. Then, the numerical experiments are conducted to demonstrate that the proposed model is more practical and can reproduce the real driving behavior and phenomena. Finally, calibration and validation results exhibit the actual vehicle trajectory can be simulated well.

Microwave response to kink oscillations of a plasma slab

ABSTRACT The modulation of the intensity of microwave emission from a plasma slab caused by a standing linear kink fast magnetoacoustic wave is considered. The slab is stretched along a straight magnetic field, and can represent, for example, a current sheet in a flaring active region in corona of the Sun, or a streamer or pseudostreamer stalk. The plasma density is non-uniform in the perpendicular direction and described by a symmetric Epstein profile. The plasma parameter β is taken to be zero, which is a good approximation for solar coronal active regions. The microwave emission is caused by mildly relativistic electrons which occupy a layer within the oscillating slab and radiate via the gyrosynchrotron (GS) mechanism. Light curves of the microwave emission were simulated in the optically thin part of the GS spectrum, and their typical Fourier spectra were analysed. It is shown that the microwave response to a linear kink magnetohydrodynamic wave is non-linear. It is found that, while the microwave light curves at the node oscillate with the same frequency as the frequency of the perturbing kink mode, the frequency of the microwave oscillations at the antinode is two times higher than the kink oscillation frequency. Gradual transformation the one type of the light curves to another occurs when sliding from the node to the antinode. This result does not depend on the width of the GS-emitting layer inside the oscillating slab. This finding should be considered in the interpretation of microwave quasi-periodic pulsations in solar and stellar flares.

Three-dimensional propagation of kink wave trains in solar coronal slabs

ABSTRACT Impulsively excited wave trains are of considerable interest in solar coronal seismology. To our knowledge, however, it remains to examine the three-dimensional (3D) dispersive propagation of impulsive kink waves in straight, field-aligned, symmetric, low-beta, slab equilibria that are structured only in one transverse direction. We offer a study here, starting with an analysis of linear oblique kink modes from an eigenvalue problem perspective. Two features are numerically found for continuous and step structuring alike, one being that the group and phase velocities may lie on opposite sides of the equilibrium magnetic field ($\boldsymbol {B}_0$), and the other being that the group trajectories extend only to a limited angle from $\boldsymbol {B}_0$. We justify these features by making analytical progress for the step structuring. More importantly, we demonstrate by a 3D time-dependent simulation that these features show up in the intricate interference patterns of kink wave trains that arise from a localized initial perturbation. In a plane perpendicular to the direction of inhomogeneity, the large-time slab-guided patterns are confined to a narrow sector about $\boldsymbol {B}_0$, with some wavefronts propagating toward $\boldsymbol {B}_0$. We conclude that the phase and group diagrams lay the necessary framework for understanding the complicated time-dependent behaviour of impulsive waves.

Deep learning based surrogate models for first-principles global simulations of fusion plasmas

The accurate identification and control of plasma instabilities is important for successful fusion experiments. First-principle simulations that can provide physics-based instability information such as the mode structure are generally not fast enough for real-time applications. In this work, a workflow has been presented to develop deep-learning based surrogate models for the first-principle simulations using the gyrokinetic toroidal code (GTC). The trained surrogate models of GTC (SGTC) can be used as physics-based fast instability simulators that run on the order of milliseconds, which fits the requirement of the real-time plasma control system. We demonstrate the feasibility of this workflow by first creating a big database from GTC systematic linear global electromagnetic simulations of the current-driven kink instabilities in DIII-D plasmas, and then developing SGTC linear internal kink instability simulators through supervised training. SGTC linear internal kink simulators demonstrate predictive capabilities for the mode instability properties including the growth rate and mode structure.

Kink Oscillations in Solar Coronal Loops with Elliptical Cross Sections. I. The Linear Regime

Abstract The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigenmode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross sections, the apparent damping of the transverse displacement of the loop axis is accompanied by the accumulation of transverse Alfvénic motions and the consequent development of small scales therein, suggesting the robustness of the concepts of resonant absorption and phase mixing. In addition, two stages can in general be told apart in the temporal evolution of the loop displacement: a Gaussian time dependence precedes an exponential one. For the two examined density ratios between loops and their surroundings, the periods of the M-modes (m-modes) tend to increase (decrease) with the major-to-minor-half-axis ratio, and the damping times in the exponential stage for the M-modes tend to exceed their m-mode counterparts. This is true for the two transverse profiles we examine. However, the relative magnitudes of the damping times in the exponential stage for different polarizations depend on the specification of the transverse profile or the density contrast. The applications of our numerical findings are discussed in the context of coronal seismology.

Polyhedral DC Decomposition and DCA Optimization of Piecewise Linear Functions

For piecewise linear functions f : R n ↦ R we show how their abs-linear representation can be extended to yield simultaneously their decomposition into a convex f ˇ and a concave part f ^ , including a pair of generalized gradients g ˇ ∈ R n ∋ g ^ . The latter satisfy strict chain rules and can be computed in the reverse mode of algorithmic differentiation, at a small multiple of the cost of evaluating f itself. It is shown how f ˇ and f ^ can be expressed as a single maximum and a single minimum of affine functions, respectively. The two subgradients g ˇ and − g ^ are then used to drive DCA algorithms, where the (convex) inner problem can be solved in finitely many steps, e.g., by a Simplex variant or the true steepest descent method. Using a reflection technique to update the gradients of the concave part, one can ensure finite convergence to a local minimizer of f, provided the Linear Independence Kink Qualification holds. For piecewise smooth objectives the approach can be used as an inner method for successive piecewise linearization.

LIFE AFTER DEBT: POSTGRADUATION CONSEQUENCES OF FEDERAL STUDENT LOANS

We estimate the causal effect of student loans on postgraduation labor market outcomes exploiting a kink in the formula determining eligibility for need‐based student loans. Using a representative sample of students graduating with a bachelor's degree in 1993, we find that student debt has nonnegative effects on earnings. This result holds with differing levels of statistical significance across a battery of different empirical designs: (1) ordinary least squares, (2) partially linear, and (3) regression kink. We find similar results for the 2008 graduating cohort. (JEL I22, I26, J32, J33)

Relaxing Kink Qualifications and Proving Convergence Rates in Piecewise Smooth Optimization

In the paper [Optim. Methods Softw., 31 (2016), pp. 904--930] we derived first order (KKT) and second order (second order sufficiency condition (SOSC)) optimality conditions for functions defined by evaluation programs involving smooth elementals and absolute values. In that analysis, a key assumption on the local piecewise linearization was the linear independence kink qualification (LIKQ), a generalization of the linear independence constraint qualification (LICQ) known from smooth nonlinear optimization. Firstly, we show here that under LIKQ and SOSC with strict complementarity, the natural algorithm of successive abs-linear minimization with a proximal term (SALMIN) achieves a linear rate of convergence. A version of SALMIN called LiPsMin has already been implemented and tested in [Math. Program., 158 (2016), pp. 383--415; Math. Program. (2018), https://doi.org/10.1007/s10107-018-1273-5]. Secondly, we observe that, even without any kink qualifications, local optimality of the nonlinear objective always requires local optimality of its piecewise linearization, and strict minimality of the latter is in fact equivalent to sharp minimality of the former. Moreover, we show that SALMIN will converge quadratically to such sharp minimizers, where the function exhibits linear growth. These results are independent of the particular function representation, and allow in particular duplications of switching variables and other intermediates. Furthermore, we derive for nonsharp minimizers necessary and sufficient optimality conditions without any kink qualification. Finally, we present numerical results to illustrate the obtained convergence results.

Influence of Total Ionizing Dose Irradiation on Low-Frequency Noise Responses in Partially Depleted SOI nMOSFETs**Supported by the National Postdoctoral Program for Innovative Talents under Grant No BX201600037, the Science and Technology Research Project of Guangdong Province under Grant Nos 2015B090901048 and 2015B090912002, and the Distinguished Young Scientist Program of Guangdong Province under Grant No 2015A030306002.

Total ionizing dose effect induced low frequency degradations in 130 nm partially depleted silicon-on-insulator (SOI) technology are studied by 60Co γ-ray irradiation. The experimental results show that the flicker noise at the front gate is not affected by the radiation since the radiation induced trapped charge in the thin gate oxide can be ignored. However, both the Lorenz spectrum noise, which is related to the linear kink effect (LKE) at the front gate, and the flicker noise at the back gate are sensitive to radiation. The radiation induced trapped charge in shallow trench isolation and the buried oxide can deplete the nearby body region and can activate the traps which reside in the depletion region. These traps act as a GR center and accelerate the consumption of the accumulated holes in the floating body. It results in the attenuation of the LKE and the increase of the Lorenz spectrum noise. Simultaneously, the radiation induced trapped charge in the buried oxide can directly lead to an enhanced flicker noise at the back gate. The trapped charge density in the buried oxide is extracted to increase from 2.21 × 1018 eV−1 cm−3 to 3.59 × 1018 eV−1 cm−3 after irradiation.

2D-ordered kinked carbyne chains: DFT modeling and Raman characterization

During the past years one-dimensional carbon allotropes containing sp1 bonds, both individual chains and carbyne-like crystals held by Van der Waals forces, were attracting much interest. One of the recent developments is the ion-assisted condensation of sp1 chains, ordered in a hexagonal structure with nearly 5 Å interchain distance – 2D-ordered linear-chained carbon (LCC). The main problem of LCC synthesis is the lack of simple characterization technique rapidly confirming its structural features. In the present work, for the first time the experimental Raman spectra of the LCC films and ab initio calculation of Raman susceptibilities using the simple structural model of LCC are combined to provide the Raman bands identification and to propose a rapid characterization technique. DFT calculations establish dependence between linear fragment length, kink angle and Raman-active phonon modes of carbon chains, giving interpretation to high frequency and low frequency vibrations, taking into account the distribution of LCC structural parameters. The calculation results explain the inversion of single-chain Raman spectrum occurring in case of chains ensemble by the interaction between chains, enhanced by the kink-related charges in the LCC structure.

First- and second-order optimality conditions for piecewise smooth objective functions

Any piecewise smooth function that is specified by an evaluation procedure involving smooth elemental functions and piecewise linear functions like and can be represented in the so-called abs-normal form. By an extension of algorithmic, or automatic, differentiation, one can then compute certain first- and second-order derivative vectors and matrices that represent a local piecewise linearization and provide additional curvature information. On the basis of these quantities, we characterize local optimality by first- and second-order necessary and sufficient conditions, which generalize the corresponding Kuhn-Tucker-Karush (KKT) theory for smooth problems. The key assumption is the linear independence kink qualification, a generalization of Linear Independence Constraint Qualification (LICQ) familiar from nonlinear optimization. It implies that the objective has locally a so-called decomposition and renders everything tractable in terms of matrix factorizations and other simple linear algebra operations. By yielding descent directions, whenever they are violated the new optimality conditions point the way to a superlinearly convergent generalized Quadratic Program solver, which is currently under development. We exemplify the theory on two nonsmooth examples of Nesterov.

Impact of processing and back-gate biasing conditions on the low-frequency noise of ultra-thin buried oxide silicon-on-insulator nMOSFETs

The analysis of the low-frequency noise of fully-depleted Silicon-On-Insulator (SOI) ultra-thin body and Ultra-Thin Buried Oxide (UTBOX) MOSFETs with different gate stacks, Si film thicknesses and extension architecture is performed. It was revealed that the extension architecture is the main factor affecting the drain current and low frequency noise behavior of the devices studied. It is revealed that the 1/f noise of extensionless MOSFETs appears to be higher than for standard ones, especially when the back interface is biased towards accumulation. The latter is accompanied by the lower drain current of extensionless devices in comparison to standard ones. Moreover, the Lorentzians accompanying the Linear Kink Effect that were revealed for standard MOSFETs, were not observed for extensionless devices. The latter is ascribed to the different architecture of the source/drain regions, which affect source/drain-body junctions characteristics and free charge carrier concentration.

Fluid electron, gyrokinetic ion simulations of linear internal kink and energetic particle modes

The internal kink mode is an important plasma instability responsible for a broad class of undesirable phenomena in tokamaks, including the sawtooth cycle and fishbones. To predict and discover ways to mitigate this behaviour in current and future devices, numerical simulations are necessary. The internal kink mode can be modelled by reduced magnetohydrodynamics (MHD). Fishbone modes are an inherently kinetic and non-linear phenomenon based on the n = 1 Energetic Particle Mode (EPM), and have been studied using hybrid codes that combine a reduced MHD bulk plasma model with a kinetic treatment of fast ions. In this work, linear simulations are presented using a hybrid model which couples a fluid treatment of electrons with a gyrokinetic treatment of both bulk and fast ions. Studies of the internal kink mode in geometry relevant to large tokamak experiments are presented and the effect of gyrokinetic ions is considered. Interaction of the kink with gyrokinetic fast ions is also considered, including the destabilisation of the linear n = 1 EPM underlying the fishbone.

Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals

We study discrete solitons (kinks) accessible in the state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-three-dimensional configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls–Nabarro) potential gets modified to a non-periodic globally trapping potential in certain parameter regimes. The kinks' rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level.

A FLUX ROPE NETWORK AND PARTICLE ACCELERATION IN THREE-DIMENSIONAL RELATIVISTIC MAGNETIC RECONNECTION

We investigate guide-field magnetic reconnection and particle acceleration in relativistic pair plasmas with three-dimensional particle-in-cell (PIC) simulations of a kinetic-scale current sheet in a periodic geometry at low magnetizations. The tearing instability is the dominant mode in the current sheet for all guide field strengths, while the linear kink mode is less important even without guide field. Oblique modes seem to be suppressed entirely. In its nonlinear evolution, the reconnection layer develops a network of interconnected and interacting magnetic flux ropes. As smaller flux ropes merge into larger ones, the reconnection layer evolves toward a three-dimensional, disordered state in which the resulting flux rope segments contain magnetic substructure on plasma skin depth scales. Embedded in the flux ropes, we detect spatially and temporally intermittent sites of dissipation reflected in peaks in the parallel electric field. Magnetic dissipation and particle acceleration persist until the end of the simulations, with simulations with higher magnetization and lower guide field strength exhibiting greater and faster energy conversion and particle energization. At the end of our largest simulation, the particle energy spectrum attains a tail extending to high Lorentz factors that is best modeled with a combination of two additional thermal components. We confirm that the primary energization mechanism is acceleration by the electric field in the X-line region. We discuss the implications of our results for macroscopic reconnection sites, and which of our results may be expected to hold in systems with higher magnetizations.

Total Dose Irradiation-Induced Degradation of Hysteresis Effect in Partially Depleted Silicon-on-Insulator NMOSFETs

In this work, we present a study of hysteresis effect degradation induced by total dose irradiation in partially depleted SOI nMOSFETs with floating bodies. In addition to traditional linear kink effect, evidence is provided for a new hysteresis effect which occurs in output characteristics during the forward and reverse sweeps. For the first time, it is shown that at a sufficiently high irradiation level, the hysteresis behaviors both in transfer and output characteristics vanish due to interface traps and oxide trapped charge. 3D process and device simulations are performed to investigate the combined effects of charge trapping in oxide and interface traps.

Electronic and transport properties of kinked graphene.

Local curvature, or bending, of a graphene sheet is known to increase the chemical reactivity presenting an opportunity for templated chemical functionalisation. Using first-principles calculations based on density functional theory (DFT), we investigate the reaction barrier reduction for the adsorption of atomic hydrogen at linear bends in graphene. We find a significant barrier lowering (≈15%) for realistic radii of curvature (≈20 Å) and that adsorption along the linear bend leads to a stable linear kink. We compute the electronic transport properties of individual and multiple kink lines, and demonstrate how these act as efficient barriers for electron transport. In particular, two parallel kink lines form a graphene pseudo-nanoribbon structure with a semimetallic/semiconducting electronic structure closely related to the corresponding isolated ribbons; the ribbon band gap translates into a transport gap for electronic transport across the kink lines. We finally consider pseudo-ribbon-based heterostructures and propose that such structures present a novel approach for band gap engineering in nanostructured graphene.

Mechanism of three kink effects in irradiated partially-depleted SOINMOSFET's

The variations in ID-VD characteristic of 0.8 μm SOINMOS transistors are studied, which are exposed to 60Co γ ray at a dose rate of 50 rad (Si)/s. The results show that the linear kink effects of these samples at each dose level ane not presente due to the optimizations of manufacture process and layout design. The drain voltage that corresponds to the impact ionization induced kink effect, increases, with dose level. An anomalous "Kink" effect in the back gate ID-VSUB characteristics of the partially depleted SOINMOS transistors is observed at a high dose level, which is attributed to interface trap states generated at the buried oxide/silicon film interface during irradiation.

A Tunnel Diode Body Contact Structure for High-Performance SOI MOSFETs

A tunnel diode body contact (TDBC) silicon-on-insulator (SOI) MOSFET structure without floating-body effects (FBEs) is proposed and successfully demonstrated. The key idea of the proposed structure is that a tunnel diode is embedded in the source region, so that the accumulated carriers can be released through tunneling. In an n-MOSFET, a heavily doped p+ layer is introduced beneath the n+ source region. The simulated and measured results show the suppressed FBE, as expected. Other phenomena that originate from the FBEs, such as the kink, linear kink effect, abnormal subthreshold swing, and small drain-tosource breakdown voltage in the properties, were also sufficiently suppressed. In addition, it should be noted that the proposed SOI MOSFETs are fully laid out and process compatible with SOI CMOS. Hysteresis effects disappear in TDBC SOI MOSFETs, which makes them attractive for digital applications. On the other hand, in analog applications, TDBC SOI MOSFETs are shown to hold the advantage over floating-body SOI MOSFETs due to their higher Gm/ID ratio. TDBC SOI MOSFETs can be considered as one of the promising candidates for digital and analog devices.

The Flare-Energy Distributions Generated by Kink-Unstable Ensembles of Zero-Net-Current Coronal Loops

It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabilities is captured by an instability threshold for linear kink modes. Each point on the threshold is associated with a unique energy release and so we can predict a distribution of nanoflare energies. When the linear instability threshold is crossed, the instability enters a nonlinear phase as it is driven by current sheet reconnection. As the ensuing flare erupts and declines, the field transitions to a lower energy state, which is modelled by relaxation theory, i.e., helicity is conserved and the ratio of current to field becomes invariant within the loop. We apply the model so that all the loops within an ensemble achieve instability followed by energy-releasing relaxation. The result is a nanoflare energy distribution. Furthermore, we produce different distributions by varying the loop aspect ratio, the nature of the path to instability taken by each loop and also the level of radial expansion that may accompany loop relaxation. The heating rate obtained is just sufficient for coronal heating. In addition, we also show that kink instability cannot be associated with a critical magnetic twist value for every point along the instability threshold.