Perturbation Strength Research Articles

On the evolution of a magnetic flux rope: Two‐dimensional MHD simulation results

AbstractWe use the time‐dependent, two‐dimensional (2‐D), ideal MHD equations to simulate and investigate the evolution of magnetic field and plasma profiles of the typical (T) and crater (C) magnetic flux ropes (FRs). The T‐FR has a magnetic pressure peak at the center of the flux rope, while the C‐FR has a local dip instead. The simulation starts with a 2‐D magnetic flux rope in magnetohydrostatic equilibrium, where pressure gradient forces are balanced by Lorentz forces. The magnetic field and plasma pressure profiles for the initial flux rope are derived from the analytical solutions by Zhang et al. (2010). The initial flux rope starts to evolve when the force balance is broken by imposing pressure or magnetic field perturbations onto the equilibrium system. The pressure perturbations are produced by increasing/decreasing the internal plasma pressure of the flux rope, while the magnetic field perturbations are produced by increasing/decreasing the transverse magnetic fields across the flux rope. We conclude that a T‐FR can be evolved into a C‐FR and vice versa, if the perturbation strength is sufficient, and that the plasma pressure and density in the new equilibrium state could be either increased or decreased for the evolution of C‐FR to T‐FR and also for the evolution of T‐FR to C‐FR.

Multifractality of quantum wave functions in the presence of perturbations.

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model, and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong-enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.

Rayleigh-type parametric chemical oscillation.

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

Self-adaptive perturbation and multi-neighborhood search for iterated local search on the permutation flow shop problem

The flow shop scheduling problem minimizing total flow time is a famous combinatorial optimization problem. Among the many algorithms proposed to solve this problem, iterated local search (ILS) is a simple, effective and efficient one. Research shows that the perturbation method and neighborhood structure play key roles in the performance of ILS. However, existing ILS lacks the self-adaptive ability to adjust the degree of perturbation relative to the search status. Also, only one basic insertion neighborhood is often used, greatly limiting the size of the search space and the ability to escape from a local optimum. In this work, a self-adaptive strategy is proposed, evaluating the neighborhoods around the local optimum and adjusting the perturbation strength according to this evaluation. If neighboring solutions are found to be considerably worse than the best known solution, indicating that it may be hard to escape from the local optimum, then the perturbation strength is amplified. Additionally, a swap neighborhood is incorporated with an insertion neighborhood to form a new version of multi-neighborhood search. Experimental results on benchmark instances show that the self-adaptive search performs significantly better than three state of the art algorithms, particularly when tested with extended CPU time. The multi-neighborhood search performs even better, also outperforming two state of the art variable neighborhood search algorithms, indicating that the hybrid use of insertion and swap neighborhoods is effective for the discussed problem.

An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances.

Nonlinear magnetohydrodynamics of edge localized mode precursors

A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ωpre∼x1/3ξ̂ψ,in2/3n, with x position in radial direction, ξ̂ψ,in strength of initial perturbation, and n toroidal mode number.

Resilience of Human Mobility Under the Influence of Typhoons

Climate change has intensified tropical cyclones, resulting in several recent catastrophic hurricanes and typhoons. Such disasters impose threats on populous coastal urban areas, and therefore, understanding and predicting human movements plays a critical role in evaluating vulnerability and resilience of human society and developing plans for disaster evacuation, response and relief. Despite its critical role, limited research has focused on tropical cyclones and their influence on human mobility. Here, we studied how severe tropical storms could influence human mobility patterns in coastal urban populations using individuals’ movement data collected from Twitter. We selected 5 significant tropical storms and examined their influences on 8 urban areas. We analyzed the human movement data before, during, and after each event, comparing the perturbed movement data to movement data from steady states. We also used different statistical analysis approaches to quantify the strength and duration of human mobility perturbation. The results suggest that tropical cyclones can significantly perturb human movements, and human mobility experienced different magnitudes in different cases. We also found that power-law still governed human movements in spite of the perturbations. The findings from this study will deepen our understanding about the interaction between urban dwellers and civil infrastructure, improve our ability to predict human movements during natural disasters, and help policymakers to improve disaster evacuation, response and relief plans.

Validity of the Rytov Approximation in the Form of Finite-Frequency Sensitivity Kernels

The first-order (or linear) Rytov or Born approximation is the foundation for formulation of wave-equation tomography and waveform inversion, so the validity of the Rytov/Born approximation can substantially affect the applicability of these theories. However, discussions and research reported in literature on this topic are insufficient or limited. In this paper we introduce five variables in scattering theory to help us discuss conditions under which the Rytov approximation, in the form of the finite frequency sensitivity kernels (RFFSK), the basis of waveform inversion and tomography, is valid. The five variables are propagation length L, heterogeneity scale a, wavenumber k, anisotropy ratio ξ, and perturbation strength ɛ. Combined with theoretical analysis and numerical experiments, we conclude that varying the conditions used to establish the Rytov approximation can lead to uninterpretable or undesired results. This conclusion has two consequences. First, one cannot rigorously apply the linear Rytov approximation to all theoretical or practical cases without discussing its validity. Second, the nonlinear Rytov approximation is essential if the linear Rytov approximation is not valid. Different from previous literature, only phase (or travel time) terms for the whole wavefield are discussed. The time shifts of two specific events between the background and observed wavefields measured by cross-correlation will serve as a reference for evaluation of whether the time shifts predicted by the FFSKs are reasonably acceptable. Significantly, the reference “cross-correlation” should be regarded as reliable only if the condition “two specific similar signals” is satisfied. We cannot expect it to provide a reasonable result if this condition is not met. This paper reports its reliability and experimental limitations. Using cross-correlation (CC) samples as the X axis and sensitivity kernel (SK) or ray tracing (RT) samples as the Y axis, a chart of cross validation among the three is established. According to experimental analysis for a random and deterministic medium, the RFFSK works well for diffraction and geometric optics enclosed by the boundaries ka > 1 and (Λ 1, Φ < 2π), where Λ is a diffraction variable and Φ is a variable used to measure scattering strength. Both Λ and Φ depend on the five variables mentioned above. However, a large perturbation will limit the applicability of the Rytov approximation and narrow the range in which it is valid, because larger ɛ results in higher-amplitude fluctuations and larger back-scattering. Therefore, large ɛ is important in making SK/RT predictions discrepant from correct CC measurements. We also confirm that the RFFSK theory has wider range of application than ray theory. All the experiments point out the importance, both practical and theoretical, of respecting the conditions used to establish the Rytov approximation.

PTspectroscopy of the Rabi problem

We investigate the effects of a time-periodic, non-hermitian, PT-symmetric perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We demonstrate that when the perturbation frequency is close to one of the system resonances, even a vanishingly small perturbation leads to PT symmetry breaking. We also find a restored PT-symmetric phase at high frequencies, and at moderate perturbation strengths, we find multiple frequency windows where PT-symmetry is broken and restored. Our results imply that the PT-symmetric Rabi problem shows surprisingly rich phenomena absent in its hermitian or static counterparts.

Cumulants of time-integrated observables of closed quantum systems andPTsymmetry with an application to the quantum Ising chain

We study the connection between the cumulants of a time-integrated observable of a quantum system and the PT-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken PT-symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetisation in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where PT-symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of PT -symmetry implies that all cumulants are sub-linear in time, a behaviour usually associated to the absence of decorrelation.

Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator

This study is devoted to analysis of semi-implicit compact finite difference (SICFD) methods for the nonlinear Schrödinger equation (NLS) perturbed by the wave operator (NLSW) with a perturbation strength described by a dimensionless parameter ε∈(0,1]. Uniform l∞-norm error bounds of the proposed SICFD schemes are built to give immediate insight on point-wise error occurring as time increases, and the explicit dependence of the mesh size and time step on the parameter ε is also figured out. In the small ε regime, highly oscillations arise in time with O(ε2)-wavelength. This highly oscillatory nature in time as well as the difficulty raised by the compact FD discretization make establishing the l∞-norm error bounds uniformly in ε of the SICFD methods for NLSW to be a very interesting and challenging issue. The uniform l∞-norm error bounds in ε are proved to be of O(h4+τ) and O(h4+τ2/3) with time step τ and mesh size h for well-prepared and ill-prepared initial data. Finally, numerical results are reported to verify the error estimates and show the sharpness of the convergence rates in the respectively parameter regimes.

Fast ion confinement in the three-dimensional helical reversed-field pinch

Fast ions are well confined in the stochastic magnetic field of the multiple-helicity (MH) reversed-field pinch (RFP), with fast ion confinement times routinely a factor of 5 to 10 higher than thermal confinement time. Recent experiments have examined the behavior and confinement of beam-born fast ions in the three-dimensional (3D) helical RFP state. In lower current discharges, where the onset of the helical state is uncertain, high power neutral beam injection (NBI) tends to suppress the transition to the single helicity mode. In high current discharges (Ip ∼ 0.5 MA), where the onset of n = 5 single helicity is quite robust, a short blip of NBI is used to probe the confinement of fast ions with minimal perturbation to the 3D equilibrium. The fast ion confinement time is measured to be substantially lower than fast ions in comparable MH RFP states, and there is a strong dependence on the strength of the helical perturbation. The established helical equilibrium is stationary in the laboratory frame but the locking occurs over the entire range of possible phase with respect to the Madison Symmetric Torus vessel. This effectively scans both the location of the NBI with respect to the helical structure and the pitch of the NBI-born fast ions. Fast ion confinement is observed to be insensitive to this angle, and in fact counter-NB injection into quasi-single helicity discharges shows fast ion confinement times similar to co-injection cases, in contrast to the MH RFP, where counter-injected fast ion confinement time is substantially lower.

Metastable States When the Fermi Golden Rule Constant Vanishes

Resonances appearing by perturbation of embedded non-degenerate eigenvalues are studied in the case when the Fermi Golden Rule constant vanishes. Under appropriate smoothness properties for the resolvent of the unperturbed Hamiltonian, it is proved that the first order Rayleigh-Schr\"odinger expansion exists. The corresponding metastable states are constructed using this truncated expansion. We show that their exponential decay law has both the decay rate and the error term of order $\varepsilon^4$, where $\varepsilon$ is the perturbation strength.

Effect of chaos on plasma filament dynamics and turbulence in the scrape-off layer

Naturally occurring error fields as well as resonant magnetic perturbations applied for stability control are known to cause magnetic field-line chaos in the scrape-off layer (SOL) region of tokamaks. Here, 2D simulations with the BOUT++ simulation framework are used to investigate the effect of the field-line chaos on the SOL and in particular on its width and peak particle flux. The chaos enters the SOL dynamics only through the connection length, which is evaluated using a Poincaré map. The variation of experimentally relevant quantities, such as the SOL gradient length scale and the intermittency of the particle flux in the SOL, is described as a function of the strength of the magnetic perturbation. It is found that the effect of the chaos is to broaden the profile of the sheath-loss coefficient, which is proportional to the inverse connection length. That is, the SOL transport in a chaotic field is equivalent to that in a model where the sheath-loss coefficient is replaced by its average over the unperturbed flux surfaces. The model does not include the effects of chaotic features other than the parallel connection length.

Modified heat load deposition of the ELM crash due to n = 2 perturbation fields at JET

Significant changes in the edge localized mode (ELM) crash heat load deposition patterns compared to typical ELMs are seen via infra-red observations during resonant magnetic perturbation experiments at the Joint European Torus (JET). These modifications result from the changed magnetic topology of the plasma, caused by the perturbations. Dependences on the perturbation strength and the edge safety factor are analysed and discussed. A thermoelectric current model shows that current filaments in the plasma edge could explain the observations. This study gives an insight into how the changed magnetic topology affects the peak heat fluxes of ELMs which is crucial for understanding ELM control.

Origin of the exponential decay of the Loschmidt echo in integrable systems.

We address the time decay of the Loschmidt echo, measuring the sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using a semiclassical analysis, we show that the Loschmidt echo may exhibit a well-pronounced regime of exponential decay, similar to the one typically observed in quantum systems whose dynamics is chaotic in the classical limit. We derive an explicit formula for the exponential decay rate in terms of the spectral properties of the unperturbed and perturbed Hamilton operators and the initial state. In particular, we show that the decay rate, unlike in the case of the chaotic dynamics, is directly proportional to the strength of the Hamiltonian perturbation. Finally, we compare our analytical predictions against the results of a numerical computation of the Loschmidt echo for a quantum particle moving inside a one-dimensional box with Dirichlet-Robin boundary conditions, and find the two in good agreement.

Counterterms in cosmological perturbation theory

Cosmological perturbation theory is the theory of fluctuations (scalar as well as tensor) around the inflationary cosmological background solution. It is important to understand the details of the process of renormalization in this theory. In more familiar applications of quantum field theory, the dependence on the external momenta of the dimensionally regulated expression of the one-loop contribution to a correlator determines the number of counterterms (and their forms) required to renormalize it. In this work, it is pointed out that in cosmological perturbation theory, though this still happens, it happens in a completely different way such that in the late time limit, the information about the number and forms of counterterms required gets erased. This is to be compared with what happens in spontaneous symmetry breaking where the use of fluctuation fields around a chosen vacuum seems to suggest that more counterterms are needed to renormalize the theory than are actually required. We also comment on how the field strength of curvature perturbation, $\ensuremath{\zeta}$, could get renormalized.

Quantifying, Comparing Human Mobility Perturbation during Hurricane Sandy, Typhoon Wipha, Typhoon Haiyan

Climate change has intensified tropical cyclones, resulting in several recent catastrophic hurricanes and typhoons. Such disasters impose threats on populous coastal urban areas, and therefore, understanding and predicting human movements plays a critical role in disaster evacuation, response and relief. Despite its critical roles, limited research has focused on tropical cyclones and their influence on human mobility. Here, we studied how severe tropical storms could influence human mobility patterns in coastal urban populations using individuals’ movement data collected from Twitter. We selected three significant tropical storms, including Hurricane Sandy, Typhoon Wipha, and Typhoon Haiyan. We analyzed the human movement data before, during, and after each event, comparing the perturbed movement data to movement data from steady states. We also used different statistical analysis approaches to quantify the strength and duration of human mobility perturbation. The results suggest that tropical cyclones can significantly perturb human movements by changing travel frequencies and displacement probability distributions; however, the nature-derived Lévy Walk model still predominantly governs human mobility. Also, human mobility exhibits a surprisingly mild and brief perturbation for Hurricane Sandy and Typhoon Wipha, while the duration of disturbance was much longer for Typhoon Haiyan. Our finding that the Lévy Walk model can still predict human mobility suggests that bio-inspired examinations of human mobility patterns may uncover solutions to improve disaster evacuation, response and relief plans.

Quantum simulations of localization effects with dipolar interactions

Quantum information processing often uses systems with dipolar interactions. Here a nuclear spin‐based quantum simulator is used to study the spreading of information in such a dipolar‐coupled system. While the information spreads with no apparent limits in the case of ideal dipolar couplings, additional perturbations limit the spreading, leading to localization. In previous work [Phys. Rev. Lett. 104, 230403 (2010)], it was found that the system size reaches a dynamic equilibrium that decreases with the square of the perturbation strength. This work examines the impact of a disordered Hamiltonian with dipolar interactions. It shows that the expansion of the cluster of spins freezes in the presence of large disorder, reminiscent of Anderson localization of non‐interacting waves in a disordered potential.

Compact Diplexer With High Isolation Using the Dual-Mode Substrate Integrated Waveguide Resonator

This letter presents a substrate integrated waveguide (SIW) diplexer using the dual-mode resonator. By enhancing the perturbation strength, the resonant frequencies of the dual-mode square cavity can be assigned to required frequencies. Thus, the cavity can be employed as the common resonator to replace the T-junction. The coupling aperture between the common resonator and the triangular resonator is parallel to one resonant mode's magnetic field and perpendicular to the other's. As a result, the isolation between the two channels is increased. Furthermore, the cavities are vertically stacked to realize a compact size. A diplexer with lower and upper channels centered at 8 and 9 GHz, respectively, is designed to verify the proposed concept. The simulated and measured results agree with each other.