Alternative Methods of Regular and Singular Perturbation Problems

Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse fields of applied mathematics and engineering. This research paper provides a comprehensive overview of algebraic methods for solving perturbation problems, featuring a comparative analysis of their strengths and limitations. Serving as a valuable resource for researchers and practitioners, it offers insights and guidance for tackling perturbation problems in various disciplines, facilitating the advancement of applied mathematics and engineering.

A proteomic landscape of pharmacologic perturbations for functional relevance

Pharmacological perturbation studies based on protein-level signatures are fundamental for drug discovery. In the present study, we used a mass spectrometry (MS)-based proteomic platform to profile the whole proteome of the breast cancer MCF7 cell line under stress induced by 78 bioactive compounds. The integrated analysis of perturbed signal abundance revealed the connectivity between phenotypic behaviors and molecular features in cancer cells. Our data showed functional relevance in exploring the novel pharmacological activity of phenolic xanthohumol, as well as the noncanonical targets of clinically approved tamoxifen, lovastatin, and their derivatives. Furthermore, the rational design of synergistic inhibition using a combination of histone methyltransferase and topoisomerase was identified based on their complementary drug fingerprints. This study provides rich resources for the proteomic landscape of drug responses for precision therapeutic medicine.

A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

Investigation on the roles of equilibrium toroidal rotation during edge-localized mode mitigated by resonant magnetic perturbations

The effects of equilibrium toroidal rotation during edge-localized mode(ELM)mitigated by resonant magnetic perturbation(RMP)are studied with the experimental equilibria of the EAST tokamak based on the four-field model in the BOUT++code.As the two main parameters to determine the toroidal rotation profiles,the rotation shear and magnitudes were separately scanned to investigate their roles in the impact of RMPs on peeling-ballooning(P-B)modes.On one hand,the results show that strong toroidal rotation shear is favorable for the enhancement of the self-generated E×B shearing rate<ω_(E×B)>with RMPs,leading to significant ELM mitigation with RMP in the stronger toroidal rotation shear region.On the other hand,toroidal rotation magnitudes may affect ELM mitigation by changing the penetration of the RMPs,more precisely the resonant components.RMPs can lead to a reduction in the pedestal energy loss by enhancing the multimode coupling in the turbulence transport phase.The shielding effects on RMPs increase with the toroidal rotation magnitude,leading to the enhancement of the multimode coupling with RMPs to be significantly weakened.Hence,the reduction in pedestal energy loss by RMPs decreased with the rotation magnitude.In brief,the results show that toroidal rotation plays a dual role in ELM mitigation with RMP by changing the shielding effects of plasma by rotation magnitude and affecting<ω_(E×B)>by rotation shear.In the high toroidal rotation region,toroidal rotation shear is usually strong and hence plays a dominant role in the influence of RMP on P-B modes,whereas in the low rotation region,toroidal rotation shear is weak and has negligible impact on P-B modes,and the rotation magnitude plays a dominant role in the influence of RMPs on the P-B modes by changing the field penetration.Therefore,the dual role of toroidal rotation leads to stronger ELM mitigation with RMP,which may be achieved both in the low toroidal rotation region and the relatively high rotation region that has strong rotational shear.

An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Research on perturbation of neutron fluence rate in a closed thermal neutron field due to medium materials

The neutron radiation field has vital applications in areas such as biomedicine,geology,radiation safety,and many others for neutron detection and neutron metrology.Correcting neutron fluence rate perturbation accurately is an important yet challenging problem.This study proposes a correction method that analyzes three physical processes.This method,which transforms the detection process from point detection to area detection,is based on a novel physical model and has been validated through theoretical analyses,experiments,and simulations.According to the average differences between the calculated and experimental results,the new method(1.67%)demonstrated better accuracy than the traditional simulation(2.17%).In a closed thermal neutron radiation field,the detector or strong neutron absorption material significantly perturbs the neutron fluence rate,whereas its impact on the energy spectrum shape and neutron directionality is relatively minor.Furthermore,based on the calculation results of the perturbation rate formula for medium materials with different compositions and sizes,the larger the volume and capture cross section of the medium,the higher the perturbation rate generated in the closed radiation field.

Generalized nth-Order Perturbation Method Based on Loop Subdivision Surface Boundary Element Method for Three-Dimensional Broadband Structural Acoustic Uncertainty Analysis

In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.

Growth of ablative Rayleigh-Taylor instability induced by time-varying heat-flux perturbation

The evolution of ablative Rayleigh–Taylor instability(ARTI)induced by single-mode stationary and time-varying perturbations in heat flux is studied numerically in two dimensions.Compared with the stationary case,time-varying heat-flux perturbation mitigates ARTI growth because of the enhanced thermal smoothing induced by the wave-like traveling heat flux.A resonance is found to form when the phase velocity of the heat-flux perturbation matches the average sound speed in the ablation region.In the resonant regime,the coherent density and temperature fluctuations enhance the electron thermal conduction in the ablation region and lead to larger ablation pressure and effective acceleration,which consequently yield higher linear growth rate and saturated bubble velocity.The enhanced effective acceleration offers increased implosion velocity but can also compromise the integrity of inertial confinement fusion shells by causing faster ARTI growth.

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

Volcanically Driven Terrestrial Environmental Perturbations during the Carnian Pluvial Episode in the Eastern Tethys

The Carnian Pluvial Episode(CPE)fingerprints global environmental perturbations and biological extinction on land and oceans and is potentially linked to the Wrangellia Large Igneous Province(LIP).However,the correlation between terrestrial environmental changes and Wrangellia volcanism in the Ordos Basin during the CPE remains poorly understood.Records of negative carbon isotopic excursions(NCIEs),mercury(Hg),Hg/TOC,and Hg enrichment factor(HgEF)from oil shales in a large-scale terrestrial Ordos Basin in the Eastern Tethys were correlated with marine and other terrestrial successions.The three significant NCIEs in the study section were consistently correlated with those in the CPE successions of Europe,the UK,and South and North China.The U-Pb geochronology indicates a Ladinian-Carnian age for the Chang 7 Member.A comprehensive overview of the geochronology,NCIE correlation,and previous bio-and chronostratigraphic frameworks shows that the Ladinian-Carnian boundary is located in the lower part of Chang 7 in the Yishicun section.HgEF may be a more reliable proxy for tracing volcanic eruptions than the Hg/TOC ratio because the accumulation rates of TOC content largely vary in terrestrial and marine successions.The records of Hg,Hg/TOC,HgEF,and NCIEs in the Ordos Basin aligned with Carnian successions worldwide and were marked by similar anomalies,indicating a global response to the Wrangellia LIP during the CPE.Anoxia,a warm-humid climate,enhancement of detrital input,and NCIEs are synchronous with the CPE interval in the Ordos Basin,which suggests that the CPE combined with the regional Qinling Orogeny should dominate the enhanced rate of terrigenous input and paleoenvironmental evolution in the Ordos Basin.

Growth and Interactions of Multi-Source Perturbations in Convection-Allowing Ensemble Forecasts

This study investigated the growth of forecast errors stemming from initial conditions(ICs),lateral boundary conditions(LBCs),and model(MO)perturbations,as well as their interactions,by conducting seven 36 h convectionallowing ensemble forecast(CAEF)experiments.Two cases,one with strong-forcing(SF)and the other with weak-forcing(WF),occurred over the Yangtze-Huai River basin(YHRB)in East China,were selected to examine the sources of uncertainties associated with perturbation growth under varying forcing backgrounds and the influence of these backgrounds on growth.The perturbations exhibited distinct characteristics in terms of temporal evolution,spatial propagation,and vertical distribution under different forcing backgrounds,indicating a dependence between perturbation growth and forcing background.A comparison of the perturbation growth in different precipitation areas revealed that IC and LBC perturbations were significantly influenced by the location of precipitation in the SF case,while MO perturbations were more responsive to convection triggering and dominated in the WF case.The vertical distribution of perturbations showed that the sources of uncertainties and the performance of perturbations varied between SF and WF cases,with LBC perturbations displaying notable case dependence.Furthermore,the interactions between perturbations were considered by exploring the added values of different source perturbations.For the SF case,the added values of IC,LBC,and MO perturbations were reflected in different forecast periods and different source uncertainties,suggesting that the combination of multi-source perturbations can yield positive interactions.In the WF case,MO perturbations provided a more accurate estimation of uncertainties downstream of the Dabie Mountain and need to be prioritized in the research on perturbation development.

Ultra-high spectral purity laser derived from weak external distributed perturbation

Ultra-high spectral purity lasers are of considerable research interests in numerous fields such as coherent optical communication,microwave photonics,distributed optical fiber sensing,gravitational wave detection,optical clock,and so on.Herein,to deeply purify laser spectrum with compact size under normal condition,we propose a novel and practical idea to effectively suppress the spontaneous radiation of the laser cavity through weak external distributed perturbation.Subsequently,a laser configuration consisting of a main lasing cavity and an external distributed feedback cavity is proposed.The feedback signal with continuous spatio-temporal phase transition controlled by a distributed feedback structure is injected into the main cavity,which can deeply suppress the coupling rate from the spontaneous radiation to the stimulated emission and extremely purify the laser spectrum.Eventually,an ultra-narrow linewidth on-chip laser system with a side mode suppression ratio greater than 80 dB,an output linewidth of 10 Hz,and a relative intensity noise less than-150 dB/Hz is successfully obtained under normal conditions.The proposed concept in this work provides a new perspective for extreme regulation of laser parameters by using weak external distributed perturbation,which can be valid for various gain-type lasers with wide wavelength bands.

Suppression of Plasma Bubbles over South America under Weak Geomagnetic Perturbations

During a long-term Equatorial Plasma Bubbles(EPBs)occurrence between October 2020 and March 2021,a significant EPB suppression event was identified on November 22 and the observations from multi-instrument have been utilized to investigate this event.Global-scale Observations of the Limb and Disk(GOLD)satellite observed prominent EPBs between 23:40 UT and 23:55 UT during the long-term occurrence days.However,no dark stripes representing EPBs were observed on November 22,and the Equatorial Ionization Anomaly(EIA)structure remained intact.The Total Electron Content(TEC)maps show that these EPBs appeared in the region between 35°W and 65°W longitudes and the magnitudes of the TEC loss in EPBs regions were about 20 TECU.Except for 22 November,the S4 index was consistently greater than 0.6 throughout November,indicating significant ionospheric scintillation.The Rate Of TEC Index(ROTI)maps revealed that the spatial extent and intensity of EPBs increased after their suppression,and the EPBs were locally generated.The swarm electron density measurements indicated that the variation amplitudes of EPBs at 510 km altitude were approximately 3 to 5 times larger than that at 460 km altitude.The impact region of EPBs at 510 km was between 15°S and 20°N latitudes,while at 460 km,it was between 0°and 17°N latitudes.During the period of EPB suppression,the average h’f at three ionosonde stations decreased by about 50 km,and the vertical drift velocity(V z)approached~0 m/s while it was more than 20 m/s during the long-term occurrence.

Observation of the poloidally asymmetrical density perturbation of sawtooth collapse on J-TEXT

The detailed density perturbations provided by the advanced polarimeter-interferometer system(Polaris) during sawtooth collapse on the Joint Texas Experimental Tokamak(J-TEXT) are reported in this article.During a sawtooth collapse and the crash of plasma pressure at the center,it is found that the increase in density in the region between the inversion radius and mixing radius is poloidally asymmetrical,while the increase in temperature is poloidally symmetrical.The poloidal location where the density increases is dependent on the phase of the precursory m/n=1/1 kink mode.It is always out of phase with the hot core of the m/n=1/1 mode.The behaviors of density perturbations during sawtooth collapse observed in J-TEXT are beyond the expectations of the standard model,and this can shed new light on the understanding of sawtooth collapse.

Fully relativistic many-body perturbation energies,transition properties,and lifetimes of lithium-like iron Fe XXIV

Employing the advanced relativistic configuration interaction(RCI)combined with the many-body perturbation theory(RMBPT)method,we report energies and lifetime values for the lowest 35 energy levels from the(1s^(2))nl configurations(where the principal quantum number n=2–6 and the angular quantum number l=0,...,n-1)of lithium-like iron Fe XXIV,as well as complete data on the transition wavelengths,radiative rates,absorption oscillator strengths,and line strengths between the levels.Both the allowed(E1)and forbidden(magnetic dipole M1,magnetic quadrupole M2,and electric quadrupole E2)ones are reported.Through detailed comparisons with previous results,we assess the overall accuracies of present RMBPT results to be likely the most precise ones to date.Configuration interaction effects are found to be very important for the energies and radiative properties for the ion.The present RMBPT results are valuable for spectral line identification,plasma modeling,and diagnosing.

The Influence of Arctic Sea Ice Concentration Perturbations on Subseasonal Predictions of North Atlantic Oscillation Events

The influence of Arctic sea ice concentration (SIC) on the subseasonal prediction of the North Atlantic Oscillation (NAO) event is investigated by utilizing the Community Atmospheric Model version 4. The optimal Arctic SIC perturbations which exert the greatest influence on the onset of an NAO event from a lead of three pentads (15 days) are obtained with a conditional nonlinear optimal perturbation approach. Numerical results show that there are two types of optimal Arctic SIC perturbations for each NAO event, with one weakening event (marked as type-1) and another strengthening event (marked as type-2). For positive NAO events, type-1 optimal SIC perturbations mainly show positive SIC anomalies in the Greenland, Barents, and Okhotsk Seas, while type-2 perturbations mainly feature negative SIC anomalies in these regions. For negative NAO events, the optimal SIC perturbations have almost opposite patterns to those in positive events, although there are some differences among these SIC perturbations due to different atmospheric initial conditions. Further diagnosis reveals that the optimal Arctic SIC perturbations first modify the surface turbulent heat flux and the temperature in the lower troposphere via diabatic processes. Afterward, the temperature in the low troposphere is mainly affected by dynamic advection. Finally, potential vorticity advection plays a crucial role in the 500-hPa geopotential height prediction in the northern North Atlantic sector during pentad 4, which influences NAO event prediction. These results highlight the importance of Arctic SIC on NAO event prediction and the spatial characteristics of the SIC perturbations may provide scientific support for target observations of SIC in improving NAO subseasonal predictions.

Revealing the potential of apparent critical current density of Li/garnet interface with capacity perturbation strategy

Apparent critical current density(j_(Ac)^(a))of garnet all-solid-state lithium metal symmetric cells(ASSLSCs)is a fundamental parameter for designing all-solid-state lithium metal batteries.Nevertheless,how much the possible maximum apparent current density that a given ASSLSC system can endure and how to reveal this potential still require study.Herein,a capacity perturbation strategy aiming to better measure the possible maximum j_(Ac)^(a)is proposed for the first time.With garnet-based plane-surface structure ASSLSCs as an exemplification,the j_(Ac)^(a)is quite small when the capacity is dramatically large.Under a perturbed capacity of 0.001 mA h cm^(-2),the j_(Ac)^(a)is determined to be as high as 2.35 mA cm^(-2)at room temperature.This investigation demonstrates that the capacity perturbation strategy is a feasible strategy for measuring the possible maximum j_(Ac)^(a)of Li/solid electrolyte interface,and hopefully provides good references to explore the critical current density of other types of electrochemical systems.

Hybrid Approach for Privacy Enhancement in Data Mining Using Arbitrariness and Perturbation

Imagine numerous clients,each with personal data;individual inputs are severely corrupt,and a server only concerns the collective,statistically essential facets of this data.In several data mining methods,privacy has become highly critical.As a result,various privacy-preserving data analysis technologies have emerged.Hence,we use the randomization process to reconstruct composite data attributes accurately.Also,we use privacy measures to estimate how much deception is required to guarantee privacy.There are several viable privacy protections;however,determining which one is the best is still a work in progress.This paper discusses the difficulty of measuring privacy while also offering numerous random sampling procedures and statistical and categorized data results.Further-more,this paper investigates the use of arbitrary nature with perturbations in privacy preservation.According to the research,arbitrary objects(most notably random matrices)have"predicted"frequency patterns.It shows how to recover crucial information from a sample damaged by a random number using an arbi-trary lattice spectral selection strategy.Thisfiltration system's conceptual frame-work posits,and extensive practicalfindings indicate that sparse data distortions preserve relatively modest privacy protection in various situations.As a result,the research framework is efficient and effective in maintaining data privacy and security.

Design of new resonant magnetic perturbation coils on the J-TEXT tokamak

The resonant magnetic perturbation(RMP)system is a powerful auxiliary system on tokamaks.On the J-TEXT tokamak,a set of new in-vessel coils is designed to enhance the amplitude of the RMP.The new coils are designed to be two-turn saddle coils.These two-turn saddle coils have been optimized in terms of their structure,support,and protection components to overcome the limitations of the narrow in-vessel space,resulting in a compact coil module that can be accommodated in the vessel.To verify the feasibility of this design,an electromagnetic simulation is performed to investigate the electrical parameters and the generated field of the coils.A multi-field coupled simulation is performed to investigate the capacity of heat dissipation.As a result of these efforts,the new RMP coils have been successfully installed on the J-TEXT tokamak.It has significantly enhanced the RMP amplitude and been widely applied in experiments.