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.

Impact of different interaction behavior on epidemic spreading in time-dependent social networks

We investigate the impact of pairwise and group interactions on the spread of epidemics through an activity-driven model based on time-dependent networks.The effects of pairwise/group interaction proportion and pairwise/group interaction intensity are explored by extensive simulation and theoretical analysis.It is demonstrated that altering the group interaction proportion can either hinder or enhance the spread of epidemics,depending on the relative social intensity of group and pairwise interactions.As the group interaction proportion decreases,the impact of reducing group social intensity diminishes.The ratio of group and pairwise social intensity can affect the effect of group interaction proportion on the scale of infection.A weak heterogeneous activity distribution can raise the epidemic threshold,and reduce the scale of infection.These results benefit the design of epidemic control strategy.

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.

A process-oriented approach for identifying potential landslides considering time-dependent behaviors beyond geomorphological features

Geomorphological features are commonly used to identify potential landslides.Nevertheless,overemphasis on these features could lead to misjudgment.This research proposes a process-oriented approach for potential landslide identification that considers time-dependent behaviors.The method integrates comprehensive remote sensing and geological analysis to qualitatively assess slope stability,and employs numerical analysis to quantitatively calculate aging stability.Specifically,a time-dependent stability calculation method for anticlinal slopes is developed and implemented in discrete element software,incorporating time-dependent mechanical and strength reduction calculations.By considering the time-dependent evolution of slopes,this method highlights the importance of both geomorphological features and time-dependent behaviors in landslide identification.This method has been applied to the Jiarishan slope(JRS)on the Qinghai-Tibet Plateau as a case study.The results show that the JRS,despite having landslide geomorphology,is a stable slope,highlighting the risk of misjudgment when relying solely on geomorphological features.This work provides insights into the geomorphological characterization and evolution history of the JRS and offers valuable guidance for studying slopes with similar landslide geomorphology.Furthermore,the process-oriented method incorporating timedependent evolution provides a means to evaluate potential landslides,reducing misjudgment due to excessive reliance on geomorphological features.

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 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.

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.

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.

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.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

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.

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.

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.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Time-dependent magnetometric resistivity anomalies of groundwater contamination: Synthetic results from computational hydro-geophysical modeling

We present a forward-modeling investigation of time-dependent ground magnetometric resistivity （MMR） anomalies associated with transient leachate transport in groundwater systems. Numerical geo-electrical models are constructed based on the hydrological simulation results of leachate plumes from a highly conceptualized landfill system and the resultant MMR responses are computed using a modified finite difference software MMR2DFD. Three transmitter configurations （i.e., single source, MMR-TE, and MMR-TM modes） and two hydrological models （i.e., uniform and faulted porous media） are considered. Our forward modeling results for the uniform porous medium indicates that the magnetic field components perpendicular to the dominant current flow contain the most information of the underground targets and the MMR-TE mode is an appropriate configuration for detecting contaminant plumes. The modeling experiments for the faulted porous medium also confirm that the MMR method is capable of mapping and monitoring the extent of contaminant plumes in aroundwater systems.

Ionospheric perturbations before Pu’er earthquake observed on DEMETER

A destructive shock with magnitude of 6.3 occurred on 2 June 2007 at 21h34min56s UT in Pu’er region (23.0°N, 101.1°E), Yunnan Province, China. The data from DEMETER satellite during the period from 23 May to 2 June, i.e., ten days before the earthquake and one day just on the day of earthquake occurrence, were analyzed. Among the 284 orbits of DEMETER during the period, 29 orbits with the trace passing through the region within 1 888 km from the epicenter were selected to be studied. Seven anomalous events were found on the dataset of the seven orbits among the 29 ones. There existed synchronous perturbations on the variations of the spectrogram of the electric field and the variations of the density and temperature of the ions and electron, in contrast with the variations of its surround- ing area. And five events appeared in the space within 1 888 km from the epicenter while the other two were out of the studied area. Electrostatic turbulences were also recorded with the synchronous perturbations with that in the electron density and ions density in plasma in the region near the epicenter in the five events, which seems to sug- gest that there be some physical relation between these events and the preparation processes of Pu’er earthquake.

Frequency characteristics and far-field effect of gravity perturbation before earthquake

We used high-pass filtering and the Fourier transform to analyze tidal gravity data prior to five earthquakes from four superconducting gravity stations around the world. A stable gravitational perturbation signal is received within a few days before the earthquakes. The gravitational perturbation signal before the Wenchuan earthquake on May 12, 2008 has main frequency of 0.1–0.3 Hz, and the other four have frequency bands of 0.12-0.17 Hz and 0.06-0.085 Hz. For earthquakes in continental and oceanic plate fault zones, gravity anomalies often appear on the superconducting gravimeters away from the epicenter, whereas the stations near the epicenter record small or no anomalies. The results suggest that this kind of gravitational perturbation signals correlate with earthquake occurrence, making them potentially useful earthquake predictors. The far-field effect of the gravitational perturbation signals may reveal the interaction mechanisms of the Earth’s tectonic plates. However, owing to the uneven distribution of gravity tide stations, the results need to be further confirmed in the future.

Perturbation Theory for Dual Cosine Function（Ⅱ）—Time－dependent Perturbation in the Sun－reflexive Case

In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.

PERTURBATION SOLUTION FOR COMPARTMENT MODEL OF VARIABLE EXTRACELLULAR VOLUME

The two compartment model with variable extracellular volume is presented and solved by using both perturbation and analytical method. The computation for both creatinine and urea show that the perturbation solution is not only simple but also accurate enough and is a good substitute for the more exact analytical solution.