Journal articles: 'Perturbation methods'

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Hinch, E. J., and Edward G. Harris. "Perturbation Methods." American Journal of Physics 60, no. 11 (1992): 1052–53. http://dx.doi.org/10.1119/1.16992.

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Heinrichs, Wilhelm. "Spectral methods for singular perturbation problems." Applications of Mathematics 39, no. 3 (1994): 161–88. http://dx.doi.org/10.21136/am.1994.134251.

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Cha, Philip D., and Austin Shin. "Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems." Shock and Vibration 2018 (October 17, 2018): 1–25. http://dx.doi.org/10.1155/2018/8609138.

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Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. They will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation method, the eigenvalue perturbation theory is used to formulate a first-order and a second-order approximation of the eigensolutions of symmetric and asymmetric systems. In the incremental perturbation method, the straightforward approach is extended to analyze systems with large perturbations using an iterative scheme. Finally, in the triple product method, the accuracy of the approximate eigenvalues is significantly improved by exploiting the orthogonality conditions of the perturbed eigenvectors. All three methods require only the eigensolutions of the nominal or unperturbed system, and in application, they involve simple matrix multiplications. Numerical experiments show that the proposed methods achieve accurate results for systems with and without damping and for systems with symmetric and asymmetric system matrices.

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Riley, N. "Perturbation methods, 1992." Journal of Fluids and Structures 6, no. 4 (1992): 523–24. http://dx.doi.org/10.1016/0889-9746(92)90029-3.

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Huang, Wei, Lei Zhang, Zizhou Wang, and Yan Wang. "GapMatch: Bridging Instance and Model Perturbations for Enhanced Semi-Supervised Medical Image Segmentation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 16 (2025): 17458–66. https://doi.org/10.1609/aaai.v39i16.33919.

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Medical image segmentation provides detailed understanding and aids in diagnosis, treatment planning, and monitoring of diseases. Due to the high cost of acquiring labeled data in the field of medical image analysis, semi-supervised segmentation methods have garnered increasing attention. Benefiting from their simplicity and effectiveness, consistency regularization-based methods have emerged as a significant research focus by utilizing perturbations. However, existing methods typically consider perturbation strategies from only a single perspective: either instance perturbation or model perturbation, thus ignoring the potential benefit of effectively combining both. In response, we propose a unified perturbation framework named GapMatch, which bridges instance and model perturbations to broaden the perturbation space and employs dual perturbation to impose consistency regularization on the model. Specifically, GapMatch involves using instance perturbation to update the decision boundary and model perturbation to further optimize it. These two steps mutually reinforce each other in an iterative manner, effectively pushing the decision boundary towards low-density regions while maximizing the class margin. Extensive experimental results on two popular medical image benchmarks demonstrate the effectiveness and generality of the proposed method.

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Duan, Jiale, Linyao Qiu, Guangjun He, Ling Zhao, Zhenshi Zhang, and Haifeng Li. "A Region-Adaptive Local Perturbation-Based Method for Generating Adversarial Examples in Synthetic Aperture Radar Object Detection." Remote Sensing 16, no. 6 (2024): 997. http://dx.doi.org/10.3390/rs16060997.

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In synthetic aperture radar (SAR) imaging, intelligent object detection methods are facing significant challenges in terms of model robustness and application security, which are posed by adversarial examples. The existing adversarial example generation methods for SAR object detection can be divided into two main types: global perturbation attacks and local perturbation attacks. Due to the dynamic changes and irregular spatial distribution of SAR coherent speckle backgrounds, the attack effectiveness of global perturbation attacks is significantly reduced by coherent speckle. In contrast, by focusing on the image objects, local perturbation attacks achieve targeted and effective advantages over global perturbations by minimizing interference from the SAR coherent speckle background. However, the adaptability of conventional local perturbations is limited because they employ a fixed size without considering the diverse sizes and shapes of SAR objects under various conditions. This paper presents a framework for region-adaptive local perturbations (RaLP) specifically designed for SAR object detection tasks. The framework consists of two modules. To address the issue of coherent speckle noise interference in SAR imagery, we develop a local perturbation generator (LPG) module. By filtering the original image, this module reduces the speckle features introduced during perturbation generation. It then superimposes adversarial perturbations in the form of local perturbations on areas of the object with weaker speckles, thereby reducing the mutual interference between coherent speckles and adversarial perturbation. To address the issue of insufficient adaptability in terms of the size variation in local adversarial perturbations, we propose an adaptive perturbation optimizer (APO) module. This optimizer adapts the size of the adversarial perturbations based on the size and shape of the object, effectively solving the problem of adaptive perturbation size and enhancing the universality of the attack. The experimental results show that RaLP reduces the detection accuracy of the YOLOv3 detector by 29.0%, 29.9%, and 32.3% on the SSDD, SAR-Ship, and AIR-SARShip datasets, respectively, and the model-to-model and dataset-to-dataset transferability of RaLP attacks are verified.

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Li, Mengyang, Fengguang Su, Ou Wu, and Ji Zhang. "Logit Perturbation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 2 (2022): 1359–66. http://dx.doi.org/10.1609/aaai.v36i2.20024.

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Features, logits, and labels are the three primary data when a sample passes through a deep neural network. Feature perturbation and label perturbation receive increasing attention in recent years. They have been proven to be useful in various deep learning approaches. For example, (adversarial) feature perturbation can improve the robustness or even generalization capability of learned models. However, limited studies have explicitly explored for the perturbation of logit vectors. This work discusses several existing methods related to logit perturbation. Based on a unified viewpoint between positive/negative data augmentation and loss variations incurred by logit perturbation, a new method is proposed to explicitly learn to perturb logits. A comparative analysis is conducted for the perturbations used in our and existing methods. Extensive experiments on benchmark image classification data sets and their long-tail versions indicated the competitive performance of our learning method. In addition, existing methods can be further improved by utilizing our method.

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Kuić, Domagoj, Alemka Knapp, and Diana Šaponja-Milutinović. "Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches." Universe 10, no. 10 (2024): 384. http://dx.doi.org/10.3390/universe10100384.

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We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric or perturbative methods. Using the formalism of FTPFT based on Wigner transforms (WTs) of projected functions, we show how to: (i) calculate the basic “bubble” diagram in the Loschmidt echo (LE) of a quenched chain to any order in the perturbation; and (ii) resum the generalized Schwinger–Dyson equation for the fermion two-point retarded functions in the “bubble” diagram, hence achieving the resummation of perturbative expansion of LE for a wide range of perturbation strengths under certain analyticity assumptions. Limitations of the assumptions and possible generalizations beyond it and also for other spin chains are further discussed.

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9

Murdock, James. "Book Review: Perturbation methods." Bulletin of the American Mathematical Society 28, no. 2 (1993): 418–22. http://dx.doi.org/10.1090/s0273-0979-1993-00378-1.

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Chacon, Monique Revoredo, and Michael C. Zerner. "Perturbation-variational methods revisited." International Journal of Quantum Chemistry 47, no. 2 (1993): 103–18. http://dx.doi.org/10.1002/qua.560470202.

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PANI, PAOLO. "ADVANCED METHODS IN BLACK-HOLE PERTURBATION THEORY." International Journal of Modern Physics A 28, no. 22n23 (2013): 1340018. http://dx.doi.org/10.1142/s0217751x13400186.

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Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in curved space–time. Current state-of-the-art techniques are pedagogically explained and exciting open problems are presented.

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Zhang, Hanbin, Min Chen, and Shuiyong Fan. "Study on the Construction of Initial Condition Perturbations for the Regional Ensemble Prediction System of North China." Atmosphere 10, no. 2 (2019): 87. http://dx.doi.org/10.3390/atmos10020087.

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The regional ensemble prediction system (REPS) of North China is currently under development at the Institute of Urban Meteorology, China Meteorological Administration, with initial condition perturbations provided by global ensemble dynamical downscaling. To improve the performance of the REPS, a comparison of two initial condition perturbation methods is conducted in this paper: (i) Breeding, which was specifically designed for the REPS, and (ii) Dynamical downscaling. Consecutive tests were implemented to evaluate the performances of both methods in the operational REPS environment. The perturbation characteristics were analyzed, and ensemble forecast verifications were conducted. Furthermore, a heavy precipitation case was investigated. The main conclusions are as follows: the Breeding perturbations were more powerful at small scales, while the downscaling perturbations were more powerful at large scales; the difference between the two perturbation types gradually decreased with the forecast lead time. The downscaling perturbation growth was more remarkable than that of the Breeding perturbations at short forecast lead times, while the perturbation magnitudes of both schemes were similar for long-range forecasts. However, the Breeding perturbations contained more abundant small-scale components than downscaling for the short-range forecasts. The ensemble forecast verification indicated a slightly better downscaling ensemble performance than that of the Breeding ensemble. A precipitation case study indicated that the Breeding ensemble performance was better than that of downscaling, particularly in terms of location and strength of the precipitation forecast.

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KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE." International Journal of Modern Physics A 01, no. 01 (1986): 265–301. http://dx.doi.org/10.1142/s0217751x86000137.

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The isocurvature perturbation in the photon-baryon universe is comprehensively studied by analytic methods in the framework of the gauge-invariant perturbation theory. In particular the evolutionary behavior of the isocurvature perturbation and its influence on the anisotropy in the cosmic microwave background are examined in detail. The results are compared with those for the adiabatic perturbation and some peculiar features of the isocurvature perturbation are pointed out and their origin is clarified. Besides these studies the ambiguities associated with the definition of non-adiabatic perturbations, especially the so-called isothermal perturbation are critically discussed and a clear definition of isocurvature perturbation is given.

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Pakdemirli, M., and H. Boyaci. "Comparison of direct-perturbation methods with discretization-perturbation methods for non-linear vibrations." Journal of Sound and Vibration 186, no. 5 (1995): 837–45. http://dx.doi.org/10.1006/jsvi.1995.0491.

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Taylor, Zoe, Gregory S. Walsh, Hannah Hawkins, Mario Inacio, and Patrick Esser. "Perturbations during Gait: A Systematic Review of Methodologies and Outcomes." Sensors 22, no. 15 (2022): 5927. http://dx.doi.org/10.3390/s22155927.

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Background: Despite extensive literature regarding laboratory-based balance perturbations, there is no up-to-date systematic review of methods. This systematic review aimed to assess current perturbation methods and outcome variables used to report participant biomechanical responses during walking. Methods: Web of Science, CINAHL, and PubMed online databases were searched, for records from 2015, the last search was on 30th of May 2022. Studies were included where participants were 18+ years, with or without clinical conditions, conducted in non-hospital settings. Reviews were excluded. Participant descriptive, perturbation method, outcome variables and results were extracted and summarised. Bias was assessed using the Appraisal tool for Cross-sectional Studies risk of bias assessment tool. Qualitative analysis was performed as the review aimed to investigate methods used to apply perturbations. Results: 644 records were identified and 33 studies were included, totaling 779 participants. The most frequent method of balance perturbation during gait was by means of a treadmill translation. The most frequent outcome variable collected was participant step width, closely followed by step length. Most studies reported at least one spatiotemporal outcome variable. All included studies showed some risk of bias, generally related to reporting of sampling approaches. Large variations in perturbation type, duration and intensity and outcome variables were reported. Conclusions: This review shows the wide variety of published laboratory perturbation methods. Moreover, it demonstrates the significant impact on outcome measures of a study based on the type of perturbation used. Registration: PROSPERO ID: CRD42020211876.

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Pratt, S., R. Zeng, Z. Yuan, and J. Keller. "Comparison of methods for the determination of KLaO2 for respirometric measurements." Water Science and Technology 50, no. 11 (2004): 153–61. http://dx.doi.org/10.2166/wst.2004.0683.

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The mass transfer coefficient for oxygen in water (KLaO2) is an important parameter for respirometric studies. But determination of KLaO2 in process conditions is not straightforward. In this paper, two distinct procedures for determining KLaO2 in process conditions are outlined and tested. The off-gas method relies on a gas mass balance over a bioreactor while the non-steady state methods rely on analysing DO recovery after perturbation. Various means for inducing perturbation are tested and compared. KLaO2 values for a bioreactor are determined by the listed methods. It was found that the off-gas method resulted in the highest KLaO2 for the given reactor, while the non-steady state method, whereby perturbation is caused by exogenous activity on acetate, resulted in the lowest KLaO2. It is shown that the gas mass balancing technique is robust to unexpected exogenous activity (caused by for example, the oxidation of storage polymers formed or nitrite accumulated), while the non-steady state methods that involve inducing perturbations by exogenous activity appear susceptible to such continued exogenous activity in the DO recovery period.

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Mendonça, Antônio Marcos, and JoséPaulo Bonatti. "Experiments with EOF-Based Perturbation Methods and Their Impact on the CPTEC/INPE Ensemble Prediction System." Monthly Weather Review 137, no. 4 (2009): 1438–59. http://dx.doi.org/10.1175/2008mwr2581.1.

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Abstract The impact of modifications of the perturbation method based on empirical orthogonal functions (EOFs) used operationally upon the ensemble prediction system (EPS) at the Center for Weather Prediction and Climate Studies/National Institute for Space Research (CPTEC/INPE) is evaluated. The main changes proposed in this study are to apply the EOF method to perturb the midlatitudes, apply additional perturbations to the surface pressure (P) and specific humidity (Q) fields, and compute regional perturbations over South America. The impact of these modifications in the characteristics of the initial perturbations and in the quality of the EPS forecasts is investigated. The EPS forecasts are evaluated through average statistical scores over the period 15 December 2004–15 February 2005. The statistical scores used in the evaluation are pattern anomaly correlation, root-mean-square error, ensemble spread, Brier skill score, and perturbation versus error correlation analysis (PECA). Results indicate that with the inclusion of perturbations on P and Q, EOF-based perturbations acquire a more baroclinic structure. It is also observed that the simultaneous application of additional perturbations both in the extratropics and to the P and Q fields improves the performance of CPTEC EPS and enhances the quality of forecast perturbations. Moreover, regional EOF-based perturbations computed over South America have positive impact on the ensemble forecasts over the target region.

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Vinter, R. B. "PERTURBATION METHODS IN OPTIMAL CONTROL." Bulletin of the London Mathematical Society 23, no. 6 (1991): 616–17. http://dx.doi.org/10.1112/blms/23.6.616.

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Ganapol, B. D. "Perturbation Methods in Heat Transfer." Nuclear Technology 73, no. 2 (1986): 252. http://dx.doi.org/10.13182/nt86-a33790.

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Shivamoggi,, BK, and J. Awrejcewicz,. "Perturbation Methods for Differential Equations." Applied Mechanics Reviews 56, no. 6 (2003): B77—B78. http://dx.doi.org/10.1115/1.1623750.

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Nayfeh, Ali H. "Numerical-perturbation methods in mechanics." Computers & Structures 30, no. 1-2 (1988): 185–204. http://dx.doi.org/10.1016/0045-7949(88)90226-x.

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Gorbunov, M. E. "Perturbation methods in geometric optics." Radiophysics and Quantum Electronics 38, no. 7 (1995): 438–43. http://dx.doi.org/10.1007/bf01060459.

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Miller, D., B. J. T. Morgan, M. S. Ridout, P. D. Carey, and P. Rothery. "Methods for exact perturbation analysis." Methods in Ecology and Evolution 2, no. 3 (2010): 283–88. http://dx.doi.org/10.1111/j.2041-210x.2010.00074.x.

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Baikov, V. A., R. K. Gazizov, and N. Kh Ibragimov. "Perturbation methods in group analysis." Journal of Soviet Mathematics 55, no. 1 (1991): 1450–90. http://dx.doi.org/10.1007/bf01097534.

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Eichhorn, R. "Perturbation methods in heat transfer." International Journal of Heat and Fluid Flow 6, no. 2 (1985): 121. http://dx.doi.org/10.1016/0142-727x(85)90046-3.

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MISHRA, R. K., and NAVYA JAIN. "Stability Analysis in Cosmological Models Using Perturbative Methods in f(R,T) Theory." Romanian Journal of Physics 69, no. 9-10 (2024): 113. https://doi.org/10.59277/romjphys.2024.69.113.

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This study examines the stability of cosmological models through perturbation theory, focusing on different formulations of the deceleration parameter (DP). By analysing the eigenvalues of perturbations, we identify key insights into the models’ long-term dynamics and stability. The results reveal the presence of stable and marginally stable modes, indicating how perturbations evolve and dissipate over cosmic time. These findings provide a deeper understanding of cosmic evolution, the formation of large-scale structures, and the behaviour of perturbations, offering significant contributions to cosmological research and theoretical modelling of the Universe.

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Nandhini, K., and M. Sumathi. "New and Modified Homotopy Perturbation Methods for Addressing Burger’s Non-linear Equation." Indian Journal Of Science And Technology 17, no. 38 (2024): 4019–29. http://dx.doi.org/10.17485/ijst/v17i38.2029.

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Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled Burger’s non-linear equation is obtained by constructing homotopies. Numerical results thus obtained are compared with the exact solution. The obtained results and the exact solutions to the stated problem are closely related. Novelty: The New and Modified Homotopy Perturbation Method proposed in this paper are effective mathematical tools for getting an exact solution to the coupled Burgers' equations. It is also a potential approach for solving various linear and nonlinear partial differential equations. Keywords: Perturbation, Homotopy, New homotopy perturbation, Modified homotopy perturbation, Twodimension, Linear, Coupled burgers' equation

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Chander, Harish, Sachini N. K. Kodithuwakku Arachchige, Christopher M. Hill, et al. "Virtual-Reality-Induced Visual Perturbations Impact Postural Control System Behavior." Behavioral Sciences 9, no. 11 (2019): 113. http://dx.doi.org/10.3390/bs9110113.

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Background: Virtual reality (VR) is becoming a widespread tool in rehabilitation, especially for postural stability. However, the impact of using VR in a “moving wall paradigm” (visual perturbation), specifically without and with anticipation of the perturbation, is unknown. Methods: Nineteen healthy subjects performed three trials of static balance testing on a force plate under three different conditions: baseline (no perturbation), unexpected VR perturbation, and expected VR perturbation. The statistical analysis consisted of a 1 × 3 repeated-measures ANOVA to test for differences in the center of pressure (COP) displacement, 95% ellipsoid area, and COP sway velocity. Results: The expected perturbation rendered significantly lower (p < 0.05) COP displacements and 95% ellipsoid area compared to the unexpected condition. A significantly higher (p < 0.05) sway velocity was also observed in the expected condition compared to the unexpected condition. Conclusions: Postural stability was lowered during unexpected visual perturbations compared to both during baseline and during expected visual perturbations, suggesting that conflicting visual feedback induced postural instability due to compensatory postural responses. However, during expected visual perturbations, significantly lowered postural sway displacement and area were achieved by increasing the sway velocity, suggesting the occurrence of postural behavior due to anticipatory postural responses. Finally, the study also concluded that VR could be used to induce different postural responses by providing visual perturbations to the postural control system, which can subsequently be used as an effective and low-cost tool for postural stability training and rehabilitation.

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DOUGLAS, JIM, and SEONGJAI KIM. "IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS." Mathematical Models and Methods in Applied Sciences 11, no. 09 (2001): 1563–79. http://dx.doi.org/10.1142/s0218202501001471.

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Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time-stepping procedure such as Crank–Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time-stepping procedure. We show that minor modifications in the AD and FS procedures can virtually eliminate the perturbation errors at an additional computational cost that is less than 10% of the cost of the original AD or FS method. Moreover, after these modifications, the AD and FS procedures produce identical approximations of the solution of the differential problem. It is also shown that the same perturbation of the Crank–Nicolson procedure can be obtained with AD and FS methods associated with the backward Euler time-stepping scheme. An application of the same concept is presented for second-order wave equations.

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Ferreira, Rafael N., Nuno Ferrete Ribeiro, Joana Figueiredo, and Cristina P. Santos. "Provoking Artificial Slips and Trips towards Perturbation-Based Balance Training: A Narrative Review." Sensors 22, no. 23 (2022): 9254. http://dx.doi.org/10.3390/s22239254.

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Humans’ balance recovery responses to gait perturbations are negatively impacted with ageing. Slip and trip events, the main causes preceding falls during walking, are likely to produce severe injuries in older adults. While traditional exercise-based interventions produce inconsistent results in reducing patients’ fall rates, perturbation-based balance training (PBT) emerges as a promising task-specific solution towards fall prevention. PBT improves patients’ reactive stability and fall-resisting skills through the delivery of unexpected balance perturbations. The adopted perturbation conditions play an important role towards PBT’s effectiveness and the acquisition of meaningful sensor data for studying human biomechanical reactions to loss of balance (LOB) events. Hence, this narrative review aims to survey the different methods employed in the scientific literature to provoke artificial slips and trips in healthy adults during treadmill and overground walking. For each type of perturbation, a comprehensive analysis was conducted to identify trends regarding the most adopted perturbation methods, gait phase perturbed, gait speed, perturbed leg, and sensor systems used for data collection. The reliable application of artificial perturbations to mimic real-life LOB events may reduce the gap between laboratory and real-life falls and potentially lead to fall-rate reduction among the elderly community.

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He, Bangyan, Jian Liu, Yiming Li, et al. "Generating Transferable 3D Adversarial Point Cloud via Random Perturbation Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 1 (2023): 764–72. http://dx.doi.org/10.1609/aaai.v37i1.25154.

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Recent studies have demonstrated that existing deep neural networks (DNNs) on 3D point clouds are vulnerable to adversarial examples, especially under the white-box settings where the adversaries have access to model parameters. However, adversarial 3D point clouds generated by existing white-box methods have limited transferability across different DNN architectures. They have only minor threats in real-world scenarios under the black-box settings where the adversaries can only query the deployed victim model. In this paper, we revisit the transferability of adversarial 3D point clouds. We observe that an adversarial perturbation can be randomly factorized into two sub-perturbations, which are also likely to be adversarial perturbations. It motivates us to consider the effects of the perturbation and its sub-perturbations simultaneously to increase the transferability for sub-perturbations also contain helpful information. In this paper, we propose a simple yet effective attack method to generate more transferable adversarial 3D point clouds. Specifically, rather than simply optimizing the loss of perturbation alone, we combine it with its random factorization. We conduct experiments on benchmark dataset, verifying our method's effectiveness in increasing transferability while preserving high efficiency.

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Johnson, Aaron, Xuguang Wang, Ming Xue, et al. "Multiscale Characteristics and Evolution of Perturbations for Warm Season Convection-Allowing Precipitation Forecasts: Dependence on Background Flow and Method of Perturbation." Monthly Weather Review 142, no. 3 (2014): 1053–73. http://dx.doi.org/10.1175/mwr-d-13-00204.1.

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Abstract Multiscale convection-allowing precipitation forecast perturbations are examined for two forecasts and systematically over 34 forecasts out to 30-h lead time using Haar Wavelet decomposition. Two small-scale initial condition (IC) perturbation methods are compared to the larger-scale IC and physics perturbations in an experimental convection-allowing ensemble. For a precipitation forecast driven primarily by a synoptic-scale baroclinic disturbance, small-scale IC perturbations resulted in little precipitation forecast perturbation energy on medium and large scales, compared to larger-scale IC and physics (LGPH) perturbations after the first few forecast hours. However, for a case where forecast convection at the initial time grew upscale into a mesoscale convective system (MCS), small-scale IC and LGPH perturbations resulted in similar forecast perturbation energy on all scales after about 12 h. Small-scale IC perturbations added to LGPH increased total forecast perturbation energy for this case. Averaged over 34 forecasts, the small-scale IC perturbations had little impact on large forecast scales while LGPH accounted for about half of the error energy on such scales. The impact of small-scale IC perturbations was also less than, but comparable to, the impact of LGPH perturbations on medium scales. On small scales, the impact of small-scale IC perturbations was at least as large as the LGPH perturbations. The spatial structure of small-scale IC perturbations affected the evolution of forecast perturbations, especially at medium scales. There was little systematic impact of the small-scale IC perturbations when added to LGPH. These results motivate further studies on properly sampling multiscale IC errors.

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HE, JI-HUAN. "SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS." International Journal of Modern Physics B 20, no. 10 (2006): 1141–99. http://dx.doi.org/10.1142/s0217979206033796.

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This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive.

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Munjal, Manish, Amit Grewal, and Harsh Yadav. "Optical Fibre Sensors and Methods." Journal of Advance Research in Electrical & Electronics Engineering (ISSN: 2208-2395) 1, no. 2 (2014): 17–19. http://dx.doi.org/10.53555/nneee.v1i2.260.

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This research paper is about a multi-mode fibre optic sensor for optically sensing a physical perturbation including a multi- mode optical fibre segment which accepts coherent monochromatic radiation from a suitable source. As the radiation is propagated in the fibre, the various modes form a complex interference pattern which changes in response to a physical perturbation of the fibre. A detector provides an output signal to a signal processor which analyzes the signal as a function of the change in intensity to provide an information signal functionally related to the perturbation.

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Johnson, Aaron, and Xuguang Wang. "A Study of Multiscale Initial Condition Perturbation Methods for Convection-Permitting Ensemble Forecasts." Monthly Weather Review 144, no. 7 (2016): 2579–604. http://dx.doi.org/10.1175/mwr-d-16-0056.1.

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Abstract The impacts of multiscale flow-dependent initial condition (IC) perturbations for storm-scale ensemble forecasts of midlatitude convection are investigated using perfect-model observing system simulation experiments. Several diverse cases are used to quantitatively and qualitatively understand the impacts of different IC perturbations on ensemble forecast skill. Scale dependence of the results is assessed by evaluating 2-h storm-scale reflectivity forecasts separately from hourly accumulated mesoscale precipitation forecasts. Forecasts are initialized with different IC ensembles, including an ensemble of multiscale perturbations produced by a multiscale data assimilation system, mesoscale perturbations produced at a coarser resolution, and filtered multiscale perturbations. Mesoscale precipitation forecasts initialized with the multiscale perturbations are more skillful than the forecasts initialized with the mesoscale perturbations at several lead times. This multiscale advantage is due to greater consistency between the IC perturbations and IC uncertainty. This advantage also affects the short-term, smaller-scale forecasts. Reflectivity forecasts on very small scales and very short lead times are more skillful with the multiscale perturbations as a direct result of the smaller-scale IC perturbation energy. The small-scale IC perturbations also contribute to some improvements to the mesoscale precipitation forecasts after the ~5-h lead time. Altogether, these results suggest that the multiscale IC perturbations provided by ensemble data assimilation on the convection-permitting grid can improve storm-scale ensemble forecasts by improving the sampling of IC uncertainty, compared to downscaling of IC perturbations from a coarser-resolution ensemble.

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36

K, Nandhini, and Sumathi M. "New and Modified Homotopy Perturbation Methods for Addressing Burger's Non-linear Equation." Indian Journal of Science and Technology 17, no. 38 (2024): 4019–29. https://doi.org/10.17485/IJST/v17i38.2029.

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Abstract Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled Burger’s non-linear equation is obtained by constructing homotopies. Numerical results thus obtained are compared with the exact solution. The obtained results and the exact solutions to the stated problem are closely related. Novelty: The New and Modified Homotopy Perturbation Method proposed in this paper are effective mathematical tools for getting an exact solution to the coupled Burgers' equations. It is also a potential approach for solving various linear and nonlinear partial differential equations. Keywords: Perturbation, Homotopy, New homotopy perturbation, Modified homotopy perturbation, Twodimension, Linear, Coupled burgers' equation

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37

Ganji, D. D., and A. Rajabi. "Assessment of homotopy–perturbation and perturbation methods in heat radiation equations." International Communications in Heat and Mass Transfer 33, no. 3 (2006): 391–400. http://dx.doi.org/10.1016/j.icheatmasstransfer.2005.11.001.

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HISLOP, PETER D., and SHU NAKAMURA. "STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS." Reviews in Mathematical Physics 02, no. 04 (1990): 479–94. http://dx.doi.org/10.1142/s0129055x90000156.

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Spectral properties of one-dimensional Schrödinger operators with unbounded potentials are studied. The main example is the Stark Hamiltonian with unbounded Anderson-type random perturbations. In this case, it is shown that if the perturbation is o(x) then the spectrum is the real line and absolutely continuous except for eigenvalues with no accumulation points. If the perturbation is larger than O(x), then the Hamiltonian has no absolutely continuous spectrum. The methods of proof involve the Mourre estimate and trace-class perturbation theory as recently used by Simon and Spencer.

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Che, Lei, Chengcong Wu, and Yan Hou. "Large Language Model Text Adversarial Defense Method Based on Disturbance Detection and Error Correction." Electronics 14, no. 11 (2025): 2267. https://doi.org/10.3390/electronics14112267.

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This study aims to effectively defend against complex and diverse adversarial attacks, enhance adversarial defense performance in the field of textual adversarial examples, and address existing issues in current defense methods such as models’ inability to accurately detect perturbations and perform effective error correction. To this end, we propose a Large Language Model Adversarial Defense (LLMAD) method based on perturbation detection and correction. The LLMAD framework consists of two modules: a perturbation detection module and a perturbation correction module. The detection module combines pre-trained models with soft-masking layers to rapidly determine whether samples contain adversarial perturbations. The correction module employs large language models fine-tuned using an adversarial example perturbation dataset constructed through data augmentation, enhancing task performance in adversarial defense and enabling efficient and accurate error correction of adversarial samples. Experimental results demonstrate that, across multiple datasets, various target models defended through the LLMAD method achieve satisfactory defense effectiveness against different types of adversarial attacks. The classification accuracy of defended models shows an average improvement of 66.8% compared to undefended baselines and outperforms existing methods by 13.4% on average. Additional perturbation detection performance tests and ablation studies further validate the accuracy of detection capabilities and the effectiveness of module combinations. A series of experiments confirm that the LLMAD method can significantly enhance defensive effectiveness against textual adversarial attacks.

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Xie, Yi, Zhuohang Li, Cong Shi, Jian Liu, Yingying Chen, and Bo Yuan. "Enabling Fast and Universal Audio Adversarial Attack Using Generative Model." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 16 (2021): 14129–37. http://dx.doi.org/10.1609/aaai.v35i16.17663.

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Recently, the vulnerability of deep neural network (DNN)-based audio systems to adversarial attacks has obtained increasing attention. However, the existing audio adversarial attacks allow the adversary to possess the entire user's audio input as well as granting sufficient time budget to generate the adversarial perturbations. These idealized assumptions, however, make the existing audio adversarial attacks mostly impossible to be launched in a timely fashion in practice (e.g., playing unnoticeable adversarial perturbations along with user's streaming input). To overcome these limitations, in this paper we propose fast audio adversarial perturbation generator (FAPG), which uses generative model to generate adversarial perturbations for the audio input in a single forward pass, thereby drastically improving the perturbation generation speed. Built on the top of FAPG, we further propose universal audio adversarial perturbation generator (UAPG), a scheme to craft universal adversarial perturbation that can be imposed on arbitrary benign audio input to cause misclassification. Extensive experiments on DNN-based audio systems show that our proposed FAPG can achieve high success rate with up to 214X speedup over the existing audio adversarial attack methods. Also our proposed UAPG generates universal adversarial perturbations that can achieve much better attack performance than the state-of-the-art solutions.

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41

Karandikar, Mandar, Cristiano Porciani, and Oliver Hahn. "Testing the assumptions of the Effective Field Theory of Large-Scale Structure." Journal of Cosmology and Astroparticle Physics 2024, no. 01 (2024): 051. http://dx.doi.org/10.1088/1475-7516/2024/01/051.

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Abstract The Effective Field Theory of Large-Scale Structure (EFTofLSS) attempts to amend some of the shortcomings of the traditional perturbative methods used in cosmology. It models the evolution of long-wavelength perturbations above a cutoff scale without the need for a detailed description of the short-wavelength ones. Short-scale physics is encoded in the coefficients of a series of operators composed of the long-wavelength fields, and ordered in a systematic expansion. As applied in the literature, the EFTofLSS corrects a summary statistic (such as the power spectrum) calculated from standard perturbation theory by matching it to N-body simulations or observations. This `bottom-up' construction is remarkably successful in extending the range of validity of perturbation theory. In this work, we compare this framework to a `top-down' approach, which estimates the EFT coefficients from the stress tensor of an N-body simulation, and propagates the corrections to the summary statistic. We consider simple initial conditions, viz. two sinusoidal, plane-parallel density perturbations with substantially different frequencies and amplitudes. We find that the leading EFT correction to the power spectrum in the top-down model is in excellent agreement with that inferred from the bottom-up approach which, by construction, provides an exact match to the numerical data. This result is robust to changes in the wavelength separation between the two linear perturbations. However, in our setup, the leading EFT coefficient does not always grow linearly with the cosmic expansion factor as assumed in the literature based on perturbative considerations. Instead, it decreases after orbit crossing takes place.

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42

Ousmane, Samba Coulibaly. "IDENTIFICATION THE HEAT SOURCE DEPENDENT ON A SPATIAL VARIABLE, REGULARIZATION AND CONTROL OF NOISE LEVEL IN CASE PERTURBATION BY SPECTRAL TRUNCATION AND KRYLOV METHODS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 9 (2017): 240–48. https://doi.org/10.5281/zenodo.886668.

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This paper deals with regularization and noise level control of source depending only on the spatial variable in the heat equation. In this problem, the Krylov method is employed to get the regularization solution and control noise level in case perturbation. Various numerical tests are given to verify the efficiency of the proposed method and until what point the method resist at the perturbations.

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43

Sun, Da Wei. "Perturbation Analysis of Diffeomorphisms in Contact Dynamical System." Advanced Materials Research 529 (June 2012): 264–67. http://dx.doi.org/10.4028/www.scientific.net/amr.529.264.

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This paper studies the perturbations of strictly contact diffeomorphisms in contact dynamical system. By constructing new lifting methods for contact system and using some perturbation techniques in Hamiltonian mechanics, this paper proves that there exists an arbitrary small perturbations such that the corresponding function of the strictly contact isotopy does not equal to a constant at any time.

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44

Itô, Masayuki. "A remark on singular perturbation methods." Hiroshima Mathematical Journal 14, no. 3 (1985): 619–29. http://dx.doi.org/10.32917/hmj/1206132941.

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Otanez, Paul G., and Mark E. Campbell. "Detection Methods for Mode Perturbation Signatures." IEEE Transactions on Automatic Control 57, no. 11 (2012): 2923–28. http://dx.doi.org/10.1109/tac.2012.2195932.

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46

Goodson, D. Z., and D. R. Herschbach. "Summation methods for dimensional perturbation theory." Physical Review A 46, no. 9 (1992): 5428–36. http://dx.doi.org/10.1103/physreva.46.5428.

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Killingbeck, J. P., and G. Jolicard. "Perturbation methods for the matrix eigenproblem." Journal of Physics A: Mathematical and General 25, no. 23 (1992): 6455–59. http://dx.doi.org/10.1088/0305-4470/25/23/037.

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Cross, M. "Perturbation Methods for Scientists and Engineers." Applied Mathematical Modelling 16, no. 8 (1992): 446. http://dx.doi.org/10.1016/0307-904x(92)90080-m.

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Buldaev, A. S. "Perturbation methods in optimal control problems." Ecological Modelling 216, no. 2 (2008): 157–59. http://dx.doi.org/10.1016/j.ecolmodel.2008.03.030.

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Hongxing, Li. "Fuzzy clustering methods based on perturbation." Fuzzy Sets and Systems 33, no. 3 (1989): 291–302. http://dx.doi.org/10.1016/0165-0114(89)90119-x.

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Journal articles on the topic 'Perturbation methods'

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