Journal articles: 'Perturbation methods'

1

Hinch, E. J., and Edward G. Harris. "Perturbation Methods." American Journal of Physics 60, no. 11 (November 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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Riley, N. "Perturbation methods, 1992." Journal of Fluids and Structures 6, no. 4 (July 1992): 523–24. http://dx.doi.org/10.1016/0889-9746(92)90029-3.

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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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Murdock, James. "Book Review: Perturbation methods." Bulletin of the American Mathematical Society 28, no. 2 (April 1, 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 (July 15, 1993): 103–18. http://dx.doi.org/10.1002/qua.560470202.

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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 (June 28, 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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PANI, PAOLO. "ADVANCED METHODS IN BLACK-HOLE PERTURBATION THEORY." International Journal of Modern Physics A 28, no. 22n23 (September 20, 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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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 (October 1995): 837–45. http://dx.doi.org/10.1006/jsvi.1995.0491.

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Vinter, R. B. "PERTURBATION METHODS IN OPTIMAL CONTROL." Bulletin of the London Mathematical Society 23, no. 6 (November 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 (May 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 (November 1, 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 (January 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 (July 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 (November 18, 2010): 283–88. http://dx.doi.org/10.1111/j.2041-210x.2010.00074.x.

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

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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 (June 1991): 1450–90. http://dx.doi.org/10.1007/bf01097534.

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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 (February 19, 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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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 (December 1, 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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KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE." International Journal of Modern Physics A 01, no. 01 (April 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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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 (August 8, 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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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 (April 1, 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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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 (March 2006): 391–400. http://dx.doi.org/10.1016/j.icheatmasstransfer.2005.11.001.

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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 (December 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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Johnson, Aaron, and Xuguang Wang. "A Study of Multiscale Initial Condition Perturbation Methods for Convection-Permitting Ensemble Forecasts." Monthly Weather Review 144, no. 7 (June 23, 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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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 (February 28, 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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HE, JI-HUAN. "SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS." International Journal of Modern Physics B 20, no. 10 (April 20, 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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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 (November 2012): 2923–28. http://dx.doi.org/10.1109/tac.2012.2195932.

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Goodson, D. Z., and D. R. Herschbach. "Summation methods for dimensional perturbation theory." Physical Review A 46, no. 9 (November 1, 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 (December 7, 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 (August 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 (August 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 (December 1989): 291–302. http://dx.doi.org/10.1016/0165-0114(89)90119-x.

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Ames, W. F., and C. Brezinski. "Perturbation methods for Engineers and Scientists." Mathematics and Computers in Simulation 34, no. 2 (August 1992): 187. http://dx.doi.org/10.1016/0378-4754(92)90062-l.

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Espriu, D., and J. Matias. "Regularization methods in chiral perturbation theory." Nuclear Physics B 418, no. 3 (May 1994): 494–528. http://dx.doi.org/10.1016/0550-3213(94)90528-2.

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Becher, Thomas, and Kirill Melnikov. "Continuum methods in lattice perturbation theory." Nuclear Physics B - Proceedings Supplements 116 (March 2003): 407–11. http://dx.doi.org/10.1016/s0920-5632(03)80209-8.

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Muralidhar, Krishnamurty, and Rathindra Sarathy. "Security of random data perturbation methods." ACM Transactions on Database Systems 24, no. 4 (December 1999): 487–93. http://dx.doi.org/10.1145/331983.331986.

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Chen, M., and J. Arvo. "Perturbation methods for interactive specular reflections." IEEE Transactions on Visualization and Computer Graphics 6, no. 3 (2000): 253–64. http://dx.doi.org/10.1109/2945.879786.

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Nicholls, David P. "Boundary Perturbation Methods for Water Waves." GAMM-Mitteilungen 30, no. 1 (April 2007): 44–74. http://dx.doi.org/10.1002/gamm.200790009.

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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 (November 28, 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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Chander, Harish, Sachini N. K. Kodithuwakku Arachchige, Christopher M. Hill, Alana J. Turner, Shuchisnigdha Deb, Alireza Shojaei, Christopher Hudson, Adam C. Knight, and Daniel W. Carruth. "Virtual-Reality-Induced Visual Perturbations Impact Postural Control System Behavior." Behavioral Sciences 9, no. 11 (November 12, 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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Johnson, Aaron, Xuguang Wang, Ming Xue, Fanyou Kong, Gang Zhao, Yunheng Wang, Kevin W. Thomas, Keith A. Brewster, and Jidong Gao. "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 (March 1, 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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Ramezani, Maziar, and Thomas Rainer Neitzert. "Assessment of Perturbation and Homotopy-Perturbation Methods for Solving Nonlinear Oscillator Equations." Applied Mechanics and Materials 376 (August 2013): 207–15. http://dx.doi.org/10.4028/www.scientific.net/amm.376.207.

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In this paper, two modified perturbation methods, namely, artificial parameter method (APM) and homotopy perturbation method (HPM) have been successfully implemented to find the solution of van der Pol nonlinear oscillator equation. Different from classical perturbation method, APM and HPM do not require small parameter and therefore, obtained approximate solutions may be uniformly valid for both weak nonlinear systems and strong nonlinear systems. Comparison of the results obtained by the proposed methods reveals that APM and HPM are more effective compared to classical perturbation method and with only a few terms, approximate the exact solution with a fairly reasonable error.

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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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HISLOP, PETER D., and SHU NAKAMURA. "STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS." Reviews in Mathematical Physics 02, no. 04 (January 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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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 (May 18, 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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Saeed, Rostam K., and Rebwar S. Muhammad. "Solving Coupled Hirota System by Using Homotopy Perturbation and Homotopy Analysis Methods." Journal of Zankoy Sulaimani - Part A 17, no. 2 (February 22, 2015): 201–18. http://dx.doi.org/10.17656/jzs.10394.

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Popescu, V. A., and I. M. Popescu. "Combination of the successive perturbation method with other common methods." Canadian Journal of Physics 65, no. 5 (May 1, 1987): 462–63. http://dx.doi.org/10.1139/p87-061.

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For the hydrogen atom in the fundamental state perturbed by βr−1, it is shown how the successive perturbation method can be combined with the method in which some fraction of a nonperturbed term (in the Hamiltonian) is included in the perturbation. Thus, the radius of convergence of the perturbation series is increased.

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Wilchinsky, Alexander V., and Vladimir A. Chugunov. "Modelling ice-divide dynamics by perturbation methods." Journal of Glaciology 43, no. 144 (1997): 352–58. http://dx.doi.org/10.3189/s0022143000003300.

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AbstractTwo-dimensional, isothermal, non-stationary, cold-glacier dynamics are analysed by perturbation methods, when the ice creep is described by Glen’s flow law. This approach allows us in model the ice-divide dynamics separately from that of the glacier and to pose a simplified problem for the ice divide. To order of the glacier-aspect ratio, all unknown characteristics near the ice divide can be searched for in an infinite layer with parallel boundaries, whose thickness coincides with that found by the shallow-ice approximation. The problem for the ice divide is stationary and does not depend on the ice and glacier characteristics, such as a flow-law constant, ice thickness and accumulation rate. At the ice divide, the ice upper surface curvature is finite and the shallow-ice approximation is inadequate.

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Journal articles on the topic 'Perturbation methods'

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