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Journal articles on the topic 'Slow-Fast asymptotic analysis'

Author: Grafiati

Published: 8 June 2024

Last updated: 31 July 2025

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1

Pan, Shing-Tai, Ching-Fa Chen, and Jer-Guang Hsieh. "Stability Analysis for a Class of Singularly Perturbed Systems With Multiple Time Delays." Journal of Dynamic Systems, Measurement, and Control 126, no. 3 (2004): 462–66. http://dx.doi.org/10.1115/1.1793172.

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The paper is to investigate the asymptotic stability for a general class of linear time-invariant singularly perturbed systems with multiple non-commensurate time delays. It is a common practice to investigate the asymptotic stability of the original system by establishing that of its slow subsystem and fast subsystem. A frequency-domain approach is first presented to determine a sufficient condition for the asymptotic stability of the slow subsystem (reduced-order model), which is a singular system with multiple time delays, and the fast subsystem. Two delay-dependent criteria, ε-dependent an

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Nave, OPhir, Israel Hartuv та Uziel Shemesh. "Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition". PeerJ 8 (21 вересня 2020): e10019. http://dx.doi.org/10.7717/peerj.10019.

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In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model of to expose the hierarchy of the model. This de

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Glizer, Valery Y. "Stability Analysis of Some Types of Singularly Perturbed Time-Delay Differential Systems: Symmetric Matrix Riccati Equation Approach." Symmetry 16, no. 7 (2024): 838. http://dx.doi.org/10.3390/sym16070838.

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Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow–fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of

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Thomas, Jim. "Resonant fast–slow interactions and breakdown of quasi-geostrophy in rotating shallow water." Journal of Fluid Mechanics 788 (January 8, 2016): 492–520. http://dx.doi.org/10.1017/jfm.2015.706.

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In this paper we investigate the possibility of fast waves affecting the evolution of slow balanced dynamics in the regime $Ro\sim Fr\ll 1$ of a rotating shallow water system, where $Ro$ and $Fr$ are the Rossby and Froude numbers respectively. The problem is set up as an initial value problem with unbalanced initial data. The method of multiple time scale asymptotic analysis is used to derive an evolution equation for the slow dynamics that holds for $t\lesssim 1/(fRo^{2})$, $f$ being the inertial frequency. This slow evolution equation is affected by the fast waves and thus does not form a cl

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Zhou, Yanli, Shican Liu, Shuang Li, and Xiangyu Ge. "The Correction of Multiscale Stochastic Volatility to American Put Option: An Asymptotic Approximation and Finite Difference Approach." Journal of Function Spaces 2021 (September 17, 2021): 1–14. http://dx.doi.org/10.1155/2021/1217665.

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It has been found that the surface of implied volatility has appeared in financial market embrace volatility “Smile” and volatility “Smirk” through the long-term observation. Compared to the conventional Black-Scholes option pricing models, it has been proved to provide more accurate results by stochastic volatility model in terms of the implied volatility, while the classic stochastic volatility model fails to capture the term structure phenomenon of volatility “Smirk.” More attempts have been made to correct for American put option price with incorporating a fast-scale stochastic volatility

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MARVÁ, M., J. C. POGGIALE, and R. BRAVO DE LA PARRA. "REDUCTION OF SLOW–FAST PERIODIC SYSTEMS WITH APPLICATIONS TO POPULATION DYNAMICS MODELS." Mathematical Models and Methods in Applied Sciences 22, no. 10 (2012): 1250025. http://dx.doi.org/10.1142/s021820251250025x.

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This work deals with the approximate reduction of a nonautonomous two time scales ordinary differential equations system with periodic fast dynamics. We illustrate this technique with the analysis of two models belonging to different fields in ecology. On the one hand, we deal with a two patches periodic predator–prey model with a refuge for prey. Considering migrations between patches to be faster than local interaction allows us to study a three-dimensional system by means of a two-dimensional one. On the other hand, a two time scales periodic eco-epidemic model is addressed by considering t

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Mustafin, Almaz T., and Aliya K. Kantarbayeva. "Clearing function in the context of the invariant manifold method." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 19, no. 2 (2023): 185–98. http://dx.doi.org/10.21638/11701/spbu10.2023.205.

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Clearing functions (CFs), which express a mathematical relationship between the expected throughput of a production facility in a planning period and its workload (or work-inprogress, WIP) in that period have shown considerable promise for modeling WIP-dependent cycle times in production planning. While steady-state queueing models are commonly used to derive analytic expressions for CFs, the finite length of planning periods calls their validity into question. We apply a different approach to propose a mechanistic model for one-resource, one-product factory shop based on the analogy between t

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Schröders, Simon, and Alexander Fidlin. "Asymptotic analysis of self-excited and forced vibrations of a self-regulating pressure control valve." Nonlinear Dynamics 103, no. 3 (2021): 2315–27. http://dx.doi.org/10.1007/s11071-021-06241-5.

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AbstractPressure vibrations in hydraulic systems are a widespread problem and can be caused by external excitation or self-exciting mechanisms. Although vibrations cannot be completely avoided in most cases, at least their frequencies must be known in order to prevent resonant excitation of adjacent components. While external excitation frequencies are known in most cases, the estimation of self-excited vibration amplitudes and frequencies is often difficult. Usually, numerical studies have to be executed in order to elaborate parameter influences, which is computationally expensive. The same

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Glizer, Valery Y. "Asymptotic Analysis of Spectrum and Stability for One Class of Singularly Perturbed Neutral-Type Time-Delay Systems." Axioms 10, no. 4 (2021): 325. http://dx.doi.org/10.3390/axioms10040325.

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In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values o

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Chabyshova, Elmira, and Gennady Goloshubin. "Seismic modeling of low-frequency “shadows” beneath gas reservoirs." GEOPHYSICS 79, no. 6 (2014): D417—D423. http://dx.doi.org/10.1190/geo2013-0379.1.

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P-wave amplitude anomalies below reservoir zones can be used as hydrocarbon markers. Some of those anomalies are considerably delayed relatively to the reflections from the reservoir zone. High P-wave attenuation and velocity dispersion of the observed P-waves cannot justify such delays. The hypothesis that these amplitude anomalies are caused by wave propagation through a layered permeable gaseous reservoir is evaluated. The wave propagation through highly interbedded reservoirs suggest an anomalous amount of mode conversions between fast and slow P-waves. The converted P-waves, which propaga

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Kathirkamanayagan, M., and G. S. Ladde. "Large scale singularly perturbed boundary value problems." Journal of Applied Mathematics and Simulation 2, no. 3 (1989): 139–67. http://dx.doi.org/10.1155/s1048953389000122.

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In this paper an alternative approach to the method of asymptotic expansions for the study of a singularly perturbed linear system with multiparameters and multiple time scales is developed. The method consists of developing a linear non-singular transformation that transforms an arbitrary n—time scale system into a diagonal form. Furthermore, a dichotomy transformation is employed to decompose the faster subsystems into stable and unstable modes. Fast, slow, stable and unstable modes decomposition processes provide a modern technique to find an approximate solution of the original system in t

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Yu, Yue, Qianqian Wang, Qinsheng Bi, and C. W. Lim. "Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation." International Journal of Bifurcation and Chaos 29, no. 05 (2019): 1930012. http://dx.doi.org/10.1142/s021812741930012x.

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Motivated by the forced harmonic vibration of complex mechanical systems, we analyze the dynamics involving different waves in a double-well potential oscillator coupling amplitude modulation control of low frequency. The combination of amplitude modulation factor significantly enriches the dynamical behaviors on the formation of multiple-S-shaped manifold and multiple jumping phenomena that alternate between epochs of slow and fast motion. We can conduct bifurcation analysis to identify two harmonic vibrations. One is that the singular orbit makes multiple jumps to a fast trajectory segment f

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13

Shen, Lu, Daniel J. Jacob, Mauricio Santillana, Kelvin Bates, Jiawei Zhuang, and Wei Chen. "A machine-learning-guided adaptive algorithm to reduce the computational cost of integrating kinetics in global atmospheric chemistry models: application to GEOS-Chem versions 12.0.0 and 12.9.1." Geoscientific Model Development 15, no. 4 (2022): 1677–87. http://dx.doi.org/10.5194/gmd-15-1677-2022.

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Abstract. Global modeling of atmospheric chemistry is a great computational challenge because of the cost of integrating the kinetic equations for chemical mechanisms with typically over 100 coupled species. Here we present an adaptive algorithm to ease this computational bottleneck with no significant loss in accuracy and apply it to the GEOS-Chem global 3-D model for tropospheric and stratospheric chemistry (228 species, 724 reactions). Our approach is inspired by unsupervised machine learning clustering techniques and traditional asymptotic analysis ideas. We locally define species in the m

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Kruparova, Oksana, Adam Szabo, Lan K. Jian, et al. "Radial Evolution of Interplanetary Shock Properties with Heliospheric Distance: Observations from Parker Solar Probe." Astrophysical Journal Letters 979, no. 1 (2025): L10. https://doi.org/10.3847/2041-8213/ada558.

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Abstract We present a comprehensive analysis of 66 interplanetary shocks observed by the Parker Solar Probe between 2018 November and 2024 January. Among these, 33 events fulfilled the Rankine–Hugoniot (R-H) conditions, ensuring reliable asymptotic plasma parameter solutions. The remaining 33 events could not be confirmed by the standard R-H approach—potentially including wave-like structures—yet were analyzed via averaging and mixed-data methods to obtain robust shock parameters. Utilizing our ShOck Detection Algorithm database, the shocks are categorized into fast-forward, fast-reverse, slow

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Gassner, Steven, and Carlo Cafaro. "Information geometric complexity of entropic motion on curved statistical manifolds under different metrizations of probability spaces." International Journal of Geometric Methods in Modern Physics 16, no. 06 (2019): 1950082. http://dx.doi.org/10.1142/s0219887819500828.

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We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian geometric properties and entropic dynamical features of a Gaussian probability space where the two distinct dissimilarity measures between probability distributions are the Fisher–Rao information metric and the [Formula: see text]-order entropy metric. In the former case, we observe an asymptotic linear temporal growth of the information geometric entropy (IGE)

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Nave, OPhir, and Manju Sharma. "Singular Perturbed Vector Field (SPVF) Applied to Complex ODE System with Hidden Hierarchy Application to Turbocharger Engine Model." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 1 (2020): 99–113. http://dx.doi.org/10.1515/ijnsns-2019-0024.

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AbstractIn this paper, we present the concept of singularly perturbed vector field (SPVF) method and its application to spark ignition turbocharger engine. Given a mathematical/physical model, which consist of hidden multi-scale variables, the SPVF methods transfer (using the change of coordinates) and decompose such system to fast and slow subsystems. This decomposition enables one to apply different asymptotic methods such as the method of the integral manifold, homotopy analysis method, singular perturbation method, etc. The resulting subsystem enables us to understand better the complex sy

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Zhang, Kexin, Caihui Yu, Hongbin Wang, and Xianghong Li. "Multi-scale dynamics of predator-prey systems with Holling-IV functional response." AIMS Mathematics 9, no. 2 (2024): 3559–75. http://dx.doi.org/10.3934/math.2024174.

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<abstract><p>In this paper, we propose a Holling-IV predator-prey system considering the perturbation of a slow-varying environmental capacity parameter. This study aims to address how the slowly varying environmental capacity parameter affects the behavior of the system. Based on bifurcation theory and the slow-fast analysis method, the critical condition for the Hopf bifurcation of the autonomous system is given. The oscillatory behavior of the system under different perturbation amplitudes is investigated, corresponding mechanism explanations are given, and it is found that the

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18

Holmes, M. H., W. M. Lai, and V. C. Mow. "Singular Perturbation Analysis of the Nonlinear, Flow-Dependent Compressive Stress Relaxation Behavior of Articular Cartilage." Journal of Biomechanical Engineering 107, no. 3 (1985): 206–18. http://dx.doi.org/10.1115/1.3138545.

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The dominant mechanism giving rise to the viscoelastic response of articular cartilage during compression is the nonlinear diffusive interaction of the fluid and solid phases of the tissue as they flow relative to one another. The present study is concerned with the role of this interaction under uniaxial stress relaxation in compression. The model is a biphasic mixture of fluid and solid which incorporates the strain-dependent permeability found earlier from permeation experiments. When a ramp-displacement is imposed on the articular surface, simple, but accurate, asymptotic approximations ar

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Pasekov, V. P. "To the analysis of weak two-locus viability selection and quasi linkage equilibrium." Доклады Академии наук 484, no. 6 (2019): 781–85. http://dx.doi.org/10.31857/s0869-56524846781-785.

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A model of weak viability selection at two multi-allele loci with standardization of approaches through the use of perturbation theory is examined. The estimate of the quasi-equilibrium value for the linkage disequilibrium coefficient D is analyzed, and results in terms of average effects in quantitative genetics and in terms of the theory of singular perturbations in mathematics are obtained. The approximation of a discrete-time model of a random mating population with non-overlapping generations under weak selection by ordinary differential equations is considered. Weak selection is consider

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Halfiani, Vera, Dwi Fadhiliani, Harish Abdillah Mardi, and Marwan Ramli. "Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations." International Journal of Differential Equations 2018 (June 3, 2018): 1–10. http://dx.doi.org/10.1155/2018/1716571.

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This article discusses the evolution of Benjamin-Bona-Mahony (BBM) wave packet’s envelope. The envelope equation is derived by applying the asymptotic series up to the third order and choosing appropriate fast-to-slow variable transformations which eliminate the resonance terms that occurred. It is obtained that the envelope evolves satisfying the Nonlinear Schrodinger (NLS) equation. The evolution of NLS envelope is investigated through its exact solution, Soliton on Finite Background, which undergoes modulational instability during its propagation. The resulting wave may experience phase sin

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Leibovich, S., S. N. Brown, and Y. Patel. "Bending waves on inviscid columnar vortices." Journal of Fluid Mechanics 173 (December 1986): 595–624. http://dx.doi.org/10.1017/s0022112086001283.

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Bending waves, perturbation modes leading to deflections of the vortex centreline, are considered for an infinitely long straight vortex embedded in an irrotational flow of unlimited extent. We first establish the general form of the dispersion relation for long waves on columnar vortices with arbitrary distributions of axial and azimuthal vorticity by a singular perturbation analysis of the Howard-Gupta equation. The asymptotic results are shown to compare favourably with numerical solutions of the Howard-Gupta equation for wavelengths comparable to the vortex core radius and longer. Dispersi

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Aubert, Julien, and Nicolas Gillet. "The interplay of fast waves and slow convection in geodynamo simulations nearing Earth’s core conditions." Geophysical Journal International 225, no. 3 (2021): 1854–73. http://dx.doi.org/10.1093/gji/ggab054.

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SUMMARY Ground observatory and satellite-based determinations of temporal variations in the geomagnetic field probe a decadal to annual timescale range where Earth’s core slow, inertialess convective motions and rapidly propagating, inertia-bearing hydromagnetic waves are in interplay. Here we numerically model and jointly investigate these two important features with the help of a geodynamo simulation that (to date) is the closest to the dynamical regime of Earth’s core. This model also considerably enlarges the scope of a previous asymptotic scaling analysis, which in turn strengthens the re

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Gurevich, Boris. "Effect of fluid viscosity on elastic wave attenuation in porous rocks." GEOPHYSICS 67, no. 1 (2002): 264–70. http://dx.doi.org/10.1190/1.1451798.

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Attenuation and dispersion of elastic waves in fluid‐saturated rocks due to pore fluid viscosity is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies can be studied using an asymptotic analysis of Rytov's exact dispersion equations. Since the wavelength of the shear wave in the fluid (viscous skin depth) is much smaller than the wavelength of the shear or compressional waves in the solid, the presence of viscous fluid layers requires a consideration of higher‐order terms in th

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Shaburov, Alexander. "Asymptotic expansion of a solution for one singularly perturbed optimal control problem with a convex integral quality index depends on slow variables and smooth control constraints." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 119–36. http://dx.doi.org/10.20310/1810-0198-2019-24-125-119-136.

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The paper deals with the problem of optimal control with a convex integral quality index depends on slow variables for a linear steady-state control system with a fast and slow variables in the class of piecewise continuous controls with a smooth control constraints x ε = A 11 x ε + A 12 y ε + B 1 u, εy ε = A 21 x ε + A 22 y ε + B 2 u, J ε u ≔φ x ε T + 0 T u(t) 2 dt→ min, t∈ 0, T , x ε0 = x 0 ,u ≤1, y ε0 = y 0 , where x ε ∈Rn , y ε ∈Rm , u∈Rr ; A ij , B i , i, j =1,2, - are constant matrices of the corresponding dimension, and φ(·) - is the strictly convex and cofinite function that is continu

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Beyer, Hans-Georg. "Convergence Analysis of Evolutionary Algorithms That Are Based on the Paradigm of Information Geometry." Evolutionary Computation 22, no. 4 (2014): 679–709. http://dx.doi.org/10.1162/evco_a_00132.

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The convergence behaviors of so-called natural evolution strategies (NES) and of the information-geometric optimization (IGO) approach are considered. After a review of the NES/IGO ideas, which are based on information geometry, the implications of this philosophy w.r.t. optimization dynamics are investigated considering the optimization performance on the class of positive quadratic objective functions (the ellipsoid model). Exact differential equations describing the approach to the optimizer are derived and solved. It is rigorously shown that the original NES philosophy optimizing the expec

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Lewi, Jeremy, Robert Butera, and Liam Paninski. "Sequential Optimal Design of Neurophysiology Experiments." Neural Computation 21, no. 3 (2009): 619–87. http://dx.doi.org/10.1162/neco.2008.08-07-594.

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Adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical models of neural systems. However, application of adaptive methods to neurophysiology has been limited by severe computational challenges. Since most neurons are high-dimensional systems, optimizing neurophysiology experiments requires computing high-dimensional integrations and optimizations in real time. Here we present a fast algorithm for choosing the most informative stimulus by maximizing the mutual information between the data and the unknown parameters

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Solodovnikov, A. N. "Models of early destruction of Scots pine needles in the middle taiga of Eastern Fennoscandia." Dokuchaev Soil Bulletin, no. 122 (March 26, 2025): 41–61. https://doi.org/10.19047/0136-1694-2025-122-41-61.

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Decomposition of needle litter was studied in a series of three successive two-year experiments in a pine forest. The effect of the weather conditions proved to be significant only in the first two months of needle decomposition. Analysis of the dynamics of needle degradation in our experiments shows the early needle destruction process falls into three phases: fast (the first warm period, up to ~30% needle mass loss); moderate (from the onset of the first cold period to the onset of the second cold period, ~30% to ~55% total needle mass loss); slow (from the onset of the second cold period, f

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Lanzerstorfer, Daniel, and Hendrik C. Kuhlmann. "Global stability of the two-dimensional flow over a backward-facing step." Journal of Fluid Mechanics 693 (November 3, 2011): 1–27. http://dx.doi.org/10.1017/jfm.2011.399.

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AbstractThe two-dimensional, incompressible flow over a backward-facing step is considered for a systematic variation of the geometry covering expansion ratios (step to outlet height) from 0.25 to 0.975. A global temporal linear stability analysis shows that the basic flow becomes unstable to different three-dimensional modes depending on the expansion ratio. All critical modes are essentially confined to the region behind the step extending downstream up to the reattachment point of the separated eddy. An energy-transfer analysis is applied to understand the physical nature of the instabiliti

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Leguillon, Dominique. "Comparison of Matched Asymptotics, Multiple Scalings and Averages in Homogenization of Periodic Structures." Mathematical Models and Methods in Applied Sciences 07, no. 05 (1997): 663–80. http://dx.doi.org/10.1142/s0218202597000359.

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Historically, homogenization of periodic structures has been first investigated by the method of multiple scalings expansions. More recently, an interpretation has been given in terms of averages and effective moduli. Both approaches involve a slow variable at the macroscopic scale, and a fast one at the microscopic level. The periodicity of the solutions with respect to the second variable is a strong assumption made prior to any analysis. Although involving similar calculations, the two approaches differ and it is not so obvious to link them together. The matched asymptotic expansions presen

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Cai, Yuhua, and Stefan A. H. Geritz. "Resident-invader dynamics of similar strategies in fluctuating environments." Journal of Mathematical Biology 81, no. 4-5 (2020): 907–59. http://dx.doi.org/10.1007/s00285-020-01532-8.

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Abstract We study resident-invader dynamics in fluctuating environments when the invader and the resident have close but distinct strategies. First we focus on a class of continuous-time models of unstructured populations of multi-dimensional strategies, which incorporates environmental feedback and environmental stochasticity. Then we generalize our results to a class of structured population models. We classify the generic population dynamical outcomes of an invasion event when the resident population in a given environment is non-growing on the long-run and stochastically persistent. Our ap

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Tulin, Marshall P., Yitao Yao, and Pei Wang. "The Generation and Propagation of Ship Internal Waves in a Generally Stratified Ocean at High Densimetric Froude Numbers, Including Nonlinear Effects." Journal of Ship Research 44, no. 03 (2000): 197–227. http://dx.doi.org/10.5957/jsr.2000.44.3.197.

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A nonlinear theory for internal wave generation and propagation is derived here for slender ships traveling at high densimetric Froude number (Fh &gt;&gt; 1) in water of small density variation. It is based on an asymptotic equation for the evolution of the internal wave vorticity generated under the ship by a known inviscid ship flow and then self-propagating in the wake. In its numerical implementation, arbitrary pycnoclines and slender ship hulls may be used, and boundary conditions on the ship hull are satisfied; the free surface is treated here as rigid, although this may be relax

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Cheng, Xin, Huashan Liu, and Wenke Lu. "Chattering-Suppressed Sliding Mode Control for Flexible-Joint Robot Manipulators." Actuators 10, no. 11 (2021): 288. http://dx.doi.org/10.3390/act10110288.

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In this paper, sliding mode tracking control and its chattering suppression method are investigated for flexible-joint robot manipulators with only state measurements of joint actuators. First, within the framework of singular perturbation theory, the control objective of the system is decoupled into two typical tracking aims of a slow subsystem and a fast subsystem. Then, considering lumped uncertainties (including dynamics uncertainties and external disturbances), a composite chattering-suppressed sliding mode controller is proposed, where a smooth-saturation-function-contained reaching law

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BABIN, A., and A. FIGOTIN. "LINEAR SUPERPOSITION IN NONLINEAR WAVE DYNAMICS." Reviews in Mathematical Physics 18, no. 09 (2006): 971–1053. http://dx.doi.org/10.1142/s0129055x06002851.

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We study nonlinear dispersive wave systems described by hyperbolic PDE's in ℝd and difference equations on the lattice ℤd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pasta–Ulam model and many other not completely integrable systems, satisfy a superposition principle. The principle essentially states that if a nonlinear evolution of a wave starts initially as a sum of ge

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Yan, Sun-ting, Xiaoli Shen, and Zhijiang Jin. "Static and dynamic symmetric snap-through of non-uniform shallow arch under a pair of end moments considering critical slowing-down effect." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 16 (2019): 5735–62. http://dx.doi.org/10.1177/0954406219855105.

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This paper presents analytical analysis of static and dynamic symmetric snap-through of non-uniform shallow circular shallow arch under a pair of end moments with the same magnitude. The non-uniformity is characterized by dividing the arch into three piecewise constant-stiffness segments. Hamilton's principle is used to derive the governing differential equations by assuming negligible axial inertia. The snap-through load and snap-through criterion are analyzed in detail and by an index plot, the stiffer center case is shown to behave distinctly when stiffer end case is compared. The dynamic s

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KUO, ALLEN C., and LORENZO M. POLVANI. "Wave–vortex interaction in rotating shallow water. Part 1. One space dimension." Journal of Fluid Mechanics 394 (September 10, 1999): 1–27. http://dx.doi.org/10.1017/s0022112099005534.

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Using a physical space (i.e. non-modal) approach, we investigate interactions between fast inertio-gravity (IG) waves and slow balanced flows in a shallow rotating fluid. Specifically, we consider a train of IG waves impinging on a steady, exactly balanced vortex. For simplicity, the one-dimensional problem is studied first; the limitations of one-dimensionality are offset by the ability to define balance in an exact way. An asymptotic analysis of the problem in the small-amplitude limit is performed to demonstrate the existence of interactions. It is shown that these interactions are not conf

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CAMASSA, ROBERTO, TERRY JO LEITERMAN, and RICHARD M. MCLAUGHLIN. "Trajectory and flow properties for a rod spinning in a viscous fluid. Part 1. An exact solution." Journal of Fluid Mechanics 612 (October 10, 2008): 153–200. http://dx.doi.org/10.1017/s0022112008000918.

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An exact mathematical solution for the low-Reynolds-number quasi-steady hydrodynamic motion induced by a rod in the form of a prolate spheroid sweeping a symmetric double cone is developed, and the influence of the ensuing fluid motion upon passive particles is studied. The resulting fluid motion is fully three-dimensional and time varying. The advected particles are observed to admit slow orbits around the rotating rods and a fast epicyclic motion roughly commensurate with the rod rotation rate. The epicycle amplitudes, vertical fluctuations, arclengths and angle travelled per rotation are ma

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NARASIMHA, RODDAM. "THE CONTRIBUTION OF THE BHATNAGAR–GROSS–KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE." International Journal of Modern Physics C 25, no. 01 (2013): 1340025. http://dx.doi.org/10.1142/s0129183113400251.

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The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of th

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Bonforte, Matteo, Gabriele Grillo, and Juan Luis Vázquez. "Special Fast Diffusion with Slow Asymptotics: Entropy Method and Flow on a Riemannian Manifold." Archive for Rational Mechanics and Analysis 196, no. 2 (2009): 631–80. http://dx.doi.org/10.1007/s00205-009-0252-7.

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WEBB, G. M., A. R. ZAKHARIAN, M. BRIO, and G. P. ZANK. "Parametric instabilities and wave coupling in Alfvén simple waves." Journal of Plasma Physics 66, no. 3 (2001): 167–212. http://dx.doi.org/10.1017/s0022377801001283.

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A wave coupling formalism for magnetohydrodynamic (MHD) waves in a non-uniform background flow is used to study parametric instabilities of the large-amplitude, circularly polarized, simple plane Alfvén wave in one Cartesian space dimension. The large-amplitude Alfvén wave (the pump wave) is regarded as the background flow, and the seven small-amplitude MHD waves (the backward and forward fast and slow magnetoacoustic waves, the backward and forward Alfvén waves, and the entropy wave) interact with the pump wave via wave coupling coefficients that depend on the gradients and time dependence of

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Spiliopoulos, Konstantinos. "Fluctuation analysis and short time asymptotics for multiple scales diffusion processes." Stochastics and Dynamics 14, no. 03 (2014): 1350026. http://dx.doi.org/10.1142/s0219493713500263.

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We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise naturally when one is interested in short time asymptotics of multiple scale diffusions. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. Depending on the order of interaction between the fast scale and the size of the noise, we get different behavior. In certain cases additional drift terms arise in

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Galí, Martí, Marcus Falls, Hervé Claustre, Olivier Aumont, and Raffaele Bernardello. "Bridging the gaps between particulate backscattering measurements and modeled particulate organic carbon in the ocean." Biogeosciences 19, no. 4 (2022): 1245–75. http://dx.doi.org/10.5194/bg-19-1245-2022.

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Abstract. Oceanic particulate organic carbon (POC) is a small but dynamic component of the global carbon cycle. Biogeochemical models historically focused on reproducing the sinking flux of POC driven by large fast-sinking particles (LPOC). However, suspended and slow-sinking particles (SPOC, here < 100 µm) dominate the total POC (TPOC) stock, support a large fraction of microbial respiration, and can make sizable contributions to vertical fluxes. Recent developments in the parameterization of POC reactivity in PISCES (Pelagic Interactions Scheme for Carbon and Ecosystem Studies model; PISC

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Chen, Nawei, Shenglong Chen, Xiaoyu Li, and Zhiming Li. "Modelling and analysis of the HIV/AIDS epidemic with fast and slow asymptomatic infections in China from 2008 to 2021." Mathematical Biosciences and Engineering 20, no. 12 (2023): 20770–94. http://dx.doi.org/10.3934/mbe.2023919.

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<abstract><p>The aim of this paper is to investigate the spread of the HIV/AIDS epidemic in China during 2008–2021. A new mathematical model is proposed to study the dynamics of HIV transmission with acute infection, fast asymptomatic infections, and slow asymptomatic infections. The basic reproduction number is obtained by the next-generation matrix method. A quantitative analysis of the model, including the local behavior, global behavior, and permanence, is performed. Numerical simulations are presented to enhance the results of these analyses. The behavior or the model's parame

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Liu, Yang, and Haixia Wu. "Analysis on Global Asymptotical Stability of Genetic Regulatory Networks with Time-Varying Delays via Convex Combination Method." Mathematical Problems in Engineering 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/303918.

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The global asymptotical stability analysis for genetic regulatory networks with time delays is concerned. By using Lyapunov functional theorem, LMIs, and convex combination method, a new delay-dependent stability criterion has been presented in terms of LMIs to guarantee the delayed genetic regulatory networks to be asymptotically stable. The restriction that the derivatives of the time-varying delays are less than one is removed. Our result is applicable to both fast and slow time-varying delays. The stability criterion has less conservative and wider application range. Experimental result ha

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Cheng, Chih-Hsiu, Kwan-Hwa Lin, Jiu-Jenq Lin, and Jaw-Lin Wang. "CERVICAL ELECTROMYOGRAPHIC ACTIVITIES DURING NECK MOVEMENTS AT DIFFERENT SPEEDS IN HEALTHY SUBJECTS: VOLUNTARY RESPONSE INDEX ANALYSIS." Biomedical Engineering: Applications, Basis and Communications 19, no. 06 (2007): 349–57. http://dx.doi.org/10.4015/s1016237207000458.

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The assessment of cervical muscle control patterns is important for the diagnosis of cervical dysfunction. Voluntary response index (VRI), including the similarity index (SI) and the magnitude (MAG), provides quantitative analysis of the surface electromyography (sEMG) pattern and total muscle voluntary activities respectively. This study was to investigate the effect of movement directions and speeds of the VRI response of cervical muscles in healthy subjects. The sEMG of bilateral sternocleidomastoid, semispinalis capitis, and splenius capitis were measured in thirteen asymptomatic young sub

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McAuliffe, Seán, Ariane Tabuena, Karen McCreesh, et al. "Altered Strength Profile in Achilles Tendinopathy: A Systematic Review and Meta-Analysis." Journal of Athletic Training 54, no. 8 (2019): 889–900. http://dx.doi.org/10.4085/1062-6050-43-18.

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Background Persistent strength deficits secondary to Achilles tendinopathy (AT) have been postulated to account for difficulty engaging in tendon-loading movements, such as running and jumping, and may contribute to the increased risk of recurrence. To date, little consensus exists on the presence of strength deficits in AT. Consequently, researchers are uncertain about the appropriate methods of assessment that may inform rehabilitation in clinical practice. Objective To evaluate and synthesize the literature investigating plantar-flexion (PF) strength in individuals with AT. Study Selection

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Lewis, Joanna, Malcolm J. Price, Paddy J. Horner, and Peter J. White. "P003 Genital c. trachomatisinfections last longer in men than women, but are less likely to become established." Sexually Transmitted Infections 93, Suppl 1 (2017): A18.1—A18. http://dx.doi.org/10.1136/sextrans-2017-053232.49.

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IntroductionRigorous estimates for the duration of untreated chlamydia infection are important for understanding its epidemiology and designing control interventions, but are only available for women. We have estimated the duration of untreated infection in men.MethodsData came from published studies in which untreated, chlamydia-infected men were re-tested at a later date. We used analysis methods that had previously been applied to data from women, which allow for a new infection to take one of multiple courses, each clearing at a different rate. We determined the optimal number of possible

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Grande-Alonso, Mónica, Manuel Estradera-Bel, Carlos Forner-Álvarez, et al. "The Effects of Action Observation Speed on Motor Function in Patients with Chronic Low Back Pain: From Observation to Execution." Brain Sciences 15, no. 1 (2024): 31. https://doi.org/10.3390/brainsci15010031.

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Objective: The objective of this study was to examine the effect of observing actions at different speeds on the speed of motor task performance in subsequent actions. Methods: Sixty individuals, divided equally between those with non-specific chronic low back pain (NSCLBP) and asymptomatic subjects, were enrolled. Participants were further split into subgroups to observe lumbar flexion and Timed Up and Go (TUG) test actions at either a slow or fast pace, following a randomized assignment. For post-video observation, participants replicated the observed actions three times without specific per

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Noguera-Julian, Antoni, Emma Wilhelmi, Maria Cussó, et al. "Pharmacokinetic Analysis of an Isoniazid Suspension Among Spanish Children Under 6 Years of Age." Antibiotics 14, no. 1 (2025): 74. https://doi.org/10.3390/antibiotics14010074.

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Background: Isoniazid (INH) remains a first-line drug for the treatment of tuberculosis (TB) in young children. In 2010, the WHO recommended an increase in the daily dose of INH up to 10 (7–15) mg/kg. Currently, there are no INH suspensions available in Europe. Methods: We aimed to characterize the pharmacokinetics of a licensed INH suspension (10 mg/mL, Pharmascience Inc., Montreal, QC, Canada) in children receiving INH daily at 10 mg/kg in a single-center, open-label, non-randomized, phase IIa clinical trial (EudraCT Number: 2016-002000-31) in Barcelona (Spain). Samples were analyzed using a

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Machado Reyes, Diego, Hanqing Chao, Juergen Hahn, Li Shen, and Pingkun Yan. "Identifying Progression-Specific Alzheimer’s Subtypes Using Multimodal Transformer." Journal of Personalized Medicine 14, no. 4 (2024): 421. http://dx.doi.org/10.3390/jpm14040421.

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Alzheimer’s disease (AD) is the most prevalent neurodegenerative disease, yet its current treatments are limited to stopping disease progression. Moreover, the effectiveness of these treatments remains uncertain due to the heterogeneity of the disease. Therefore, it is essential to identify disease subtypes at a very early stage. Current data-driven approaches can be used to classify subtypes during later stages of AD or related disorders, but making predictions in the asymptomatic or prodromal stage is challenging. Furthermore, the classifications of most existing models lack explainability,

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Dave, A., K. E. Sprecher, K. K. Lui, et al. "0422 Apocalypse Tau: The Relationship Between Inflammaging and Local Sleep Disruption in Older Adults is Mediated by Tau Burden." Sleep 43, Supplement_1 (2020): A161—A162. http://dx.doi.org/10.1093/sleep/zsaa056.419.

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Abstract Introduction Chronic inflammation in aging is independently associated with tau burden and sleep disruption, though the mechanism linking inflammation with sleep disruption remains unknown. Recent evidence associates tau burden with deficits in local expression of sleep spindles and slow wave activity (SWA). Here we test the hypothesis that age-related central inflammation disrupts local sleep by influencing tau pathology. Methods Cognitively asymptomatic older adults from the Wisconsin Alzheimer’s Disease Research Center underwent overnight polysomnography with high-density electroen

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