scholarly journals The Nonlinear Dynamics of Time-Dependent Subcritical Baroclinic Currents

2007 ◽  
Vol 37 (4) ◽  
pp. 1001-1021 ◽  
Author(s):  
G. R. Flierl ◽  
J. Pedlosky
Keyword(s):  
Nonlinear Dynamics ◽  
Small Degree ◽  
Mean Value ◽  
Time Dependent ◽  
Unstable Wave ◽  
Amplitude Dependence ◽  
Strongly Nonlinear ◽  
System A ◽  
Turbulent Characteristics ◽  
Baroclinic Currents

Abstract The nonlinear dynamics of baroclinically unstable waves in a time-dependent zonal shear flow is considered in the framework of the two-layer Phillips model on the beta plane. In most cases considered in this study the amplitude of the shear is well below the critical value of the steady shear version of the model. Nevertheless, the time-dependent problem in which the shear oscillates periodically is unstable, and the unstable waves grow to substantial amplitudes, in some cases with strongly nonlinear and turbulent characteristics. For very small values of the shear amplitude in the presence of dissipation an analytical, asymptotic theory predicts a self-sustained wave whose amplitude undergoes a nonlinear oscillation whose period is amplitude dependent. There is a sensitive amplitude dependence of the wave on the frequency of the oscillating shear when the shear amplitude is small. This behavior is also found in a truncated model of the dynamics, and that model is used to examine larger shear amplitudes. When there is a mean value of the shear in addition to the oscillating component, but such that the total shear is still subcritical, the resulting nonlinear states exhibit a rectified horizontal buoyancy flux with a nonzero time average as a result of the instability of the oscillating shear. For higher, still subcritical, values of the shear, a symmetry breaking is detected in which a second cross-stream mode is generated through an instability of the unstable wave although this second mode would by itself be stable on the basic time-dependent current. For shear values that are substantially subcritical but of order of the critical shear, calculations with a full quasigeostrophic numerical model reveal a turbulent flow generated by the instability. If the beta effect is disregarded, the inviscid, linear problem is formally stable. However, calculations show that a small degree of nonlinearity is enough to destabilize the flow, leading to large amplitude vacillations and turbulence. When the most unstable wave is not the longest wave in the system, a cascade up scale to longer waves is observed. Indeed, this classically subcritical flow shows most of the qualitative character of a strongly supercritical flow. This result supports previous suggestions of the important role of background time dependence in maintaining the atmospheric and oceanic synoptic eddy field.

Three-Dimensional Computations of Transport and Growth for Crystal Growth Systems

2000 ◽  
Author(s):  
Jeffrey J. Derby ◽  
Andrew Yeckel
Keyword(s):  
Finite Element ◽  
Crystal Growth ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Bulk Crystal ◽  
Time Dependent ◽  
Engineering Systems ◽  
Bulk Crystal Growth ◽  
Strongly Nonlinear ◽  
Parallel Supercomputers

Abstract Modern finite element methods implemented on parallel supercomputers promise to allow the study of three-dimensional, time-dependent continuum phenomena in many engineering systems. This paper shows several examples of the fruitful application of these approaches to bulk crystal growth systems, where strongly nonlinear coupled phenomena are important.

Localized and Non-Localized Normal Modes in a Strongly Nonlinear Discrete System

1991 ◽  
Author(s):  
Alexander F. Vakakis
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Linear Vibration ◽  
Mode Localization ◽  
Linear Mode ◽  
Strongly Nonlinear ◽  
System A ◽  
Coupling Stiffness ◽  
Nonlinear Normal ◽  
Nonlinear Discrete System

Abstract The free oscillations of a strongly nonlinear, discrete oscillator are examined by computing its “nonsimilar nonlinear normal modes.” These are motions represented by curves in the configuration space of the system, and they are not encountered in classical, linear vibration theory or in existing nonlinear perturbation techniques. For an oscillator with weak coupling stiffness and “mistiming,” both localized and nonlocalized modes are detected, occurring in small neighborhoods of “degenerate” and “global” similar modes of the “tuned” system. When strong coupling is considered, only nonlocalized modes are found to exist. An interesting result of this work is the detection of mode localization in the “tuned” periodic system, a result with no counterpart in existing theories on linear mode localization.

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Comparative DFT study for molecular geometries and spectra of methyl pheophorbides-a: test of M06-2X and two other functionals

2010 ◽  
Vol 14 (07) ◽  
pp. 592-604 ◽  
Author(s):  
Do Sung Huh ◽  
Sang Joon Choe
Keyword(s):  
Density Functional Theory ◽  
Standard Deviation ◽  
Density Functional ◽  
Visible Spectrum ◽  
Mean Value ◽  
Time Dependent ◽  
Dft Methods ◽  
Functional Theory ◽  
Td Dft ◽  
The Mean

The recent interest in the application of density functional theory (DFT) has prompted us to test several functions in molecular geometries of methyl pheophorbides-a (MPa), an important starting material in photodynamic therapy (PDT). In this study, we report on tests for three popular DFT methods: M06-2X, B3LYP, and LSDA. Based on the standard deviation and the mean value, and by using the difference between optimized calculated value and experimental value in geometries, we drew the following conclusions: M06-2X/6-311+G(d,p) attained the smallest standard deviation of difference among the tested DFT methods in terms of bond length, whereas the standard deviation of bond angle in LSDA/6-311+G(d,p) was the smallest. In terms of absolute value, the mean value of LSDA/6-311+G(d,p) calculation was larger than that of M06-2X/6-311+G(d,p). We found that M06-2X/6-311+G(d,p) gave the best performance for MPa in the molecular geometries. The UV-visible spectrum was calculated with time-dependent density-functional theory (TD-DFT). Time-dependent M06-2X/6-311+G(d,p) gave the best performance for MPa in CH2Cl2 solution. In general, TD-DFT calculations in CH2Cl2 solution were more red-shifted compared with those in the solid state.

scholarly journals Compacting the description of a time-dependent multivariable system and its multivariable driver by reducing the state vectors to aggregate scalars: the Earth's solar-wind-driven magnetosphere

2019 ◽  
Vol 26 (4) ◽  
pp. 429-443 ◽  
Author(s):  
Joseph E. Borovsky ◽  
Adnane Osmane
Keyword(s):  
Solar Wind ◽  
State Vector ◽  
Complexity Analysis ◽  
Low Noise ◽  
Time Dependent ◽  
Permutation Entropy ◽  
System Response ◽  
System A ◽  
Driven System ◽  
Time Dependent System

Abstract. Using the solar-wind-driven magnetosphere–ionosphere–thermosphere system, a methodology is developed to reduce a state-vector description of a time-dependent driven system to a composite scalar picture of the activity in the system. The technique uses canonical correlation analysis to reduce the time-dependent system and driver state vectors to time-dependent system and driver scalars, with the scalars describing the response in the system that is most-closely related to the driver. This reduced description has advantages: low noise, high prediction efficiency, linearity in the described system response to the driver, and compactness. The methodology identifies independent modes of reaction of a system to its driver. The analysis of the magnetospheric system is demonstrated. Using autocorrelation analysis, Jensen–Shannon complexity analysis, and permutation-entropy analysis the properties of the derived aggregate scalars are assessed and a new mode of reaction of the magnetosphere to the solar wind is found. This state-vector-reduction technique may be useful for other multivariable systems driven by multiple inputs.

Prolonged incubation of skeletal muscle increases system A amino acid transport

1991 ◽  
Vol 260 (1) ◽  
pp. C88-C95 ◽  
Author(s):  
E. A. Gulve ◽  
G. D. Cartee ◽  
J. H. Youn ◽  
J. O. Holloszy
Keyword(s):  
Skeletal Muscle ◽  
Amino Acids ◽  
Amino Acid ◽  
Amino Acid Transport ◽  
Time Dependent ◽  
Acid Transport ◽  
Minimum Essential Medium ◽  
Prolonged Incubation ◽  
System A ◽  
Nonessential Amino Acids

During the course of experiments involving prolonged incubation of skeletal muscle, we observed large increases in system A amino acid transport activity. System A activity was monitored with the nonmetabolizable amino acid analogue alpha-(methylamino)isobutyrate (MeAIB). When rat epitrochlearis muscles are incubated in Krebs-Henseleit buffer supplemented with 0.1% bovine serum albumin and 8 mM glucose, basal MeAIB transport doubles after 5 h and is elevated approximately sevenfold after 9 h compared with rates measured in muscles incubated for 1 h. Insulin-stimulated transport also doubles after 5 h and increases by fourfold after 9 h. The increases in basal and insulin-stimulated system A transport over time can be prevented by incubating muscles in the presence of cycloheximide. Addition of minimum essential medium essential amino acids (EAA) to the incubation medium blocks the increase in basal and insulin-stimulated MeAIB transport measured after 9 h by 85-90 and 60%, respectively. A single amino acid, glutamine, can account for half of the inhibitory effect of EAA on the time-dependent increase in basal system A transport. Amino acid metabolism is not necessary for inhibition of the rise in basal MeAIB transport. At concentrations normally present in minimum essential medium, nonessential amino acids are less effective (51% inhibition) in preventing the rise in basal transport occurring over 9 h. At three times normal concentrations, however, the ability of nonessential amino acids to prevent the time-dependent increases in basal and insulin-stimulated MeAIB transport is comparable to that of EAA. These changes in MeAIB transport with prolonged incubation are not due to muscle deterioration.(ABSTRACT TRUNCATED AT 250 WORDS)

Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty

2005 ◽  
Vol 128 (2) ◽  
pp. 503-508 ◽  
Author(s):  
Michael Kokkolaras ◽  
Zissimos P. Mourelatos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Uncertainty Propagation ◽  
Mean Value ◽  
Multilevel Systems ◽  
System A ◽  
Engine Design ◽  
Advanced Mean Value ◽  
Mean Value Method ◽  
Propagation Technique ◽  
Bottom To Top

This paper presents a methodology for design optimization of hierarchically decomposed systems under uncertainty. We propose an extended, probabilistic version of the deterministic analytical target cascading (ATC) formulation by treating uncertain quantities as random variables and posing probabilistic design constraints. A bottom-to-top coordination strategy is used for the ATC process. Given that first-order approximations may introduce unacceptably large errors, we use a technique based on the advanced mean value method to estimate uncertainty propagation through the multilevel hierarchy of elements that comprise the decomposed system. A simple yet illustrative hierarchical bilevel engine design problem is used to demonstrate the proposed methodology. The results confirm the applicability of the proposed probabilistic ATC formulation and the accuracy of the uncertainty propagation technique.

NONLINEAR DYNAMICS AND THE SYNTHESIS OF ZEBRA FINCH SONG

2012 ◽  
Vol 22 (10) ◽  
pp. 1250235 ◽  
Author(s):  
YONATAN SANZ PERL ◽  
EZEQUIEL M. ARNEODO ◽  
ANA AMADOR ◽  
GABRIEL B. MINDLIN
Keyword(s):  
Nonlinear Dynamics ◽  
Animal Model ◽  
Nervous System ◽  
Zebra Finch ◽  
Brain Structures ◽  
Complex Behavior ◽  
Acoustic Features ◽  
System A ◽  
Zebra Finch Song ◽  
Vocal Organ

Behavior emerges as the interaction between a nervous system, a peripheral biomechanical device and the environment. In birdsong production, this observation is particularly important: songbirds are an adequate animal model to unveil how brain structures reconfigure themselves during learning of a complex behavior as song. Therefore, it is important to understand which features of behavior are controlled by independent tuning of neurophysiological parameters, and which are constrained by the biomechanics of the peripheral vocal organ. In this work, we show that many of the acoustic features in the Zebra finch song are in fact conditioned by the biomechanics involved.

Secondary Instabilities in Breaking Inertia–Gravity Waves

2012 ◽  
Vol 69 (1) ◽  
pp. 303-322 ◽  
Author(s):  
Mark D. Fruman ◽  
Ulrich Achatz
Keyword(s):  
Normal Mode ◽  
Gravity Waves ◽  
Singular Vector ◽  
Initial Conditions ◽  
Velocity Shear ◽  
Time Dependent ◽  
Unstable Wave ◽  
Singular Vectors ◽  
Secondary Instabilities ◽  
Inertia Gravity Waves

Abstract The three-dimensionalization of turbulence in the breaking of nearly vertically propagating inertia–gravity waves is investigated numerically using singular vector analysis applied to the Boussinesq equations linearized about three two-dimensional time-dependent basic states obtained from nonlinear simulations of breaking waves: a statically unstable wave perturbed by its leading transverse normal mode, the same wave perturbed by its leading parallel normal mode, and a statically stable wave perturbed by a leading transverse singular vector. The secondary instabilities grow through interaction with the buoyancy gradient and velocity shear in the basic state. Which growth mechanism predominates depends on the time-dependent structure of the basic state and the wavelength of the secondary perturbation. The singular vectors are compared to integrations of the linear model using random initial conditions, and the leading few singular vectors are found to be representative of the structures that emerge in the randomly initialized integrations. A main result is that the length scales of the leading secondary instabilities are an order of magnitude smaller than the wavelength of the initial wave, suggesting that the essential dynamics of the breaking might be captured by tractable nonlinear three-dimensional simulations in a relatively small triply periodic domain.

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