Frequency Selection Criterion Research Articles

Effects of Electroacupuncture at Varied Frequencies on Analgesia and Mechanisms in Sciatic Nerve Cuffing-Induced Neuropathic Pain Mice

Addressing the intricate challenge of chronic neuropathic pain has significant implications for the physical and psychological well-being of patients, given its enduring nature. In contrast to opioids, electroacupuncture (EA) may potentially provide a safer and more efficacious therapeutic alternative. Our objective is to investigate the distinct analgesic effects and potential mechanisms of EA at frequencies of 2 Hz, 100 Hz, and 18 kHz in order to establish more precise frequency selection criteria for clinical interventions. Analgesic efficacy was evaluated through the measurement of mice’s mechanical and thermal pain thresholds. Spinal cord inflammatory cytokines and neuropeptides were quantified via Quantitative Real-time PCR (qRT-PCR), Western blot, and immunofluorescence. Additionally, RNA sequencing (RNA-Seq) was conducted on the spinal cord from mice in the 18 kHz EA group for comprehensive transcriptomic analysis. The analgesic effect of EA on neuropathic pain in mice was frequency-dependent. Stimulation at 18 kHz provided superior and prolonged relief compared to 2 Hz and 100 Hz. Our research suggests that EA at frequencies of 2 Hz, 100 Hz, and 18 kHz significantly reduce the release of inflammatory cytokines. The analgesic effects of 2 Hz and 100 Hz stimulation are due to frequency-dependent regulation of opioid release in the spinal cord. Furthermore, 18 kHz stimulation has been shown to reduce spinal neuronal excitability by modulating the serotonergic pathway and downstream receptors in the spinal cord to alleviate neuropathic pain.

Linear analysis of a swirling jet with a realistic swirler model

The dynamics of an axisymmetrical swirling jet is studied via global linear stability and resolvent analyses. The modeled flow represents a combustor-like swirling jet, that is turbulent, compressible, non-parallel, and enclosed. In particular, the computational domain embeds a realistic axisymmetrical swirler model to resolve the mode conversion process. Swirl fluctuations are non-negligible on this configuration representative of a swirl burner, and match the analytical mode shapes of inertial waves of an inviscid uniform flow as obtained from global stability analysis. The stability map presents two eigenvalues driving a modal amplification. These eigenmodes couple a standing acoustic wave sustained in the mixing duct and the combustion chamber with the Kelvin-Helmholtz mechanism at the mixing duct exit and the acoustic-vorticity mode conversion process at the swirler, and act as a frequency selection criterion. Finally, the most amplified forcing from the resolvent analysis is similar to an unsteady heat source in the combustion chamber, and the identified optimal amplification mechanism is likely to be triggered in reacting flow with unsteady heat release rate.

An improved protection scheme of the ground electrode line based on two frequency components injection

The ground electrode line plays an important part in the high-voltage direct current (HVDC) systems. For the protection of the ground electrode line, the electrode line impedance supervision system is designed. However, the system has a dead zone problem. And the existing analysis on the protection scheme is not complete, because the model used in the analysis is not accurate. Therefore, an accurate analysis of the measured impedance under the normal operation and different types of faults was given in this paper, to find the property of the impedance. Based on the derivation, an improved protection scheme was proposed, which mainly consists of the injection of the signal of two frequency components to eliminate the dead zones of each other, and the frequency selection criterion. The dead zones can be eliminated greatly with the proposed scheme, and the proposed scheme has a high reliability and a strong ability to endure high transition resistance, which was verified by lots of simulation cases based on the PSCAD/EMTDC.

Phase Difference Measurement of Under-Sampled Sinusoidal Signals for InSAR System Phase Error Calibration.

Phase difference measurement of sinusoidal signals can be used for phase error calibration of the spaceborne single-pass interferometric synthetic aperture radar (InSAR) system. However, there are currently very few papers devoted to the discussion of phase difference measurement of high-frequency internal calibration signals of the InSAR system, especially the discussion of sampling frequency selection and the corresponding measuring method when the high-frequency signals are sampled under the under-sampling condition. To solve this problem, a phase difference measurement method for high-frequency sinusoidal signals is proposed, and the corresponding sampling frequency selection criteria under the under-sampling condition is determined. First, according to the selection criteria, the appropriate under-sampling frequency was chosen to sample the two sinusoidal signals with the same frequency. Then, the sampled signals were filtered by limited recursive average filtering (LRAF) and coherently accumulated in the cycle of the baseband signal. Third, the filtered and accumulated signals were used to calculate the phase difference of the two sinusoidal signals using the discrete Fourier transform (DFT), digital correlation (DC), and Hilbert transform (HT)-based methods. Lastly, the measurement accuracy of the three methods were compared respectively by different simulation experiments. Theoretical analysis and experiments verified the effectiveness of the proposed method for the phase error calibration of the InSAR system.

Three-Step Switching Frequency Selection Criteria for Symmetrical CLLC-Type DC Transformer in Hybrid AC/DC Microgrid

In a hybrid ac/dc microgrid, the symmetrical CLLC-type dc transformer (CLLC-DCT) generally operates at the resonant frequency with the simple and low-cost semi-regulated open-loop scheme to ensure the power transmission (PT). However, more than one resonant frequency may exist, and they feature different characteristics for DCT. Meanwhile, the practical resonant frequencies are varying with temperature and power, which will degrade the PT ability if the switching frequency selection is not considered. Therefore, a switching frequency selection criteria (SFSC) approach is put forward for the symmetrical CLLC-DCT. For convenience, the active PT ratio (APTR) is employed as evaluation index of SFSC. First of all, the number and accurate values of resonant frequency are achieved in Step I. Then, in Step II, the optimal resonant frequency is determined as APTR-based criterion. In Step III, the parameter-variation-based criterion is presented to determine switching frequency. Finally, the experimental results verify that the semiregulated DCT based on the proposed approach not only improves efficiency, but also achieves the approximate PT ability with the relatively high-cost closed-loop controlled DCT.

Three-Step Switching Frequency Selection Criteria for the Generalized CLLC-Type DC Transformer in Hybrid AC–DC Microgrid

For hybrid ac–dc microgrids, the widely applied high-frequency dc transformer (DCT) is usually scheduled to operate at resonant frequency with 50% duty-cycle-based semiregulated control to ensure the power transmission (PT), improve its power-density, and simplify the system-level control. However, for a real DCT, it may exist more than one resonant frequency that exhibit totally different features, which may seriously degrade the PT ability if the inappropriate switching frequency is selected. Meanwhile, the actual values of the DCT inductances and capacitances are also changing with the power, temperature, etc., which may lead to the practical resonant frequency's variation. Thus, how to select the suitable switching frequency to guarantee the PT ability against the parameter variation becomes a challenge. In this paper, three-step switching frequency selection criteria (SFSC) are proposed. A generalized CLLC -type DCT (GCLLC-DCT) model is extracted to make the proposed approach available for the LLC -, CLL -, symmetric CLLC -, and asymmetric CLLC -type topologies. For convenience, the definition of the active power transmission ratio (APTR) is introduced to help evaluate the PT ability. First, the number, value, and impact variables of the resonant frequency are derived and analyzed in Step I as the preliminary. Afterward, the optimum resonant frequency is confirmed for the GCLLC-DCT as the criterion based on the APTR in Step II. At last, the criterion in Step III is given to finally determine the switching frequency against the parameter variations. The proposed SFSC method is also validated by the experiments.

Transient evolution of the global mode in turbulent swirling jets: Experiments and modal stability analysis

Swirling jets undergoing vortex breakdown are dominated by a strong coherent structure that is characterized by a precessing vortex core and the large-scale roll-up of the shear layers. These fully synchronized flow dynamics play an important role for the stabilization of swirl flames commonly applied in gas-turbine combustion. It is now well accepted that these flow dynamics are the manifestation of a saturated global instability triggered by a hydrodynamic feedback loop. Yet, the origin of this instability is still discussed controversially. Nonlinear wavefront theory predict the global mode to be selected in the lee of the breakdown bubble, while linear local and global stability analysis predict the region upstream of the breakdown bubble to be more influential. In this work, we intend to clarify this controversy. We consider a turbulent swirling jet undergoing a control parameter transient. The flow undergoes a transition from a globally stable non-vortex breakdown state to a state with a strong recirculation bubble and the associated global mode. High-speed Particle Image Velocimetry measurements are the basis for a local linear stability analysis of the temporarily evolving base flow. This analysis reveals that the onset of the global mode is strongly linked to the formation of the internal stagnation point. Several transition scenarios are discussed and the ability of a frequency selection criterion to predict the wavemaker location, frequency and growth rate of the global mode are evaluated. We find excellent agreement between the linear global mode frequency and the experimental results throughout the entire transient. The corresponding growth rate qualitatively conforms to experimental observations. We find no indication for a global mode that is selected in the lee of the breakdown bubble. The present study confirms that the flow upstream of the vortex breakdown bubble is most influential for the onset of the global mode. Given that the flow under investigation is fully turbulent, these results provide important guidelines for the control of this instability mechanism in real scale combustion applications.

Parametric resonance in unsteady watertable flow

The stability of unsteady open-channel flow down an inclined plane is studied using an iterative approach based on the direct and adjoint stability equations combined with a physically justified energy measure. An efficient parametric resonance mechanism has been identified between the exogenous base-flow oscillations and the intrinsic frequencies of streamwise disturbance vortices. This resonance results in strong amplification over a substantial range of the governing parameters, favouring streamwise elongated structures. The optimal frequency for a maximal disturbance response can be efficiently approximated from simpler steady calculations; two frequency-selection criteria are given for this purpose. The analysis generalizes earlier work on steady watertable flow and provides an effective framework and starting point for further work on pattern formation in harmonically forced open-channel flows.

A Skywave OTHR Adaptive Frequency Selection Method Based on Preliminary Criterion and Weighted Criterion

A skywave radar adaptive frequency selection method based on the preliminary criterion and the weighted criterion is presented. In this method, according to the various operational tasks, the frequency selection criterion is divided into the preliminary criterion and the weighted criterion based on the characteristic of the targets. The adaptive frequency selection of the skywave radar is achieved by the weighted computed of the frequency selection criterion. The feasibility and availability is demonstrated by an example.

Global modes with multiple saddle points

Significant progress has been made towards understanding the global stability of slowly-developing shear flows. The WKBJ theory developed by Patrick Huerre and his co-authors has proved absolutely central, with the result that both the linear and the nonlinear stability of a wide range of flows can now be understood in terms of their local absolute/convective instability properties. In many situations, the local absolute frequency possesses a single dominant saddle point in complex X-space (where X is the slow streamwise coordinate of the base flow), which then acts as a single wavemaker driving the entire global linear dynamics. In this paper we consider the more complicated case in which multiple saddles may act as the wavemaker for different values of some control parameter. We derive a frequency selection criterion in the general case, which is then validated against numerical results for the linearized third-order Ginzburg–Landau equation (which possesses two saddle points). We believe that this theory may be relevant to a number of flows, including the boundary layer on a rotating disk and the eccentric Taylor–Couette–Poiseuille flow.

EEG phase synchrony differences across visual perception conditions may depend on recording and analysis methods

Objective (1) To investigate the neural synchrony hypothesis by examining if there was more synchrony for upright than inverted Mooney faces, replicating a previous study; (2) to investigate whether inverted stimuli evoke neural synchrony by comparing them to a new scrambled control condition, less likely to produce face perception. Methods Multichannel EEG was recorded via nose reference while participants viewed upright, inverted, and scrambled Mooney face stimuli. Gamma-range spectral power and inter-electrode phase synchrony were calculated via a wavelet-based method for upright stimuli perceived as faces and inverted/scrambled stimuli perceived as non-faces. Results When the frequency of interest was selected from the upright condition exhibiting maximal spectral power responses (as in the previous study) greater phase synchrony was found in the upright than inverted/scrambled conditions. However, substantial synchrony was present in all conditions, suggesting that choosing the frequency of interest from the upright condition only may have been biased. In addition, artifacts related to nose reference contamination by micro-saccades were found to be differentially present across experimental conditions in the raw EEG. When frequency of interest was selected instead from each experimental condition and the data were transformed to a laplacian ‘reference free’ derivation, the between-condition phase synchrony differences disappeared. Spectral power differences were robust to the change in reference, but not the combined changes in reference and frequency selection criteria. Conclusions Synchrony differences between face/non-face perceptions depend upon frequency selection and recording reference. Optimal selection of these parameters abolishes differential synchrony between conditions. Significance Neural synchrony is present not just for face percepts for upright stimuli, but also for non-face percepts achieved for inverted/scrambled Mooney stimuli.

On the onset of nonlinear oscillations in a separating boundary-layer flow

The stability of a separating boundary-layer flow at the rear of a two-dimensional bump mounted on a flat plate is numerically investigated. Above a critical Reynolds number, the flow field is shown to undergo self-sustained two-dimensional low-frequency fluctuations in the upstream region of the separation bubble, evolving into aperiodic vortex shedding further downstream. The computed steady flow states below the critical Reynolds number are shown to be convectively unstable. On extrapolating the flow field to Reynolds numbers above criticality, some evidence is found that the onset of the oscillatory behaviour coincides with topological flow changes near the reattachment point leading to the rupture of the (elongated) recirculation bubble. The structural changes near reattachment are shown to trigger an abrupt local transition from convective to absolute instability, at low frequencies. On preventing the separation bubble from bursting by reaccelerating the flow by means of a second bump further downstream, the separated flow remains steady for increasing Reynolds numbers, until a local region of absolute instability in the upper part of the geometrically controlled recirculation bubble is produced. The resulting global instability consists of self-sustained nonlinear saturated perturbations oscillating at a well-defined frequency, very distinct from the the low-frequency motion of the elongated recirculation bubble in the single-bump geometry. A frequency selection criterion based on local absolute frequencies, which has been successfully applied to wake flows, is shown to accurately predict the global frequency.

Global and absolute instabilities of spatially developing open flows and media with algebraically decaying tails

In this paper we extend our recently developed theory of absolute instability of spatially developing localized open flows and media to treating the case when the physical properties of the base state tend algebraically to constant properties at ±∞. The Laplace–transformed problem Z x ( x , ω ) = [ A ( ω ) + ( x ) ] Z ( x , ω ) + g ( x , ω ) , governing the perturbation dynamics of the flow is treated as a dynamical system. Here, Z ( x, ω ) is the Laplace–transformed perturbation, x e R is the spatial coordinate, ω e C is a frequency (and a Laplace transform parameter) and g( x, ω ) is the source function. The analysis assumes that the entries of the tail matrix R ( x ) decay as | x |– α , when x → ± ∞, where α > 0 is sufficiently large. We impose no restriction on the rate of variability of R ( x ) in the finite domain. The Levinson theorem is used for obtaining decompositions of the fundamental matrix of the system, Φ ( x , ω ) = B ± ( x , ω ) e A ( ω ) x [ B ± ( 0 , ω ) ] - 1 with the asymptotics B±( x, ω ) = I + 0 |x|− ϵ), ϵ > 0, when x → ± ∞ , respectively, where I is the identity matrix, which parallel the Floquet decomposition in the spatially periodic case. By using these decompositions, the boundary conditions of decay of Z ( x, ω ), when x → ±∞, are formulated in terms of B ±( x,ω ) and of two projectors on the subspaces spanned by the eigenvectors and generalized eigenvectors of A ( ω ) having the eigenvalues with positive and, correspondingly, negative real parts. The boundary–value problem for Z ( x, ω ) is solved formally, and the dispersion relation functions, Dn ( ω ), for the global normal modes, for the corresponding regions, R n ⊂ C, n ⩾ 1, are expressed in terms of the projectors and the matrices B ±(0, ω ). When the associated uniform state, i.e. the one with R ( x ) being zero, is stable, the flow is shown to be globally unstable if and only if the function D 1( ω ) has a root in the upper ω –half–plane. A formal solution of the initial–value linear stability problem is obtained, and it is shown that the flow is absolutely unstable if and only if either the analytic continuation, D∼ 1( ω ), of D 1( ω ) has a root or one of the matrix functions B ±(0, ω ) has a singularity, for ω with Im ω > 0, or the associated uniform flow is absolutely unstable or a combination of the above holds. It is argued that the concept of local stability cannot be consistently defined for open inhomogeneous flows treated. We present a procedure for analysing a spatially developing open flow on global and absolute instabilities, and suggest a frequency–selection criterion for open flows with self–sustained oscillations.

Adolescents' Clothing Purchase Motivations, Information Sources, and Store Selection Criteria: A Comparison of Male/Female and Impulse/Nonimpulse Shoppers

The purpose of this study was to examine high school adolescents' clothing shopping frequency, expenditure, purchase motivations, information sources, and store selection criteria and to determine the similarities and differences between male and female as well as impulse and nonimpulse shoppers. A survey design was used to collect the data. One hundred thirty‐seven high school students, in 9th to 12th grade, 69 males and 68 females, were recruited. Similarities were found between male and female participants. They spent similar amounts of money on clothing and had similar degrees of conformity, sexual attraction, and recognition motivations. For both genders, friends were the most important clothing information source, and price was the most important criterion for store selection. Significant differences were also found between genders. Female participants shopped significantly more often than males and had higher recreation clothing purchase motivation. Certain information sources, such as friends and magazines/books, had more influence over clothing purchase decisions made by females compared to males. Certain criteria such as product variety/availability and store display carried more weight for females than males when making a store selection. When impulse and nonimpulse shoppers were compared, significant differences were found in all the clothing behaviors examined in the study (i.e., clothing shopping frequency, expenditure, purchase motivations, information sources, store selection criteria). Educational and marketing implications are recommended.

A dynamical system approach to the absolute instability of spatially developing localized open flows and media

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Brevdo Leonid 2002A dynamical system approach to the absolute instability of spatially developing localized open flows and mediaProc. R. Soc. Lond. A.4581375–1397http://doi.org/10.1098/rspa.2001.0912SectionRestricted accessA dynamical system approach to the absolute instability of spatially developing localized open flows and media Leonid Brevdo Leonid Brevdo Ecole Supérieure de Mécanique de Marseille, Université de la Méditerranée, IMT–Technopôle de Chôteau–Gombert, F 13451 Marseille Cedex 20, France Google Scholar Find this author on PubMed Search for more papers by this author Leonid Brevdo Leonid Brevdo Ecole Supérieure de Mécanique de Marseille, Université de la Méditerranée, IMT–Technopôle de Chôteau–Gombert, F 13451 Marseille Cedex 20, France Google Scholar Find this author on PubMed Search for more papers by this author Published:08 June 2002https://doi.org/10.1098/rspa.2001.0912AbstractAbsolute instability of spatially developing localized open flows is analysed by applying the Laplace transform in time to the corresponding initial–value linear stability problem, and treating the resulting boundary–value problem on R for the vector equation Zx(x, ω) = [A(ω) + R(x)]Z(x, ω) + g(x, ω) as a dynamical system. Here Z(x, ω) is the perturbation, x ϵR is the spatial coordinate, ω ϵC is a frequency (and a Laplace transform parameter), and g(x, ω) is the source function. The analysis assumes that the tail matrix R(x) decays faster than any exponential, when x → ±∞. No restriction on the rate of variability of R(x) in the finite domain is imposed. The boundary conditions of decay for Z(x, ω), when x → ±∞, are formulated in terms of two projectors on the subspaces spanned by the eigenvectors and generalized eigenvectors of A(ω) having the eigenvalues with positive and, correspondingly, negative real parts. The boundary–value problem is solved formally, and the dispersion relation function, D1(ω), for the global modes is expressed in terms of the projectors. It is shown that a spatially developing localized flow or medium is absolutely unstable if and only if either the associated uniform state, i.e. the one with R(x) being zero, is absolutely unstable, or D1(ω) = 0 has roots in the upper ω–half–plane, or both. When the associated uniform state is absolutely stable then D1(ω) is analytic in {ω ϵC | Im ω > 0}, the roots of D1(ω) with Im ω > 0 are the contributors to the absolute instability, and, in the analysis of absolute instability of the spatially localized flow, neither a consideration of the complexified physical coordinate nor the concept of saddle point in the complexified physical space is involved. This is in contrast to the currently widely used WKBJ approach to the absolute instability of spatially non–localized flows. We present a practically implementable procedure for analysing spatially developing localized flows on absolute instability, and suggest a frequency selection criterion for such flows with self–sustained oscillations. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Avery M and Scheel A (2022) Universal selection of pulled fronts, Communications of the American Mathematical Society, 10.1090/cams/8, 2:5, (172-231) Brevdo L (2018) Absolute and Convective Instabilities of Semi-bounded Spatially Developing Flows, Proceedings of the Steklov Institute of Mathematics, 10.1134/S0081543818010029, 300:1, (13-33), Online publication date: 1-Jan-2018. Holzer M and Scheel A (2014) Criteria for Pointwise Growth and Their Role in Invasion Processes, Journal of Nonlinear Science, 10.1007/s00332-014-9202-0, 24:4, (661-709), Online publication date: 1-Aug-2014. Brevdo L and Cirpka O (2012) Absolute/Convective Instability Dichotomy in a Soret-Driven Thermosolutal Convection Induced in a Porous Layer by Inclined Thermal and Vertical Solutal Gradients, Transport in Porous Media, 10.1007/s11242-012-0053-6, 95:2, (425-446), Online publication date: 1-Nov-2012. Brevdo L and Il'ichev A (2006) Uni-modal destabilization of a visco-elastic floating ice layer by wind stress, European Journal of Mechanics - A/Solids, 10.1016/j.euromechsol.2005.11.002, 25:3, (509-525), Online publication date: 1-May-2006. Langthjem M and Nakano M (2005) A numerical simulation of the hole-tone feedback cycle based on an axisymmetric discrete vortex method and Curle's equation, Journal of Sound and Vibration, 10.1016/j.jsv.2004.12.023, 288:1-2, (133-176), Online publication date: 1-Nov-2005. Brevdo L (2005) Convectively unstable wave packets in spatially developing open flows and media with algebraically decaying tails, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461:2053, (1-20), Online publication date: 8-Jan-2005.Brevdo L (2004) Linear stability theory for fronts with algebraically decaying tails, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460:2050, (3013-3035), Online publication date: 8-Oct-2004.Brevdo L (2003) Global and absolute instabilities of spatially developing open flows and media with algebraically decaying tails, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 459:2034, (1403-1425), Online publication date: 8-Jun-2003. This Issue08 June 2002Volume 458Issue 2022 Article InformationDOI:https://doi.org/10.1098/rspa.2001.0912Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/06/2002Published in print08/06/2002 License: Citations and impact Keywordsfrequency selection mechanismabsolute instabilityglobal discrete and continuous normal modesopen spatially developing localized flows and mediaglobal dispersion relationdynamical system approach

NONLINEAR SYNCHRONIZATION IN OPEN FLOWS

The selection criteria governing finite-amplitude synchronized oscillating states are discussed for model systems and real wake flows in a domain of infinite streamwise extent. Two types of nonlinear global modes are possible:hat modes with overall smoothly varying amplitude and elephant modes with a sharp front. The vortex street in wake flows is of elephant type, as observed in direct numerical simulations of a real spatially developing wake. Furthermore, the elephant frequency selection criterion is in excellent agreement with the numerically determined vortex shedding frequency.

Steep nonlinear global modes in spatially developing media

A new frequency selection criterion valid in the fully nonlinear regime is presented for extended oscillating states in spatially developing media. The spatial structure and frequency of these modes are dominated by the existence of a sharp front connecting linear to nonlinear regions. A new type of fully nonlinear time harmonic solutions called steep global modes is identified in the context of the supercritical complex Ginzburg–Landau equation with slowly spatially varying coefficients. A similar formulation is likely to be applicable to fully nonlinear synchronized global oscillations in spatially developing free shear flows.

Fully nonlinear global modes in spatially developing media

Global modes on a doubly infinite one-dimensional domain −∞ < x < +∞ are studied in the context of the complex Ginzburg-Landau equation with slowly spatially varying coefficients, i.e., coefficients depending only on a slow streamwise coordinate X = ϵx, where ϵ is a small parameter. A fully nonlinear frequency selection criterion is derived for global mode solutions under the assumption of weak inhomogeneity of the medium. The global mode is found to be governed by the fully nonlinear equations in a region of finite size, and by the linearized equations in the vicinity of X = ±∞. Asymptotic matching techniques are used to relate the wkbj approximations in the linear and nonlinear regions through appropriate transition layers. The real global frequency is determined by requiring that spatial branches issuing from X = −∞ and X = +∞ be continuously connected at a saddle point of the local nonlinear dispersion relation ω = Ω nℓ (k, R 2, X) between the frequency ω, the wave number k and amplitude R at a given station X. The results constitute a fully nonlinear generalization of the linear frequency selection criteria previously obtained by Chomaz et al. (1991), Monkewitz et al. (1993), and Le Dizès et al. (1996).

A Frequency Selection Criterion in Spatially Developing Flows

The possible existence of global modes or self‐excited linear resonances in spatially developing systems is explored within the framework of the WKBJ approximation. It is shown that the existence and properties of the dominant global mode may be deduced from the variations of the local absolute frequency ω0 with distance X. The main results are summarized in two theorems: (1) A system with no region of absolute instability does not sustain temporally growing global modes with an O(1) growth rate. (2) If the singularity X, closest to the real X‐axis of the complex function ω0(X) is a saddle point, the most unstable global mode has, to leading order in the WKBJ approximation, a complex frequency ω0(Xs). Thus, it will be temporally growing only if ω0(Xs) is positive.

Criteria for Selection of Frequency of Electromagnetic Radiation for Underwater proximity Fuzes

Electromagnetic proximity fuzes play important role in underwater weapons. The characteristics of the electromagnetic field, i.e., the wavelength, penetration, propagation constant, velocity, etc in sea water are different from those in air. The conducting properties of the medium are strongly dependent on the frequency of the electromagnetic waves. This paper highlights the basis for selection of frequency of electromagnetic propagation for such applications as proximity fuze for underwater weapons.