Resonance Domains Research Articles

Complete Sequences of the Velvet Worm Slime Proteins Reveal that Slime Formation is Enabled by Disulfide Bonds and Intrinsically Disordered Regions.

The slime of velvet worms (Onychophora) is a strong and fully biodegradable protein material, which upon ejection undergoes a fast liquid‐to‐solid transition to ensnare prey. However, the molecular mechanisms of slime self‐assembly are still not well understood, notably because the primary structures of slime proteins are yet unknown. Combining transcriptomic and proteomic studies, the authors have obtained the complete primary sequences of slime proteins and identified key features for slime self‐assembly. The high molecular weight slime proteins contain cysteine residues at the N‐ and C‐termini that mediate the formation of multi‐protein complexes via disulfide bonding. Low complexity domains in the N‐termini are also identified and their propensity for liquid‐liquid phase separation is established, which may play a central role in slime biofabrication. Using solid‐state nuclear magnetic resonance, rigid and flexible domains of the slime proteins are mapped to specific peptide domains. The complete sequencing of major slime proteins is an important step toward sustainable fabrication of polymers inspired by the velvet worm slime.

Experimentally realization of dual nonlinear dielectric resonance and electromagnetic characteristics of Manganese-doped ZnO NPs in X-Band

In this paper, the electromagnetic details of Manganese-doped Zinc Oxide (Mn–ZnO) nanoparticles (NPs) were measured using the waveguide measurement method in the frequency range 8–12.5 GHz. The evaluations have been utilized by the Nicolson-Ross-Weir method for electromagnetic properties such as permittivity and permeability. The results indicate, dual nonlinear dielectric resonance in X-band at 9.446 and 10.47 GHz. The equivalent circuit and simulated waveguide structure are inserted to explain and verify the dual dielectric resonance. Consequently, Inductance-Capacitance properties are detected by the obtained impedance regarding the reaction of the NPs to the electromagnetic waves and, the outgoing power for the simulated waveguide has a sharp drop at around the two main resonance domains. The evaluated magnetic susceptibility quantity affirms that the Mn–ZnO NPs act as ferro and paramagnetic material at less and above than 10.39 GHz.

Effect of an External Magnetic Field on the Absorption Efficiency of the RF Power in a Spatially Bounded Inductive Plasma Source

The measured dependences of the equivalent plasma resistance on the external magnetic field (0–50 G) in a 46-cm-diameter RF inductive plasma source operating at frequencies of 2, 4, and 13.56 MHz and a power of 100–500 W are presented. The experiments were carried out in argon at pressures of 0.1–30 mTorr. The presence of the external magnetic field leads to the appearance of resonance domains of efficient RF power absorption corresponding to the conditions of resonance excitation of helicons coupled with Trivelpiece–Gould modes. It is shown that RF power absorption at frequencies of 2 MHz can be optimized by applying an external magnetic field corresponding to the domains of resonance absorption. The effect is enhanced with increasing operating frequency.

Study of left-handed characteristics of parallel microwires based metastructures

The aim of this work is to present a complex experimental and theoretical study of the ferromagnetic resonance frequencies and plasma behavior for CoFe-based, Co-based, Fe-based and FINEMETTM glass covered amorphous microwires (GCAWs), arranged in parallel configurations as free-standing systems, as well as combinations thereof, in order to obtain metastructures with tailored and enlarged left-handed frequency domain. The negative magnetic properties interval of the metastructures is expanded by alternating different types of GCAWs with close natural ferromagnetic resonance (NFMR) and natural antiferromagnetic resonance (NFMAR) domains, respectively.

Improvement of impedance spectroscopy methods: resonance analysis of samples

An impedance spectroscopy method, using an Agilent E4991A RF Impedance/Material Analyzer, was employed for the investigation of radiofrequency and microwave dielectric characteristics for some ceramic materials with high dielectric permittivity. Experimental observations recorded single, double and even triple resonances in the permittivity spectra, while for the selected samples significantly different values of permittivity from the ones found in existing literature were directly measured and observed in the frequency range of 100 MHz–1 GHz. The specified material analyzer is designed to work within certain permittivity-frequency domains; working outside these limits leads to significant errors when carrying out direct measurements of permittivity. Having observed that the resonance measurements are not associated with the intrinsic material properties but with the sample resonances, we proposed a dielectric resonance cavity model for sample purposes and we determined the dielectric permittivity at different resonance frequencies. A scaling procedure, based on the computed values of permittivity, was applied in order to correct the directly measured permittivity spectra where the frequency was outside the resonance domains. The corrected data are in good agreement with those measured using other techniques and suggest that the proposed procedure extends the spectroscopy method currently used for high permittivity measurements. The sources of error for the proposed method were investigated.

Effect of local environment in resonant domains of polydisperse plasmonic nanoparticle aggregates on optodynamic processes in pulsed laser fields**Project supported by the Russian Academy of Sciences (Grant Nos. 24.29, 24.31, III.9.5, 43, SB RAS-SFU (101), and 3-9-5).

Interactions of pulsed laser radiation with resonance domains of multiparticle colloidal aggregates having an increasingly complex local environment are studied via an optodynamic model. The model is applied to the simplest configurations, such as single particles, dimers, and trimers consisting of mono- and polydisperse Ag nanoparticles. We analyze how the local environment and the associated local field enhancement by surrounding particles affect the optodynamic processes in domains, including their photomodification and optical properties.

Parametric vibrations of a mechanical system and their stability for an arbitrary modulation coefficient

The natural frequencies and modes of parametric vibrations of a mechanical system are studied, by way of example, for a pendulum of variable length with modulation coefficient varying from arbitrarily small to maximum admissible values. Analytic and numerical methods are used to construct and study the boundaries of the resonance domains for the first four vibration modes, and the main qualitative properties of higher modes are found. The complete degeneration of modes with even numbers, i.e., the coincidence of the frequencies of symmetric and nonsymmetric naturalmodes for admissible values of the modulation parameter, is proved. The global picture of boundaries of stability domains for the lower equilibriumis constructed, and a significant difference from the Ince-Strutt diagram is shown. Specific properties of the natural modes are established.

Cauchy problem for the Mathieu equation away from parametric resonance

Four solutions of the Cauchy problem for Mathieu’s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

Evolution of convective patterns in a binary-mixture layer subjected to a periodical change of the gravity field

A theoretical study has been made of the convective stability and developed heat transfer regimes in a horizontal, binary-mixture layer with negative Soret coupling. The system is under temperature gradient and finite-frequency vibration. Both analytical and numerical examinations are presented. The limiting case of long-wave disturbances is studied using the perturbation method. To find instability thresholds in the linear approximation the Floquet theory is applied. The stability borders and characteristics of critical disturbances are determined depending on the vibration frequency for typical gaseous, liquid, and colloidal mixtures. The phase mapping and the Fourier spectra are used to describe the nonlinear evolution of the convective system. It is shown that supercritical flows within the first and second resonance domains develop via soft-mode transitions at critical parameter values which are consistent with the predictions of the linear stability theory. The nonlinear convection patterns demonstrate the synchronous, subharmonic, or quasiperiodic dynamics. The hysteretic transitions between nonlinear regimes are also investigated. The influence of the vibrational Grashof number on the concentration field is discussed for standing wave and traveling wave modes.

Effect of vertical vibrations on a two-layer system with a deformable interface

The effect of single- and two-frequency vibrations on the behavior of a system consisting of two homogeneous viscous fluids bounded by rigid walls is analyzed. It is assumed that the system as a whole is under vertical vibrations obeying a certain law. An eigenvalue problem is obtained in order to analyze the stability of the relative equilibrium. The case of finite frequencies and arbitrary modulation amplitudes is treated along with the case of high frequencies and small modulation amplitudes. In the former case, the parametric resonance domains are examined depending on the parameters of the system. In the latter case, the high-frequency vibration is shown to create effective surface tension, thus flattening the interface, and can suppress instability when the heavy fluid is over the light one.

Chaotic advection and nonlinear resonances in an oceanic flow above submerged obstacle

The effect of an isolated submarine obstacle on the motion of fluid particles in a periodic external flow is studied within the framework of the barotropic, quasi-geostrophic approximation on f -plane. The concept of background currents advanced by Kozlov [1995. Background currents in geophysical hydrodynamics. Izvestia, Atmos. Oceanic Phys. 31 (2), 245–250] is used to construct a dynamically consistent stream function satisfying the potential vorticity conservation law. It is shown that a system of two topographic vortices revolving about a rotation center can form in a circular external flow. Unsteady periodic perturbations, associated with either variations in the background current or deviations of the external flow from circulation, are analyzed. Unsteadiness in the external flow essentially complicates the pattern of the motion of fluid particles. Vortex-type quasi-periodic structures, identified with nonlinear resonances that form in Lagrangian equations of fluid particle advection, are examined. They either surround the stationary configuration by a vortex chain—a ringlet-like structure [ Kennelly, M.A., Evans, R.H., Joyce, T.M., 1985. Small-scale cyclones on the periphery of Gulf Stream warm-core rings. J. Geophys. Res. 90(5), 8845–8857], or they form a complex-structure multivortex domain. Asymptotic estimates and numerical modeling are used to study the distribution and widths of the nonlinear resonance domains that appear under unsteady perturbations of different types. The onset of chaotic regimes owing to the overlapping of nonlinear resonance domains is analyzed. Transport fluxes determined by chaotic advection and barriers for transport (KAM-tori) and the conditions of their existence are studied. The relation of the rotation frequency of fluid particles on their initial position (when the dependence is calculated in the undisturbed system) is shown to completely determine the main features of the pattern of Lagrangian trajectories and chaotization effects. Because of nonlinear effects, the domain involved in quasi-periodic and chaotic motions can be much larger than the domain occupied by steady topographic vortices. The results of study by Sokolovskiy et al. [1988. On the influence of an isolated submerged obstacle on a barotropic tidal flow. Geophys. Astrophys. Fluid Dyn. 88(1), 1–30] concerning the due regard on the irrotational background component as the necessary factor for the transportation of fluid particles from the vortex domain to infinity are confirmed.

Cauchy problem for Mathieu’s equation at parametric resonance

Mathieu’s equation is solved by an asymptotic averaging method in the fourth approximation for the first to fourth resonance domains and in the third approximation for the zero resonance domain. The general periodic and aperiodic solutions on characteristic curves are found, and the general solution is obtained in instability domains and stability-domain areas adjacent to the characteristic curves. All the solutions are explicitly found in the form of functions of an argument without using the auxiliary parameter employed in Whittaker’s method. Simple formulas depending on two parameters of the equation are derived for the characteristic exponent in instability domains and for the frequency of slow oscillations in stability domains near the characteristic curves. The theory is developed by analyzing the resonances exhibited by Mathieu’s equation.

Periodic time dependent electrogravitational instability of a fluid cylinder

The electrogravitational instability of a dielectric fluid cylinder dispersed in a gravitational dielectric medium of negligible motion has been developed on using the macroscopic perturbation technique based on the normal mode analysis. The model is acting upon the pressure gradient, self-gravitating and electrodynamic (with periodic time dependent electric field) forces. For all axisymmetric and non-axisymmetric disturbances the system is governed by the Hill's second-order integro-differential equation in the disturbed surface displacement. The self-gravitating forces are destabilizing only in the axisymmetric disturbances domain 0⩽x⩽1.0668 and stabilizing in all other domains, where x is the dimensionless longitudinal wavenumber. The electric field is always stabilizing not only in the axisymmetric mode m= 0 but also in those of non-axisymmetric m≠ 0. The frequency of the time dependent periodic electric field is only destabilizing in a few axisymmetric states of perturbations while it is strongly stabilizing in the remaining axisymmetric disturbance states and also stable in all states of the non-axisymmetric perturbations. Resonance domains may arise due to the periodicity of the electric field and in some ranges of the wavenumber, the stability conditions depend solely on the frequency of the field. The self-gravitating destabilizing influence could not be suppressed whatever is the greatest value of the magnitude and frequency of the periodic electric field because the gravitational destabilizing influence will persist.

Multipolar polarizabilities of the sodium atom by a variationally stable procedure

We present a formalism that combines a semiempirical model potential with a second-order energy correction variationally stable method to evaluate the multipolar dynamic polarizabilities of the sodium atom. In this framework, the alpha(L)(omega) up to L=4 were calculated achieving good precision including the resonance domains of omega.

Wave–particle interaction investigated in a travelling wave tube

For wave–particle interaction studies, the one-dimensional beam-plasma system can be advantageously replaced by a travelling wave tube (TWT). This allowed us to carefully check the saturation mechanisms by the trapping of a cold electron beam, or by diffusion in the broad spectrum excited by a warm beam. While the former case is well understood, the latter case raises the question of the unsolved quasilinear paradox. When the beam intensity is low enough to ensure that beam-plasma instabilities are ruled out, a beam of test electrons is propagated in the TWT. By recording the test beam energy distribution at the output of the tube, we report the first experimental observation of the resonant domain of a single wave and of the overlap of the resonance domains responsible for the transition to large scale chaos common to many Hamiltonian systems. The fractal structure of phase space associated with this transition can also be explored.

Experimental observation of resonance overlap responsible for Hamiltonian chaos

A test electron beam is propagated in a specially designed traveling wave tube. The beam intensity is low enough to ensure that beam-plasma instabilities are ruled out. By recording the beam energy distribution at the output of the tube, we report the experimental observation of the resonant domain of a single wave and of the overlap of the resonance domains of two waves associated to the destruction of Kolmogorov–Arnold–Moser tori constituting barriers in phase space. This overlap mechanism is responsible for the transition to large scale chaos common to a large class of Hamiltonian systems.

Quasi-periodicity and border-collision bifurcations in a DC-DC converter with pulsewidth modulation

The paper considers the dynamics of a dc-dc converter with pulsewidth modulation. The typical scenario for the transition to chaos in such systems proceeds via quasi-periodicity, resonance cycles, and torus destruction. Detailed bifurcation analysis shows that the resonance solutions arise via border-collision bifurcations (BCB) on a two-dimensional torus. The arrangement of the resonance domains within the parameter plane is related to the Farey series, and their internal structure is described. It is shown that transitions to chaos mainly occur through finite sequences of BCB. Some other possible causes of complex dynamics are considered, including a subcritical Neimark-Sacker (Andronov-Hopf) bifurcation and the associated hysteretic phenomena.

Modeling the 5 : 2 Mean-Motion Resonance in the Jupiter–Saturn Planetary System

The motion of the Jupiter–Saturn planetary system near the 5 : 2 mean-motion resonance is modeled analytically in the frame of the planar general three-body problem. The topology of the phase space in the resonance and near-resonance domains is investigated in detail by means of surfaces of section and spectral map techniques. Various regimes of motion of the Jupiter–Saturn system are observed, and their domains are represented on the parameter plane defined by the total energy of the system and the parameter of proximity to the 5 : 2 resonance. The regions of transition between domains of different regimes of motion are characterized by chaotic motion. We show that there is a significant chaotic zone associated with the 5 : 2 mean-motion resonance, but large-scale excursions of the planet eccentricities are not possible in the planar three-body model.

Parametric resonance in systems with small dissipation

A linear oscillatory system having multiple degrees of freedom with periodic coefficients is considered. The system involves three independent parameters: the frequency and amplitude of the periodic exitation and a parameter of the dissipative forces, the last two being assumed small. Instability of the trivial solution (parametric resonance) is investigated. For an arbitrary periodic exitation matrix and a positive-definite matrix of the dissipative forces, general expressions are obtained for the domains of fundamental and combination resonances. Two special cases of the periodic exitation matrix, frequently encountered in applications, are studied: a symmetric matrix, and a time-independent matrix multiplied by a scalar periodic function. It is proved that in the first case the system is subject only to fundamental and sum-type combination resonances; in the second case fundamental resonance and sum or difference type combination resonance may occur, depending on the sign of a certain constant. It is shown that in both cases the resonance domains in the first approximation are cones in three-dimensional parameter space. Examples considered are the problem of the dynamic stability of a two-dimensional bending mode of an elastic beam subject to periodic torques, and the problem of the stability of an elastic rod of variable cross-section compressed by a periodic longitudinal force.

Resonance domains for the Hill equation with allowance for damping

In this paper, resonance domains for the Hill equation with allowance for damping are found using formulas for derivatives of a monodromy matrix with respect to parameters [1, 2]. The problem is solved by the asymptotic method for small amplitudes of an exciting force and a low damping coefficient. A description of these domains (represented by halves of cones) in a three-dimensional parameter space is given. 1. We consider a system of linear differential equations (1) where G = G ( t , p ) is an m -dimensional real square matrix smoothly depending on the vector of actual parameters p = ( p 1 , p 2 , …, p n ) , which is a continuous periodic function of time G ( t , p ) = G ( t + T , p ) , where T is a period. We denote linear independent solutions to system (1) as x 1 ( t ), x 2 ( t ), …, x m ( t ) and use them to form a fundamental matrix X ( t ) = [ x 1 ( t ), x 2 ( t ), …, x m ( t )] . This matrix, satisfying the equations (2) where I is the m -dimensional identity matrix, is called the matriciant, and the matrix F = X ( T ) is called the monodromy matrix [3]. Along with Eqs. (2), we consider a conjugate system of equations for the matrix Y : (3) The solutions X ( t ) and Y ( t ) to Eqs. (2) and (3) are linked by the equation [3]