Nonlinear coupling of waves in a plasma in a strong dissipation limit

We study the nonlinear resonant coupling of two waves in a plasma for strong dissipation. We show that the corresponding system of differential equations has a saddle-focus fixed point and study its stable and unstable manifolds. The results we obtain suggest that the stochasticity which is numerically observed might be due to the existence of a spiral-type strange attractor.     

Noise-based logic: Binary, multi-valued, or fuzzy, with optional superposition of logic states

A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises. The orthogonality of these processes provides a natural way to construct binary or multi-valued logic circuitry with arbitrary number N of logic values by using analog circuitry. Moreover, the logic values on a single wire can be made a (weighted) superposition of the N distinct logic values. Fuzzy logic is also naturally represented by a two-component superposition within the binary case (N=2). Error propagation and accumulation are suppressed. Other relevant advantages are reduced energy dissipation and leakage current problems, and robustness against circuit noise and background noises such as 1/f, Johnson, shot and crosstalk noise. Variability problems are also non-existent because the logic value is an AC signal. A similar logic system can be built with orthogonal sinusoidal signals (different frequency or orthogonal phase) however that has an extra 1/N type slowdown compared to the noise-based logic system with increasing number of N furthermore it is less robust against time delay effects than the noise-based counterpart.     

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg–Landau equation instead of a Korteweg–de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.     

Dissipative Nonlinear Schrödinger Equation with External Forcing in Rotational Stratified Fluids and Its Solution

The dissipative nonlinear Schrödinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schrödinger equation and forced nonlinear Schrödinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves.     

On the spectrum of the system of interacting quantum nonlinear resonances

Correlation functions of the density matrix components and the frequency spectrum are numerically analysed in the system of two interacting quantum nonlinear resonances. For overlapping resonances and a sufficiently large number of resonance-trapped levels the motion of the system is shown to be close to stochasticity.     

QUANTUM EFFECT AND ONE-BODY DISSIPATION

The influence of quantum effects on the one-body dissipation has been studied in a Monte Carlo simulation method.The results show that the influence of quantum effects decreases and finally dissappears as the frequency and amplitude of the collective oscillation increases.The wall formula with quantum effect taken taken into account to some extent is given analytically.     

Theoretical and experimental study of phase optimization of tapping mode atomic force microscope

Phase image in tapping-mode atomic force microscope (TM-AFM) results from various dissipations in a microcantilever system. The phases mainly reflect the tip-sample contact dissipations which allow the nanoscale characteristics to be distinguished from each other. In this work, two factors affecting the phase and phase contrast are analyzed. It is concluded from the theoretical and experimental results that the phases and phase contrasts in the TM-AFM are related to the excitation frequency and energy dissipation of the system. For a two-component blend, it is theoretically and experimentally proven that there exists an optimal excitation frequency for maximizing the phase contrast. Therefore, selecting the optimal excitation frequency can potentially improve the phase contrast results. In addition, only the key dissipation between the tip and sample is found to accurately reflect the sample properties. Meanwhile, the background dissipation can potentially reduce the contrasts of the phase images and even mask or distort the effective information in the phase images. In order to address the aforementioned issues, a self-excited method is adopted in this study in order to eliminate the effects of the background dissipation on the phases. Subsequently, the real phase information of the samples is successfully obtained. It is shown in this study that the eliminating of the background dissipation can effectively improve the phase contrast results and the real phase information of the samples is accurately reflected. These results are of great significance in optimizing the phases of two-component samples and multi-component samples in atomic force microscope.     

梯度磁场中静电波引起的粒子随机运动

本文讨论了一般非均匀梯度磁场下任意方向传播的静电波引起粒子随机运动的非线性效应。用正则久期扰动理论给出包含粒子周期运动和波振荡之间非线性共振的哈密顿量。根据Chirikov岛重叠条件给出一般梯度磁场下粒子进入随机态的临界波幅值。分析表明,相对均匀磁场,在弱非均匀情形下,该临界值降低,意味着粒子更易进入随机态。 关键词：     

Terrestrial pole oscillations with allowance for fluctuation-dissipation perturbations

Based on a numerical-analytical model of the terrestrial pole oscillations, we investigate the effects of fluctuation-dissipation perturbations due to the pole tide. We consider the fluctuation perturbations at a frequency close to the Chandler one using the sea level data as an example. Allowance for the small irregular perturbations in tidal processes is shown to lead to variations in the Chandler component of the oscillations. We note that the amplitude of the Chandler pole oscillations is sensitive to the difference of the Chandler frequency and a frequency close to it and to the dissipation coefficients.     

Stochastic Nature in Cellular Processes

The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.     

高频电磁波驱动等离子体电流

本文分析了高频电磁波驱动等离子体电流的效应,指出,波的电场力和洛仑兹力都对驱动电流有贡献;l=0或l≠0的共振都可能成为主要驱动机制,不同l的驱动效果有区别;非共振效应也可能超过共振效应而成为主要驱动机制,同时,波的碰撞耗散可能超过共振耗散而成为主要耗散机制。 关键词：     

Acoustic modes in a dusty plasma

The propagation of the dust ion acoustic and dust acoustic modes in a dusty plasma is studied. The effect of the coupling of the charge fluctuation on the dust particles to the modes is taken into account self-consistently. It is found that the charge fluctuation leads to frequency down shift as well as dissipation of the modes. For the dust ion acoustic modes, these are significant only when the frequency characterizing the rate of capture of electrons by the dust particles in the equilibrium state is of the order of the frequency of the mode, and the mode can propagate without significant dissipation only when its frequency is well above this characteristic frequency. For the dust acoustic modes, these are significant only when the frequency characterizing the rate of capture of ions by the dust particles in the equilibrium state is of the order of the frequency of the mode, and the mode can propagate without significant dissipation only when its frequency is well above this characteristic frequency.     

Long-term effect of inter-mode transitions in quantum Markovian process

The combinatorial frequency generation by periodic and quasiperiodic stacks of nonlinear semiconductor layers has been studied in the self-consistent problem formulation, taking into account mobility of carriers. The three-wave mixing technique is applied to study the nonlinear processes. It is shown that the mixing processes in passive semiconductor structures are driven by the competitive effects of the collision of charges and resonance interactions of carriers with pump waves. The effects of the pump wave dissipation, layer parameters and stack arrangements on the efficiency of the combinatorial frequency generation are discussed.     

Continuous versus discrete quasi-energy spectrum in the quantal description of a simple parametric resonator

We investigate the quasi-energy spectrum of a quantal parametric resonator, whose frequency is modulated by a periodic δ (t) term. The system displays two distinct phases, depending on the nature (discrete or continuous) of the quasi-energy spectrum. We investigate the dynamics in the two phases and the transition between them which is induced by varying the coupling strength. Special attention is given to those observables which might be used as indicators of stochasticity in the quantum dynamics.     

致密双星后牛顿偏心轨道的引力波研究

本文主要研究非保守的后牛顿哈密顿自旋致密双星偏心轨道的引力辐射,数值比较保守的和非保守的自旋致密双星系统轨道参量偏心率大小与 引力波形的关系及引力辐射耗散效应项对轨道动力特性的影响. 数值研究表明：由于系统能量积分被保持,保守的双星轨道偏心率值改变对时域引力波形变化影响不是很明显,但辐射的引力波频率分布范围随着偏心率的增大而扩大. 而当运动方程中包含2.5PN引力耗散效应项时,由于引力辐射时伴随着能量和角动量损失,导致双星两体之间的距离和轨道偏心率逐渐衰减,轨道动力特性变得更加复杂. 双星旋进合并过程中辐射的引力波受到轨道偏心率的调制,引力辐射的强度随着偏心率的增大而增强,而引力辐射持续的时间缩短,且自旋与自旋耦合效应项对引力的贡献增大了. 关键词： 非保守的 引力辐射 耗散 偏心率     

Damping mechanism in dynamic force microscopy

A general theory is presented which describes the damping in dynamic force microscopy due to the proximity of the surface, consistently with resonant frequency shift effects. Orders of magnitude for the experimentally measured "dissipation" and image corrugation are reproduced. It is suggested that the damping does not mainly result from energy dissipation, but arises because not all solutions of the microlever equation of motion are accessible. The damping is related to the multivalued nature of the analytical resonance curve, which appears at some critical tip-surface separation.     

Thermoelastic damping effect on in-extensional vibration of rotating thin ring

Sensitive devices such as resonant sensors and radio frequency micro-electro-mechanical system (RF-MEMS) filters etc., require high Quality factors (Q-factors) defined as the ratio of total system energy to dissipation that occurs due to various damping mechanisms. Also, thermoelastic damping is considered to be one of the most important factors to elicit energy dissipation due to the irreversible heat flow of oscillating structures in the micro scales. In this study, the Q-factor for thermoelastic damping is investigated in rotating thin rings with in-plane vibration. First, in order to obtain the temperature profile of the model, a heat conduction equation for the thermal flow across the radial direction is solved based on the bending approximation so-called in-extensional approximation of the ring. Using the temperature distribution coupled with a displacement, a governing equation of the ring model can then be derived. Eventually, an eigen-value analysis is performed to obtain the natural frequency of rotating thin rings, and the analytical and numerical values of Q-factors can then be determined by the definition. Furthermore, the effects of rotating speed, dimensions of the ring, mode numbers and ambient temperatures on the Q-factor are discussed in detail.     

Microwave specific loss power of magnetic fluids subjected to a static magnetic field

This paper reports on the frequency dependence of the magnetic and electric power dissipation in a magnetic fluid sample, in the microwave frequency range (0.5 to 8GHz), at various values of the static magnetic field (0 to 167.8kA/m). The computation of the power dissipation relies on the experimental values measured for the complex dielectric permittivity, ɛ = ɛ′ - iɛ″, and the complex magnetic permeability, μ = μ′ - iμ″, over the same frequency range. The results show that the magnetic power dissipation is much larger than the electric one for the investigated sample. At a specific frequency, f (Hz) , the power dissipation, p, depends on the external magnetic field, and exhibits a maximum. The result obtained suggests the possibility of controlling the energy absorption in the microwave range by means of the application of an external magnetic field.     

Overlapping of resonances and stochasticity of electron trajectories in cyclotron masers

When an electromagnetic (EM) wave has a large amplitude and electrons have a large energy, the electron cyclotron frequency in the process of interaction with an EM wave can vary significantly. This can lead to overlapping of cyclotron resonances at different harmonics. It is shown that such an overlapping causes the stochasticity of electron orbits. Estimates show that this effect can be present in relativistic gyrodevices currently under development for driving future accelerators.