Microsphere femtosecond laser sub-50 nm structuring in far field via non-linear absorption

Creation of arbitrary features with high resolution is critically important in the fabrication of nano-optoelectronic devices.Here,sub-50 nm surface structuring is achieved directly on Sb2S3 thin films via microsphere femtosecond laser irradi-ation in far field.By varying laser fluence and scanning speed,nano-feature sizes can be flexibly tuned.Such small patterns are attributed to the co-effect of microsphere focusing,two-photons absorption,top threshold effect,and high-repetition-rate femtosecond laser-induced incubation effect.The minimum feature size can be reduced down to~30 nm(λ/26)by manipulating film thickness.The fitting analysis between the ablation width and depth predicts that the feature size can be down to~15 nm at the film thickness of~10 nm.A nano-grating is fabricated,which demonstrates desirable beam diffraction performance.This nano-scale resolution would be highly attractive for next-generation laser nano-lithography in far field and in ambient air.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations

In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z) is a rational function, and are polynomials in w(z) with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of , its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.

Experimental and Numerical Study of Structural Identification Using Non-Linear Resonant Decay Method

One of the practical approaches in identifying structures is the non-linear resonant decay method which identifies a non-linear dynamic system utilizing a model based on linear modal space containing the underlying linear system and a small number of extra terms that exhibit the non-linear effects.In this paper,the method is illustrated in a simulated system and an experimental structure.The main objective of the non-linear resonant decay method is to identify the non-linear dynamic systems based on the use of a multi-shaker excitation using appropriated excitation which is obtained from the force appropriation approach.The experimental application of the method is indicated to provide suitable estimates of modal parameters for the identification of non-linear models of structures.

Load Frequency Control of Small Hydropower Plants Using One-Input Fuzzy PI Controller with Linear and Non-Linear Plant Model

This study presents an intelligent approach for load frequency control (LFC) of small hydropower plants (SHPs). The approach which is based on fuzzy logic (FL), takes into account the non-linearity of SHPs—something which is not possible using traditional controllers. Most intelligent methods use two- input fuzzy controllers, but because such controllers are expensive, there is economic interest in the relatively cheaper single-input controllers. A non- linear control model based on one-input fuzzy logic PI (FLPI) controller was developed and applied to control the non-linear SHP. Using MATLAB/Si- mulink SimScape, the SHP was simulated with linear and non-linear plant models. The performance of the FLPI controller was investigated and compared with that of the conventional PI/PID controller. Results show that the settling time for the FLPI controller is about 8 times shorter;while the overshoot is about 15 times smaller compared to the conventional PI/PID controller. Therefore, the FLPI controller performs better than the conventional PI/PID controller not only in meeting the LFC control objective but also in ensuring increased dynamic stability of SHPs.

Non-linearity Analysis of Ship Roll Gyro-stabilizer Control System

A gyro-stabilizer is the interesting system that it can apply to marine vessels for diminishes roll motion.Today it has potentially light weight with no hy­drodynamics drag and effective at zero forward speed.The twin-gyroscope was chosen.Almost,the modelling for designing the system use linear model that it might not comprehensive mission requirement such as high sea condition.The non-linearity analysis was proved by comparison the re­sults between linear and non-linear model of gyro-stabilizer throughout fre­quency domain also same wave input,constrains and limitations.Moreover,they were cross checked by simulating in time domain.The comparison of interested of linear and non-linear close loop model in frequency domain has demonstrated the similar characteristics but gave different values at same frequency obviously.The results were confirmed again by simulation in irregular beam sea on time domain and they demonstrate the difference of behavior of both systems while the gyro-stabilizers are switching on and off.From the resulting analysis,the non-linear gyro-stabilizer model gives more real results that correspond to more accuracy in a designing gyro-sta­bilizer control system for various amplitudes and frequencies operating condition especially high sea condition.

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES

In this paper the authors study a class of non-linear singular partial differential equation in complex domain C-t x C-x(n). Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of C-t x C-x(n).

Modelling of the Vortex-Induced Motion of A Single-Column Platform with Non-Linear Mooring Stiffness Using the Coupled Wake Oscillators

A phenomenological model for predicting the vortex-induced motion (VIM) of a single-column platform with non- linear stiffness has been proposed. The VIM model is based on the couple of the Duffing-van der Pol oscillators and the motion equations with non-linear terms. The model with liner stiffness is presented for comparison and their results are compared with the experiments in order to calibrate the model. The computed results show that the predicted VIM amplitudes and periods of oscillation are in qualitative agreements with the experimental data. Compared with the results with linear stiffness, it is found that the application of non-linear stiffness causes the significant reductions in the in-line and transverse motion amplitudes. Under the non-linear stiffness constraint, the lock-in behavior is still identified at 8<Ur<15, and the trajectories of the VIM on the xy plane with eight-figure patterns are maintained. The results with different non-linear geometrically parameters show that both in-line and transverse non-linear characteristics can significantly affect the predict in-line and transverse motion amplitudes. Furthermore, the computed results for different aspect ratios indicate that the in-line and transverse motion amplitudes increase with the growth of aspect ratio, and the range of lock-in region is enlarged for the large aspect ratio.

The SPH approach to the process of container filling based on non-linear constitutive models

In this work, the transient free surface of con- tainer filling with non-linear constitutive equation＇s fluids is numerically investigated by the smoothed particle hydrody- namics （SPH） method. Specifically, the filling process of a square container is considered for non-linear polymer fluids based on the Cross model. The validity of the presented SPH is first verified by solving the Newtonian fluid and Oldroyd- B fluid jet. Various phenomena in the filling process are shown, including the jet buckling, jet thinning, splashing or spluttering, steady filling. Moreover, a new phenomenon of vortex whirling is more evidently observed for the Cross model fluid compared with the Newtonian fluid case.

Non-linear characteristics of Rayleigh-Taylor instable perturbations

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh-Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The ampli- tude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh-Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.

Numerical Simulation of Non-Linear Wave Propagation in Waters of Mildly Varying Topography with Complicated Boundary

In this paper, the characteristics of different forms of mild slope equations for non-linear wave are analyzed, and new non-linear theoretic models for wave propagation are presented, with non-linear terms added to the mild slope equations for non-stationary linear waves and dissipative effects considered. Numerical simulation models are developed of non-linear wave propagation for waters of mildly varying topography with complicated boundary, and the effects are studied of different non-linear corrections on calculation results of extended mild slope equations. Systematical numerical simulation tests show that the present models can effectively reflect non-linear effects.

A convenient look-up-table based method for the compensation of non-linear error in digital fringe projection

Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based （LUT-based） method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.

Analytical Solutions of System of Non-Linear Differential Equations in the Single-Enzyme, Single-Substrate Reaction with Non-Mechanism-Based Enzyme Inactivation

A closed form of an analytical expression of concentration in the single-enzyme, single-substrate system for the full range of enzyme activities has been derived. The time dependent analytical solution for substrate, enzyme-substrate complex and product concentrations are presented by solving system of non-linear differential equation. We employ He’s Homotopy perturbation method to solve the coupled non-linear differential equations containing a non-linear term related to basic enzymatic reaction. The time dependent simple analytical expressions for substrate, enzyme-substrate and free enzyme concentrations have been derived in terms of dimensionless reaction diffusion parameters ε, λ1, λ2 and λ3 using perturbation method. The numerical solution of the problem is also reported using SCILAB software program. The analytical results are compared with our numerical results. An excellent agreement with simulation data is noted. The obtained results are valid for the whole solution domain.

Non-Linear Numerical Simulation of Coal and Gas Outburst as a Coupling Instability Problem of Solid-Fluid Biphase Media

Based on the theory of continuum mechanics of multi-pbase media, a mathematical model and non-linear FEM equation of the coupling instability problem of solid-fluid biphase media for coal-methane outburst under finite deformation are established. The critical conditions of the surface instability are presented as the singularity of the total stiffness matrices of the coal body for coal-methaue outburst. That means the deformtion or the coal body emerges bifurcatiou phenomena. The numerical simulation of a typical outburst is made.

Approximate Solution of Non-Linear Reaction Diffusion Equations in Homogeneous Processes Coupled to Electrode Reactions for CE Mechanism at a Spherical Electrode

A mathematical model of CE reaction schemes under first or pseudo-first order conditions with different diffusion coefficients at a spherical electrode under non-steady-state conditions is described. The model is based on non-stationary diffusion equation containing a non-linear reaction term. This paper presents the complex numerical method (Homotopy perturbation method) to solve the system of non-linear differential equation that describes the homogeneous processes coupled to electrode reaction. In this paper the approximate analytical expressions of the non-steady-state concentrations and current at spherical electrodes for homogeneous reactions mechanisms are derived for all values of the reaction diffusion parameters. These approximate results are compared with the available analytical results and are found to be in good agreement.

A DECISION FEEDBACK EQUALIZER FOR NON-LINEAR CHANNELS

A Simple and useful decision feedback equalizer used for non-linear channels with severe linear distortion and mild non-linear distortion is proposed. It is a combination of a nonlinear channel equalizer based on connectionist model and a common decision feedback equalizer for linear channels. For a typical non-linear channel model it is shown that the equalization performances of the proposed equalizer are improved significantly.

POSTBUCKLING RESPONSE OF CANTILEVER BEAMS OF NON-LINEAR ELASTIC MATERIAL SUBJECTED TO SUBTANGENTIAL FOLLOWER FORCES

This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvature relation, the proposed problem is reduced to a specialeigenvalue problem of non-linear differential equation. An approximate solution is achieved byusing a simple and very effective technique, which leads to reliable results even in the case of verylarge deflections. The initial postbuckling path depending on the subtangential follower forces inequilibrium is then obtained. Moreover, the individual and coupling effect of the subtangential fol-lower force, the material non-linearity and the beam slenderness ratio on the initial postbucklingpath are also discussed in detail.

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reffect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.