Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Wave analysis of sound decay in rectangular rooms

The decay of sound in a rectangular room is analyzed for various boundary conditions on one of its walls. It is shown that the decay of the sound-intensity level is in general nonlinear. But for specific areas and impedances of the material it is possible to obtain a linear initial decay. It is also shown that the coefficients derived from the initial decay rates neither correspond to the predictions of Sabine's or Eyring's geometrical theories nor to the normal coefficients of Morse's wave theory. The dependence of the coefficients on the area of the material is discussed. The influence of the real and the imaginary parts of the specific acoustic impedance of the material on the coefficients is also discussed. Finally, the existence of a linear initial decay corresponding to the decay of a diffuse field in the case of a highly absorbing material partially covering a wall is explained on the basis of modal coupling.

Multicarrier analysis of magnetotransport data at low and high electric fields

We present some results on multicarrier analysis of magnetotransport data, Both synthetic as well as data from narrow gap Hg0.8Cd0.2Te samples are used to demonstrate applicability of various algorithms vs. nonlinear least square fitting, Quantitative Mobility Spectrum Analysis (QMSA) and Maximum Entropy Mobility Spectrum Analysis (MEMSA). Comments are made from our experience oil these algorithms, and, on the inversion procedure from experimental R/sigma-B to S-mu specifically with least square fitting as an example. Amongst the conclusions drawn are: (i) Experimentally measured resistivity (R-xx, R-xy) should also be used instead of just the inverted conductivity (sigma(xx), sigma(xy)) to fit data to semiclassical expressions for better fits especially at higher B. (ii) High magnetic field is necessary to extract low mobility carrier parameters. (iii) Provided the error in data is not large, better estimates to carrier parameters of remaining carrier species can be obtained at any stage by subtracting highest mobility carrier contribution to sigma from the experimental data and fitting with the remaining carriers. (iv)Even in presence of high electric field, an approximate multicarrier expression can be used to guess the carrier mobilities and their variations before solving the full Boltzmann equation.

Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

R1SVM: A randomised nonlinear approach to large-scale anomaly detection

The problem of unsupervised anomaly detection arises in a wide variety of practical applications. While one-class support vector machines have demonstrated their effectiveness as an anomaly detection technique, their ability to model large datasets is limited due to their memory and time complexity for training. To address this issue for supervised learning of kernel machines, there has been growing interest in random projection methods as an alternative to the computationally expensive problems of kernel matrix construction and sup-port vector optimisation. In this paper we leverage the theory of nonlinear random projections and propose the Randomised One-class SVM (R1SVM), which is an efficient and scalable anomaly detection technique that can be trained on large-scale datasets. Our empirical analysis on several real-life and synthetic datasets shows that our randomised 1SVM algorithm achieves comparable or better accuracy to deep auto encoder and traditional kernelised approaches for anomaly detection, while being approximately 100 times faster in training and testing.

A constraint Jacobian based approach for static analysis of pantograph masts

This paper presents a constraint Jacobian matrix based approach to obtain the stiffness matrix of widely used deployable pantograph masts with scissor-like elements (SLE). The stiffness matrix is obtained in symbolic form and the results obtained agree with those obtained with the force and displacement methods available in literature. Additional advantages of this approach are that the mobility of a mast can be evaluated, redundant links and joints in the mast can be identified and practical masts with revolute joints can be analysed. Simulations for a hexagonal mast and an assembly with four hexagonal masts is presented as illustrations.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

A nonlinear theory of wake development

A simple new series, using an expansion of the velocity profile in parabolic cylinder functions, has been developed to describe the nonlinear evolution of a steady, laminar, incompressible wake from a given arbitrary initial profile. The first term in this series is itself found to provide a very satisfactory prediction of the decay of the maximum velocity defect in the wake behind a flat plate or aft of the recirculation zone behind a symmetric blunt body. A detailed analysis, including higher order terms, has been made of the flat plate wake with a Blasius profile at the trailing edge. The same method yields, as a special case, complete results for the development of linearized wakes with arbitrary initial profile under the influence of arbitrary pressure gradients. Finally, for purposes of comparison, a simple approximate solution is obtained using momentum integral methods, and found to predict satisfactorily the decay of the maximum velocity defect. © 1970 Wolters-Noordhoff Publishing.

Some new concepts in nonlinear systems

Some new concepts characterizing the response of nonlinear systems are developed. These new concepts are denoted by the terms, the transient system equivalent, the response vector, and the space-phase components. This third concept is analyzed in comparison with the well-known technique of symmetrical components. The performance of a multiplicative feedback control system is represented by a nonlinear integro-differential equation; its solution is obtained by the principle of variation of parameters. The system response is treated as a vector and is resolved into its space-phase components. The individual effects of these components on the performance of the system are discussed. The suitability of the technique for the transient analysis of higher order nonlinear control systems is discussed.

L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Nonlinear aeroelasticity of rotating and flapping wings - a review

The interaction between large deflections, rotation effects and unsteady aerodynamics makes the dynamic analysis of rotating and flapping wing a nonlinear aeroelastic problem. This problem is governed by nonlinear periodic partial differential equations whose solution is needed to calculate the response and loads acting on vehicles using rotary or flapping wings for lift generation. We look at three important problems in this paper. The first problem shows the effect of nonlinear phenomenon coming from piezoelectric actuators used for helicopter vibration control. The second problem looks at the propagation on material uncertainty on the nonlinear response, vibration and aeroelastic stability of a composite helicopter rotor. The third problem considers the use of piezoelectric actuators for generating large motions in a dragonfly inspired flapping wing. These problems provide interesting insights into nonlinear aeroelasticity and show the likelihood of surprising phenomenon which needs to be considered during the design of rotary and flapping wing vehicle

Response of nonlinear systems to narrow-band excitation

The hardening cubic spring oscillator is studied under narrow-band gaussian excitation. Equivalent linearization leads to multiple steady states. The realizability of the solution is discussed through stochastic stability analysis. Theoretical results are supported by numerical simulation.

Analysis of solar radiation pressure induced coupled liberations of a gravity stabilized axisymmetric satellite

This paper presents an analysis of solar radiation pressure induced coupled librations of gravity stabilized cylindrical spacecraft with a special reference to geostationary communication satellites. The Lagrangian approach is used to obtain the corresponding equations of motion. The solar induced torques are assumed to be free of librational angles and are represented by their Fourier expansion. The response and periodic solutions are obtained through linear and nonlinear analyses, using the method of harmonic balance in the latter case. The stability conditions are obtained using Routh-Hurwitz criteria. To establish the ranges of validity the analytic response is compared with the numerical solution. Finally, values of the system parameters are suggested to make the satellite behave as desired. Among these is a possible approach to subdue the solar induced roll resonance. It is felt that the approximate analysis presented here should significantly reduce the computational efforts involved in the design and stability analysis of the systems.

Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate.