Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation

The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2 μm (diameter) polystyrene. The liquid mixtures, in the proper proportions of water (H2O), deuterium oxide (D2O) and methanol (MeOH) as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes (reduction) in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary corrections for all factors, our experiments show that the influence of the sedimentation on coagulation rates at the initial stage of the coagulation is not observable.

Non-Linear Wave-Induced Transient Response of Soil Around a Trenched Pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot’s poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Ultrafast non-linear optical properties of Ge20As25Se55 chalcogenide films

The non-resonant third-order non-linear optical properties of amorphous Ge20As25Se55 films were studied experimentally by the method of the femtosecond optical heterodyne detection of optical Kerr effect. The real and imaginary parts of complex third-order optical non-linearity could be effectively separated and their values and signs could be also determined, which were 6.6 x 10(-12) and -2.4 x 10(-12) esu, respectively. Amorphous Ge20As25Se55 films showed a very fast response in the range of 200 fs under ultrafast excitation. The ultrafast response and large third-order non-linearity are attributed to the ultrafast distortion of the electron orbitals surrounding the average positions of the nucleus of Ge, As and Se atoms. The high third-order susceptibility and a fast response time of amorphous Ge20As25Se55 films makes it a promising material for application in advanced techniques especially in optical switching. (c) 2005 Elsevier B.V. All rights reserved.

Non-resonant third-order non-linear optical properties of amorphous GeSe2 film

The real and imaginary parts of third-order susceptibility of amorphous GeSe2 film were measured by the method of the femtosecond optical heterodyne detection of optical Kerr effect at 805 nm with the 80 fs ultra fast pulses. The results indicated that the values of real and imaginary parts were 8.8 x 10(-12) esu and -3.0 x 10(-12) esu, respectively. An amorphous GeSe2 film also showed a very fast response within 200 fs. The ultra fast response and large third-order non-linearity are attributed to the ultra fast distortion of the electron orbits surrounding the average positions of the nucleus of Ge and Se atoms. (c) 2005 Elsevier B.V. All rights reserved.

A non-linear perturbation model considering catchment wetness and its application in river flow forecasting

A non-linear perturbation model for river flow forecasting is developed, based on consideration of catchment wetness using an antecedent precipitation index (API). Catchment seasonality, of the form accounted for in the linear perturbation model (the LPM), and non-linear behaviour both in the runoff generation mechanism and in the flow routing processes are represented by a constrained nan-linear model, the NLPM-API. A total of ten catchments, across a range of climatic conditions and catchment area magnitudes, located in China and in other countries, were selected for testing daily rainfall-runoff forecasting with this model. It was found that the NLPM-API model was significantly more efficient than the original linear perturbation model (the LPM). However, restric tion of explicit nan-linearity to the runoff generation process, in the simpler LPM-API form of the model, did not produce a significantly lower value of the efficiency in flood forecasting, in terms of the model efficiency index R-2. (C) 1997 Elsevier Science B.V.

Structure and non-linear optical properties of beta-barium borate

The non-linear optical (NLO) properties of crystalline beta-BaB2O4 (beta-barium borate, BBO) have been investigated from the chemical bond viewpoint. The contributions of each type of chemical bond to the total NLO coefficient have been quantitatively determined. The calculations indicate that the true space group of BBO is R3 rather than R3c.

Comparison of non-linear optical susceptibilities of KNbO3 and LiNbO3

From the chemical bond viewpoint, second-order non-linear optical (NLO) tenser coefficients of KNbO3 and LiNbO3 crystals have been calculated. By using the bond-valence theory of complex crystals and the modified bond-charge model, we were able to determine contributions of each type of constituent chemical bond to the total second-order NLO susceptibility. The tenser values thus calculated are in good agreement with experimental data. From the comparison of NLO tenser coefficients of these two crystals, we found that the major NLO contributors are KO12 groups and LiO6 octahedra not the distorted NbO6 octahedra. The difference between their NLO properties arises from their different structural characters, and the high coordination number of constituent elements in KNbO3 makes its valence electrons become more delocalised compared with those of LiNbO3. (C) 1997 Elsevier Science Ltd. All rights reserved.

Effective response of a non-linear composite in external AC electric field

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets <(. . .)> denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

Study on system identification of linear and non-linear liquid chromatography separation

The paper proposes the identification method of linear and non-linear chromatographic system. The non-linear isotherms and lumped mass transfer coefficients of chromatography separating sorbitol and mannitol are determined. And the theoretical elution curves calculated by non-linear chromatographic model are more accurate than those calculated by linear chromatographic model.

XPM-induced pulse compression in birefringent dispersion decreasing fiber

The pulse compression induced by cross-phase modulation in birefringent dispersion decreasing fiber is discussed theoretically by solving the coupled Schrodinger equations which include the contribution of the high-order non-linear effects, and third-order dispersion. In particular, it is found that a high quality compressed signal pulse can be obtained by a pump pulse of low intense through the technique. The dependence of optimum compression on the non-linear factor N, time delay tau(d) and the dispersive ratio f is also discussed in detail. (c) 2005 Elsevier B.V. All rights reserved.

Mechanical effects of the self-organization of dislocations and related critical characteristics

The effects of the dislocation pattern formed due to the self-organization of the dislocations in crystals on the macroscopic hardening and dynamic internal friction (DIF) during deformation are studied. The classic dislocation models for the hardening and DIF corresponding to the homogeneous dislocation configuration are extended to the case for the non-homogeneous one. In addition, using the result of dislocation patterning deduced from the non-linear dlislocation dynamics model for single slip, the correlation between the dislocation pattern and hardening as well as DIF is obtained. It is shown that in the case of the tension with a constant strain rate, the bifurcation point of dislocation patterning corresponds to the turning point in the stress versus strain and DIF versus strain curves. This result along with the critical characteristics of the macroscopic behavior near the bifurcation point is microscopically and macroscopically in agreement with the experimental findings on mono-crystalline pure aluminum at temperatures around 0.5T(m). The present study suggests that measuring the DIF would be a sensitive and useful mechanical means in order to study the critical phenomenon of materials during deformation.