Solid state fermentation (SSF) which involves the growth of microorganism on moist solid substrates in the absence of free flowing water, has gained renewed attention over submerged fermentation for specific applications. During the SSF process in fermenter, there are three main engineering problems encountered such as the removal of metabolic heat from the substrate, diffusion of O2 and moisture through the substrate, and heterogeneity of the substrate and inoculum. A fluidized bed fermenter in which the particles move independently like a fluid was proposed to conduct the study. Throughout the study, rapid heat transfer from PKC to air was experimentally observed within the first 150s with a temperature drop of 30°C. This indicated that the excellent heat transfer between palm kernel cake and air allows solid state fermentation of PKC without accumulation of metabolic heat in the fermenter. Apart from heat removal, water adsorption study on PKC from air to bed was carried out. It showed that the increase of adsorbed water in PKC was proportional to air relative humidity and inversely proportional to superficial air velocity. The maximum moisture content adsorbed by PKC under fluidization conditions was around 10% (on dry basis). Finally, mathematical models for heat and mass transfer were proposed which can predict the experimental data quite satisfactorily.

The hydration properties of palm kernel cake (PKC) were investigated for the bioconversion of PKC to poultry feed via solid state fermentation. At room temperature, the swelling capacity of PKC was found to be constant and unaffected by different particle sizes, while the water retention capacity was affected by different particle sizes. PKC swelling was affected by moisture content and particle size. Swelling was linearly proportional to moisture content (MC). Maximum swelling at room temperature was achieved by 2.675 mm PKC for 50% MC and above, with the final volume to initial volume (V-f/V-i) ratio up to 1.71 at 210% MC. For 50% MC and below, maximum swelling was achieved by 1.500 mm PKC, with the V-f/V-i ratio up to 1.29 at 50% MC. At a constant particle size of 1.500 mm, increasing temperature increased the rate of PKC swelling, but the effect of temperature on the V-f/V-i ratio was significantly minimal at different moisture content and temperature. Mathematical expressions for the swelling of PKC at room temperature with different particle sizes, and 1.500 mm PKC at different temperatures, were developed in relations to initial volume, final volume, and moisture content. (c) 2008 Elsevier Ltd. All rights reserved.

A comparison of the beam propagation method (BPM) in two transverse dimensions and for a cylindrically symmetric laser beam with a direct FFT based method is presented for self-focusing of laser beam in a plasma with saturating type (ponderomotive) nonlinearity and cubic nonlinearity.

We report on the computer simulation of the dynamical effects of a collection of gyrating electrons in a magnetoplasma. The effects being looked into are the detailed microscopic current attractions that lead to synchronization and coherence amongst the gyrating electrons to give rise to gyro-phase coherence. We use a simplified model that uses the Darwin Hamiltonian and also the assumption that the inter-electron distances are all equal in this version of the simulation.

The task for the present study is to make an investigation of self-similarity in a self-focusing laser beam both theoretically and numerically using graphical user interface based interactive computer simulation model in MATLAB (matrix laboratory) software in the presence of saturating ponderomotive force based and relativistic electron quiver based plasma nonlinearities. The corresponding eigenvalue problem is solved analytically using the standard eikonal formalism and the underlying dynamics of self-focusing is dictated by the corrected paraxial theory for slow self-focusing. The results are also compared with computer simulation of self-focusing by the direct fast Fourier transform based spectral methods. It is found that the self-similar solution obtained analytically oscillates around the true numerical solution equating it at regular intervals. The simulation results are the main ones although a feasible semianalytical theory under many assumptions is given to understand the process. The self-similar profiles are called as self-organized profiles (not in a strict sense), which are found to be close to Laguerre-Gaussian curves for all the modes, the shape being conserved. This terminology is chosen because it has already been shown from a phase space analysis that the width of an initially Gaussian beam undergoes periodic oscillations that are damped when any absorption is added in the model, i.e., the beam width converges to a constant value. The research paper also tabulates the specific values of the normalized phase shift for solutions decaying to zero at large transverse distances for first three modes which can, however, be extended to higher order modes. (C) 2005 American Institute Of Physics.

When a lens is not prepared with an exact quadratic profile but is approximated by such a profile, there is considerable arbitrariness in the choice of the quadratic profile. Only one of these choices is optimal and gives the correct description of the physical optics involved. Laser beam self-focusing is chosen as the example in case, and it is shown that the optimal energy-conserving solution is equivalent to the variational and moments theories of self-focusing while at the same time it is paraxial in nature. Hankel-transformation techniques are used to prove this. (C) 2004 Optical Society of America.

We present a theory of slow self-focusing that is paraxial in nature, gives the field including the phase and eikonal explicitly, while it also agrees with the results of variational and moments theories. After presenting the features of the theory, particularly its similarity to the central force problem, we go on to reformulate the theory for an absorbing medium. We find that the laser beam focuses to a constant beamwidth with a small phase-front curvature depending on the extent of absorption. The theory is applicable to a whole range of saturating nonlinearities although it specializes to two plasma cases, the ponderomotive force based and the relativistic electron quiver based nonlinearities, for definitive results.

Ionic mass transfer in a circular conduit in the presence of ring promoter assembly is measured by limiting current technique using diffusion controlled electrochemical reactions (reduction of ferricyanide and oxidation of ferrocyanide). A supporting rod on which rings are mounted at equidistance is concentrically fixed in the conduit of 0.05 m I.D. to augment the mass transfer rates. Cross-sectional diameter of the ring is changed from 0.0065 m to 0.0125 m and the spacing in between the rings is varied from0.03 m and 0.15 m respectively. The improvement in mass transfer coefficients is up to 6.5. The data are correlated by the following dimensionless equation.

Propagation algorithm for computer simulation of stationary paraxial self-focusing laser beam in a medium with saturating nonlinearity is given in Lie-optic form. Accordingly, a very natural piece-wise continuous Lie transformation that reduces to a restricted Lorentz group of the beam results. It gives rise to a matrix method for self-focusing beam propagation that is constructed and implemented. Although the results use plasma nonlinearities of saturable type, and a gaussian initial beam, these results are applicable for other media like linear optical fibers and to more general situations.

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.

Laser-beam or soliton propagation is best modelled for fast computation using a split-step Fourier method based on an orthogonal transform technique known as the beam-propagation method. The beam-propagation split-step Fourier-transform technique in one and two dimensions for the propagation of a soliton or laser beam respectively in a nonlinear plasma and a split-step Hankel-transform-based algorithm for cylindrical-beam propagation close to circular cross-sectional symmetry and its computational implementation are discussed, Attention is particularly focused on the verification of the paraxial approximations of the soliton or the laser beam using these techniques, after a brief review of the beam-propagation method.

The precipitation reaction between cadmium chloride and thiourea in the presence of ammonia in a well-stirred reactor is studied at various temperatures. This scheme of reaction is utilized to form CdS thin films by the solution growth technique. Equilibrium particle size (thin film thickness) decreased with increase in temperature. The Arrhenius parameter for the kinetics of nucleation was measured as 24 kcal mol(-1). (C) 1998 Elsevier Science B.V.

A paraxial formulation of steady-state self-focusing is presented, taking due care of the correct paraxial approximation of the plasma frequency and the resultant nonlinear refractive index of the plasma in the presence of the electromagnetic field of a high-powered laser beam. For the laser beam and plasma refractive index description, the correct momentum space of the photons in circular cylindrical geometry of the laser beam is the transformation in terms of the Laguerre-Gauss modes that lead to the correct non-Taylor series paraxial approximation of the beam and its propagation equation. For self-trapping, the same conditions as the moments and variational approaches result. The natural way to express the results for self-focusing in this approximation is in terms of the so-called ABCD laws for the beam parameters, presented here for the self-similar beam propagation of a centrally humped (Gaussian) beam. These laws define a one-complex-parameter group of transformations [the SU(2) group for the absorptionless case and the restricted Lorentz group in general] that describe the evolution of the self-focusing beam; they naturally lead to the application of the concept of geometric phase to the self-focusing beam presented in the paper.

The evolution of a complex beam width parameter g describing focusing or defocusing of a paraxial Gaussian beam is considered as the cause of an additional topological (Berry) phase of the electromagnetic field associated with the beam. It is pointed out that the well-known Gouy phase is a special case of such a phase that should arise in general in all symplectic systems.

Because of the obvious advantage in long time predictions it is useful to convert dynamical problems of flows into problems involving maps. For Hamiltonian flows this in effect is equivalent to identifying an area preserving map in the Poincare surface of section. The preservation of canonical structure of the Hamiltonian flow in the surface of section can lead to a description in terms of discrete canonical equations in the surface of section. This property is utilized here to convert the Hamiltonian flow problem of the dynamic evolution of the nonlinear Schrodinger Equation which is thereby converted to a map in a restricted sense. The evolution of perturbed soliton with initial inhomogeneous chirp factor is governed by this equation and the corresponding map is analyzed.

Because of the obvious advantage in long time predictions it is useful to convert dynamical problems of flows into problems involving maps. For Hamiltonian flows this in effect is equivalent to identifying an area preserving map in the Poincare surface of section. The preservation of canonical structure of the Hamiltonian flow in the surface of section can lead to a description in terms of discrete canonical equations in the surface of section. This property is utilized here to convert the Hamiltonian flow problem of the dynamic evolution of self-focusing of an electromagnetic beam (width/phase front curvature dynamics) with beam propagation distance into an equivalent mapping problem for a wide range of initial conditions. The nonlinear Schrodinger equation is thereby converted to a map in a restricted sense.

. We prove a basic result for collisionless galactic models that collective motion not only introduces Landau damping but also intrinsic chaos of typical star dynamics in the phase plane when a small perturbative wave disturbance is present. The Melnikov method is used; the consequences of the chaos and quasilinear diffusion are pointed out.

The linear plasma response to an electrostatic wave is described by the Van Kampen–Case–Siewert (VCS) modal structure using Lie transform techniques. The VCS structure, which is well known to give rise to Landau damping, is also proved to be responsible for chaotic particle response and diffusion in phase space in the quasilinear limit.