Observability for a Class of Nonlinear Systems

t - N m and sufficient computable conditions are obtained for the obsemabii of systems with linear state equations and polgwmIal outputs. Based on these, initial state reconstmctors are also described.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Superfluid vacuum carrying real Einstein-de Broglie waves

An earlier superfluid aether model pairing fermionic and antifermionic fields is invoked to explain Rauch's time dependent neutron interference results which now suggest that microobjects are waves and particles simultaneously. The covariant superfluid provides a medium which carries real Einstein-de Broglie “pilot” waves. Further consequences are discussed.

Finite-amplitude love-waves on an isotropic layered half-space

A pair of semi-linear hyperbolic partial differential equations governing the slow variations in amplitude and phase of a quasi-monochromatic finite-amplitude Love-wave on an isotropic layered half-space is derived using the method of multiple-scales. The analysis of the exact solution of these equations for a signalling problem reveals that the amplitude of the wave remains constant along its characteristic and that the phase of the wave increases linearly behind the wave-front.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

Structure of shock waves at re-entry speeds

The unified structure of steady, one-dimensional shock waves in argon, in the absence of an external electric or magnetic field, is investigated. The analysis is based on a two-temperature, three-fluid continuum approach, using the Navier—Stokes equations as a model and including non-equilibrium collisional as well as radiative ionization phenomena. Quasi charge neutrality and zero velocity slip are assumed. The integral nature of the radiative terms is reduced to analytical forms through suitable spectral and directional approximations. The analysis is based on the method of matched asymptotic expansions. With respect to a suitably chosen small parameter, which is the ratio of atom-atom elastic collisional mean free-path to photon mean free-path, the following shock morphology emerges: within the radiation and electron thermal conduction dominated outer layer occurs an optically transparent discontinuity which consists of a chemically frozen heavy particle (atoms and ions) shock and a collisional ionization relaxation layer. Solutions are obtained for the first order with respect to the small parameter of the problem for two cases: (i) including electron thermal conduction and (ii) neglecting it in the analysis of the outer layer. It has been found that the influence of electron thermal conduction on the shock structure is substantial. Results for various free-stream conditions are presented in the form of tables and figures.

Two-Mode Structure of Alfvén Surface Waves

The Alfvén surface waves propagating along a viscous conducting fluid-vacuum interface have been studied. It is found that besides the "ordinary" Alfvén surface waves, modified by viscosity effects, the interface can support a second mode which is the over-damped solution of the dispersion equation. The possibility of observation of a two-mode structure of Alfvén surface waves in the laboratory and in the solar coronal plasmas is discussed.

Effect of ion temperature on propagation of ion-acoustic solitary waves of small amplitudes in collisionless plasma

By using a perturbation technique, the Korteweg-de Vries equation is derived for a mixture of warm-ion fluid and hot, isothermal electrons. Stationary solutions are obtained for this equation and are compared with the corresponding solutions for a mixture consisting of cold-ion fluid and hot, isothermal electrons.

A note on the existence of Alfven surface waves

The Alfven surface waves can arise due to the discontinuity in the Alfven speed across the interface along which these waves propagate. This note studies the relationship between v A1 and v A2 which is required for the existence of Alfven surface waves in low-beta plasma.

Ultrafast Switching Time and Third Order Nonlinear Coefficients of Microwave Treated Single Walled Carbon Nanotube Suspensions

Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta(0) similar to 250 cm/GW (650 cm/GW) and nonlinear index, gamma similar to 15 cm(2)/pW (-30 cm(2)/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

Study of linear and nonlinear optical properties of dendrimers using density matrix renormalization group method

We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser–Parr–Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.

Long waves in inviscid compressible atmosphere II

Solitary waves have been found in an adiabatic compressible atmosphere which, in ambient state, has winds and temperature gradient, generalizing our earlier results for the isothermal atmosphere. Explicit results are obtained for the special case of linear temperature and linear wind distributions in the undisturbed conditions. An important result of the study is that the number of possible critical speeds of the flow depends crucially on whether the maximum Richardson number (which is variable in the present example) is greater or less than 1/4.

Stabilization of linear and nonlinear dynamical systems using an observer-controller configuration

In this paper the problem of stabilization of systems by means of stable compensations is considered, and results are derived for systems using observer�controller structures, for systems using a cascade structure, and for nonlinear systems

Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Self-tuning is applied to the control of nonlinear systems represented by the Hammerstein model wherein the nonlinearity is any odd-order polynomial. But control costing is not feasible in general. Initial relay control is employed to contain the deviations.