Application of nonlinear filtering to credit risk

Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the `Expectation-Maximization' method for estimating parameters. (C) 2010 Elsevier B.V. All rights reserved.

Analysis of Nonlinear Optical Properties of Photonic Crystal Beam-splitters

The paper analyses electromagnetic wave propagation through nonlinear photonic crystal beam-splitters. Different lattice configurations of Y-junction beam-splitters are simulated and propagation properties are investigated with introducing nonlinearity with varying the rod size in crystal lattice. It is seen that nonlinear photonic crystal shows a considerable band-gap even at low refractive contrast. The division of power in both arms of beam-splitters can be controlled by varying the nonlinearity.

Exact nonlinear travelling hydromagnetic wave solutions

Exact travelling wave solutions for hydromagnetic waves in an exponentially stratified incompressible medium are obtained. With the help of two integrals it becomes possible to reduce the system of seven nonlinear PDE's to a second order nonlinear ODE which describes an one dimensional harmonic oscillator with a nonlinear friction term. This equation is studied in detail in the phase plane. The travelling waves are periodic only when they propagate either horizontally or vertically. The reduced second order nonlinear differential equation describing the travelling waves in inhomogeneous conducting media has rather ubiquitous nature in that it also appears in other geophysical systems such as internal waves, Rossby waves and topographic Rossby waves in the ocean.

Coupled substitution of niobium and silicon in potassium titanyl phosphate and arsenate (KTiOPO4 and KTiOAsO4. Synthesis and nonlinear optical properties of KTi1-xNbxOX1-xSixO4 (X = P, As)

Coupled substitution of Nb(V) and Si(IV) for Ti(IV) and P(V)/As(V) in KTiOP04 (KTP) and KTiOAsO4 (KTA) giving new series of nonlinear optical materials, KTi1-xNbxOX1-xSixO4 (X=P,As), has been investigated. Substitution up to x = 0.40 readily occurs, the members retaining the orthorhombic (Pna2(1)) structure of KTP. The second harmonic generation (SHG) property of the parent KTP and KTA is not adversely affected by the coupled substitution. SHG intensity of the powder samples of the X = P series shows a slight increase with x up to x = 0.15; for 0.15 < x less-than-or-equal-to 0.40, there is a decrease in SHG intensity as compared to that for KTP. A similar trend in SHG intensity is seen for the arsenic analogs.

Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear Loads

In this paper, a wireless control strategy for parallel operation of three-phase four-wire inverters is proposed. A generalized situation is considered where the inverters are of unequal power ratings and the loads are nonlinear and unbalanced in nature. The proposed control algorithm exploits the potential of sinusoidal domain proportional+multiresonant controller ( in the inner voltage regulation loop) to make the system suitable for nonlinear and unbalanced loads with a simple and generalized structure of virtual output-impedance loop. The decentralized operation is achieved by using three-phase P/Q droop characteristics. The overall control algorithm helps to limit the harmonic contents and the degree of unbalance in the output-voltage waveform and to achieve excellent power-sharing accuracy in spite of mismatch in the inverter output impedances. Moreover, a synchronized turn on with consequent change over to the droop mode is applied for the new incoming unit in order to limit the circulating current completely. The simulation and experimental results from-1 kVA and -0.5 kVA paralleled units validate the effectiveness of the scheme.

Nonlinear finite element analysis of reinforced concrete corbel

Reinforced concrete corbels have been analysed using the nonlinear finite element method. An elasto-plastic-cracking constitutive formulation using Huber-Hencky-Mises yield surface augmented with a tension cut-off is employed. Smeared-fixed cracking with mesh-dependent strain softening is employed to obtain objective results. Multiple non-orthogonal cracking and opening and closing of cracks are permitted. The model and the formulation are verified with respect to available numerical solution for an RC corbel. Results of analyses of nine reinforced concrete corbels are presented and compared with experimental results. Nonlinear finite element analysis of reinforced concrete structures is shown to be a complement and also a feasible alternative to laboratory testing.

Nonlinear hydrodynamics of a hard-sphere fluid near the glass transition

We conduct a numerical study of the dynamic behavior of a dense hard-sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free-energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through a stretched exponential decay and a two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wave-number dependence of the kinetics is extensively explored. The connection of our results with experiment, mode-coupling theory, and molecular-dynamics results is discussed.

Spectral approach for the soliton and periodic solutions of the nonlinear wave equation

A spectral method that obtains the soliton and periodic solutions to the nonlinear wave equation is presented. The results show that the nonlinear group velocity is a function of the frequency shift as well as of the soliton power. When the frequency shift is a function of time, a solution in terms of the Jacobian elliptic function is obtained. This solution is periodic in nature, and, to generate such an optical pulse train, one must simultaneously amplitude- and frequency-modulate the optical carrier. Finally, we extend the method to include the effect of self-steepening.

Aspects of coherent states of nonlinear algebras

Various aspects of coherent states of nonlinear su(2) and su(1,1) algebras are studied. It is shown that the nonlinear su(1,1) Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived. (C) 2010 American Institute of Physics. doi:10.1063/1.3514118]

Average lattices and aperiodic structures

Statistically averaged lattices provide a common basis to understand the diffraction properties of structures displaying deviations from regular crystal structures. An average lattice is defined and examples are given in one and two dimensions along with their diffraction patterns. The absence of periodicity in reciprocal space corresponding to aperiodic structures is shown to arise out of different projected spacings that are irrationally related, when the grid points are projected along the chosen coordinate axes. It is shown that the projected length scales are important factors which determine the existence or absence of observable periodicity in the diffraction pattern more than the sequence of arrangement.

Growth and characterization of some novel crystals for nonlinear optical applications

The advent of high intensity lasers coupled with the recent advances in crystal technology has led to rapid progress in the field of nonlinear optics. This article traces the history of materials development that has taken place over the past forty odd years and dwells on the current status in this important area. The materials aspect is discussed under three classes viz. inorganic, organic and semiorganic crystals. In the end, some of the crystal growth work that has been carried out in author's laboratory is presented.

Nonlinear effects on rotating disk flow in a cylindrical casing

The flow due to a finite disk rotating in an incompressible viscous fluid has been studied. A modified Newton-gradient finite difference scheme is used to obtain the solution of full Navier-Stokes equations numerically for different disk and cylinder sizes for a wide range of Reynolds numbers. The introduction of the aspect ratio and the disk-shroud gap, significantly alters the flow characteristics in the region under consideration, The frictional torque calculated from the flow data reveals that the contribution due to nonlinear terms is not negligible even at a low Reynolds number. For large Reynolds numbers, the flow structure reveals a strong boundary layer character.

Physical characterization of the organic nonlinear optical crystal � 3-methoxy 4-hydroxy benzaldehyde

We highlight our recent experimental work on an efficient molecular nonlinear optical crystal, 3-methoxy 4-hydroxy benzaldehyde (MHBA). Optical quality single crystals of MHBA were grown from mixtures of solvents and from melt. The overall absorption and transparency window were improved by growing them in a mixture of chloroform and acetone. The grown crystals were characterized for their optical transmission, mechanical hardness and laser damage. We have observed a strong correlation between mechanical properties and laser induced damage.

A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems

Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the �Single Network Adaptive Critic (SNAC)� is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.