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.

Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

A geodesic constant method for computing high-frequency mutual coupling between antennas on general quadric cylinders

A Geodesic Constant Method (GCM) is outlined which provides a common approach to ray tracing on quadric cylinders in general, and yields all the surface ray-geometric parameters required in the UTD mutual coupling analysis of conformal antenna arrays in the closed form. The approach permits the incorporation of a shaping parameter which permits the modeling of quadric cylindrical surfaces of desired sharpness/flatness with a common set of equations. The mutual admittance between the slots on a general parabolic cylinder is obtained as an illustration of the applicability of the GCM.

Analysis of continuum using boundary compatibility conditions of integrated force method

Static and vibration problems of an indeterminate continuum are traditionally analyzed by the stiffness method. The force method is more or less non-existent for such problems. This situation is primarily due to the incomplete state of development of the compatibility conditions which are essential for the analysis of indeterminate structures by the flexibility method. The understanding of the Compatibility Conditions (CC) has been substantially augmented. Based on the understanding of CC, a novel formulation termed the Integrated Force Method (IFM) has been established. In this paper IFM has been extended for the static and vibration analyses of a continuum. The IFM analysis is illustrated taking three examples: 1. (1) rectangular plate in flexure 2. (2) analysis of a cantilevered dam 3. (3) free vibration analysis of a beam. From the examples solved it is observed that the force response of an indeterminate continuum with mixed boundary conditions can be generated by IFM without any reference to displacements in the field or on the boundary. Displacements if required can be calculated by back substitution.

An efficient marching algorithm for waterhammer analysis by the method of characteristics

A new fast and efficient marching algorithm is introduced to solve the basic quasilinear, hyperbolic partial differential equations describing unsteady, flow in conduits by the method of characteristics. The details of the marching method are presented with an illustration of the waterhammer problem in a simple piping system both for friction and frictionless cases. It is shown that for the same accuracy the new marching method requires fewer computational steps, less computer memory and time.

Integral method for the calculation of incompressible two-dimensional transitional boundary layers

The method proposed here considers the mean flow in the transition zone as a linear combination of the laminar and turbulent boundary layer in proportions determined by the transitional intermittency, the component flows being calculated by approximate integral methods. The intermittency distribution adopted takes into account the possibility of subtransitions within the zone in the presence of strong pressure gradients. A new nondimensional spot formation rate, whose value depends on the pressure gradient, is utilized to estimate the extent of the transition zone. Onset location is determined by a correlation that takes into account freestream turbulence and facility-specific residual disturbances in test data. Extensive comparisons with available experimental results in strong pressure gradients show that the proposed method performs at least as well as differential models, in many cases better, and is always faster.

A parametric method 3 (PM3) study of trans‐stilbene

We report a comparative modified neglect of diatomic overlap (MNDO), Austin method one (AM1), and parametric method 3 (PM3) study of trans‐stilbene (tS) in its ground, excited (singlet and triplet), and ionic (positive and negative polarons and bipolarons) states. We have also calculated the barrier for ring rotation about the backbone single bond. Our results show that PM3 geometries are superior to MNDO and AM1, at least for tS. PM3 predicts, in contrast with MNDO, AM1 and even ab initio 3‐21G, a coplanar structure for tS, in accordance with recent experimental data. Singlet and triplet energies obtained from heats of formation are in surprisingly good agreement with experimental data.

Biorthogonal series method for Oseen type flows

A biorthogonal series method is developed to solve Oseen type flow problems. The theory leads to a new set of eigenfunctions for a specific class of linear non-selfadjoint operators containing the biharmonic one. These eigenfunctions differ from those given earlier in the literature for the biharmonic operator. The method is applied to the problem of thermocapillary flow in a cylindrical liquid bridge of finite length with axial through flow. Flow and temperature distributions are obtained at leading order of an expansion for small surface tension Reynolds number and Prandtl number. Another related problem considered is that of cylindrical cavity flow. Solutions for both cases are presented in terms of biorthogonal series. The effect of axial through flow on velocity and temperature fields is discussed by numerical evaluation of the truncated analytical series. The presence of axial through flow not only convectively shifts the vortices induced by surface forces in the direction of the through flow, but also moves their centers toward the outer cylindrical boundary. This process can lead to significantly asymmetric flow structures.

Interruption and Uncooperativeness in Academic ELF Group Work : An Application of Linear Unit Grammar

This study addresses the challenge of analyzing interruption in spoken interaction. It begins with my observation of eight hours of academic group work among speakers of English as a lingua franca (ELF) in a university course. Unlike the common findings of ELF research which underscore the cooperative orientation of ELF users, this particular group gave strong impressions of interruption and uncooperativeness as they prepared a scientific group presentation. In the effort to investigate these impressions, I found that no satisfactory method exists for systematically identifying and analyzing interruptions. A useful tool was found in Linear Unit Grammar or LUG (Sinclair & Mauranen 2006), which analyzes spoken interaction prospectively as linear text. In the course of transcribing one of the early group work meetings, I developed a model of LUG-based criteria for identifying individual instances of interruption. With this system in place, I was then able to evaluate the aggregate occurrences of interruption in the group work and identify co-occurring interactive features which further influenced the perception of uncooperativeness. Finally, these aggregate statistics directed a return to the data and a contextually sensitive, qualitative analysis. This research cycle illuminates the interactive features which contributed to my own impressions of uncooperativeness, as well as the group members orientations to their own interruptive practice.

A simple method for potential flow simulation of cascades

A simple method using a combination of conformal mapping and vortex panel method to simulate potential flow in cascades is presented. The cascade is first transformed to a single body using a conformal mapping, and the potential flow over this body is solved using a simple higher order vortex panel method. The advantage of this method over existing methodologies is that it enables the use of higher order panel methods, as are used to solve flow past an isolated airfoil, to solve the cascade problem without the need for any numerical integrations or iterations. The fluid loading on the blades, such as the normal force and pitching moment, may be easily calculated from the resultant velocity field. The coefficient of pressure on cascade blades calculated with this methodology shows good agreement with previous numerical and experimental results.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part II. Computed results and experimental corroboration thereof

Time-domain-finite-wave analysis of engine exhaust systems is usually carried out by means of the method of characteristics. The theory and the computational details of the stationary-frame method have been worked out in the accompanying paper (part I). In this paper (part II), typical computed results are given and discussed. A setup designed for experimental corroboration is described. The results obtained from the simulation are found to be in good agreement with experimental observations.

A hybrid technique of modeling of cracks using displacement discontinuity and direct boundary element method

A hybrid technique to model two dimensional fracture problems which makes use of displacement discontinuity and direct boundary element method is presented. Direct boundary element method is used to model the finite domain of the body, while displacement discontinuity elements are utilized to represent the cracks. Thus the advantages of the component methods are effectively combined. This method has been implemented in a computer program and numerical results which show the accuracy of the present method are presented. The cases of bodies containing edge cracks as well as multiple cracks are considered. A direct method and an iterative technique are described. The present hybrid method is most suitable for modeling problems invoking crack propagation.

A novel method for diameter estimation of small opaque objects using Fraunhofer diffraction

A novel optical method is proposed and demonstrated, for real-time dimension estimation of thin opaque cylindrical objects. The methodology relies on free-space Fraunhofer diffraction principle. The central region, of such tailored diffraction pattern obtained under suitable choice of illumination conditions, comprises of a pair of `equal intensity maxima', whose separation remains constant and independent of the diameter of the diffracting object. An analysis of `the intensity distribution in this region' reveals the following. At a point symmetrically located between the said maxima, the light intensity varies characteristically with diameter of the diffracting object, exhibiting a relatively stronger intensity modulation under spherical wave illumination than under a plane wave illumination. The analysis reveals further, that the said intensity variation with diameter is controllable by the illumination conditions. Exploiting these `hitherto unexplored' features, the present communication reports for the first time, a reliable method of estimating diameter of thin opaque cylindrical objects in real-time, with nanometer resolution from single point intensity measurement. Based on the proposed methodology, results of few simulation and experimental investigations carried-out on metallic wires with diameters spanning the range of 5 to 50 mu m, are presented. The results show that proposed method is well-suited for high resolution on-line monitoring of ultrathin wire diameters, extensively used in micro-mechanics and semiconductor industries, where the conventional diffraction-based methods fail to produce accurate results.