Approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic

In 1956 Whitham gave a nonlinear theory for computing the intensity of an acoustic pulse of an arbitrary shape. The theory has been used very successfully in computing the intensity of the sonic bang produced by a supersonic plane. [4.] derived an approximate quasi-linear equation for the propagation of a short wave in a compressible medium. These two methods are essentially nonlinear approximations of the perturbation equations of the system of gas-dynamic equations in the neighborhood of a bicharacteristic curve (or rays) for weak unsteady disturbances superimposed on a given steady solution. In this paper we have derived an approximate quasi-linear equation which is an approximation of perturbation equations in the neighborhood of a bicharacteristic curve for a weak pulse governed by a general system of first order quasi-linear partial differential equations in m + 1 independent variables (t, x1,…, xm) and derived Gubkin's result as a particular case when the system of equations consists of the equations of an unsteady motion of a compressible gas. We have also discussed the form of the approximate equation describing the waves propagating upsteam in an arbitrary multidimensional transonic flow.

Analytical method for solving a set of inhomogeneous infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of inhomogeneous infinite simultaneous equations encountered in the analysis of surface acoustic wave propagation along the periodically perturbed surface of a piezoelectric medium.

A critical analysis of the shear difference method

The shear difference method which is commonly used for the separation of normal stresses using photoelastic techniques depends on the step-by-step integration of one of the differential equations of equilibrium. It is assumed that the isoclinic and the isochromatic parameters measured by the conventional methods pertain to the state of stress at the midpoint of the light path. In practice, a slice thin enough for the above assumption to be true and at the same time thick enough to give differences in the shear-stress values over the thickness is necessary. The paper discusses the errors introduced in the isoclinic and isochromatic values by the conventional methods neglecting the variation of stresses along the light path. It is shown that while the error introduced in the measurement of the isochromatic parameter may not be serious, the error caused in the isoclinic measurement may lead to serious errors. Since the shear-difference method involves step-by-step integration the error introduced will be of a cumulative nature.

An analytical approach to the study of a class of bi-state social interaction processes

Sufficient conditions for obtaining an equivalent linear model to classes of non-linear, bi-state, social interaction processes are derived. These parametric constraints, when satisfied, permit analytical determination of the dynamics of the non-linear process of social interaction.

Conformationally Restricted Nucleocyclitols: a Study into their Conformational Preferences and Supramolecular Architecture in the Solid State

With the intent of probing the feasibility of employing annulation as a tactic to engender axial rich conformations in nucleoside analogues, two adenine-derived, ``conformationally restricted'' nucleocylitols, 9 and 10, have been conceptualized as representatives of a hitherto unexplored class of nucleic acid base-cyclitol hybrids. A general synthetic strategy, with an inherent scope for diversification, allowed rapid functionalization of indane and tetralin to furnish 9 and 10 respectively in fair yield. Single-crystal X-ray diffraction analysis revealed that the two nucleocyclitols under study, though homologous, present completely dissimilar modes of molecular packing, marked, in particular, by the nature of involvement of the adenynyl NH2 group in the supramolecular assembly. In addition, the crystal structures of 9 and 10 also exhibit two different conformations of the functionalized cyclohexane ring. Thus, while the six-membered carbocycle in cyclopenta-annulated 9 exists in the expected chair (C) conformation that in cyclohexaannulated 10, which crystallizes as a dihydrate, shows an unusual twist-boat (TB) conformation. From a close analysis of the (HNMR)-H-1 spectroscopic data recorded for 9 and 10 in CD3OD, it was possible to put forth a putative explanation for the uncanny conformational preferences of crystalline 9 and 10.

Nonlinear Control Design for an Air-breathing Engine with State Estimation

A nonlinear control design approach is presented in this paper for a challenging application problem of ensuring robust performance of an air-breathing engine operating at supersonic speed. The primary objective of control design is to ensure that the engine produces the required thrust that tracks the commanded thrust as closely as possible by appropriate regulation of the fuel flow rate. However, since the engine operates in the supersonic range, an important secondary objective is to ensure an optimal location of the shock in the intake for maximum pressure recovery with a sufficient margin. This is manipulated by varying the throat area of the nozzle. The nonlinear dynamic inversion technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs have also been carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, an extended Kalman Filter based state estimation design has been carried out both to filter out the process and sensor noises as well as to make the control design operate based on output feedback. Promising simulation results indicate that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing system.

An appendix to the paper "approximation of the perturbation equations of a quasi-linear hyperbolic system in the neighborhood of a bicharacteristic"

The theory of Varley and Cumberbatch [l] giving the intensity of discontinuities in the normal derivatives of the dependent variables at a wave front can be deduced from the more general results of Prasad which give the complete history of a disturbance not only at the wave front but also within a short distance behind the wave front. In what follows we omit the index M in Eq. (2.25) of Prasad [2].

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Thermal decomposition of hydrazinium monoperchlorate in the molten state

The thermal decomposition of hydrazinium monoperchlorate (HP-1) in the molten state has been investigated using differential thermal analysis, thermogravimetric analysis, a constant volume manometric technique and mass-spectrometry. The stoichiometry of the reaction can be represented by the equation: 20 N2H5C1O4 13 NH4C1O4 + 3.5 Cl2 + 2 O2 + 13 N2 + 0.5 N2O + 0.5 H2 + + 23.5 H2O The data seem to indicate that the mechanism, which involves an associated complex, remains unchanged from 140 to 190°. Consequently, impurities capable of forming associated complexes with the hydrazinium or the perchlorate ion desensitize the thermal decomposition of HP-1, the extent of desensitization being determined by the size, the charge and the concentration of the impurity.

Analytical method for solving a set of infinite simultaneous equations

It is shown that a method based on the principle of analytic continuation can be used to solve a set of infinite simultaneous equations encountered in solving for the electric field of a periodic electrode structure.