Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Phase relations between Al2O3---Cr2O3 and FeAl2O4---FeCr2O4 solid solutions at 1823 K

Tie-lines between the corundum and spinel solid solutions have been determined experimentally at 1823 K. Next, activities of FeCr2O4 and FeAl2O4 in the spinel solid solution were determined by combining the tie-line data with literature values for the activities of Cr2O3 and Al2O3 in the corundum phase. Activities and the Gibbs energy of mixing for the spinel solid solution were also obtained from a model based on cation distribution between nonequivalent crystallographic sites in the oxide lattice. The difference between the Gibbs energy of mixing obtained experimentally and from the model has been attributed to a strain enthalpy term which is relatively unchanged in magnitude from the reported at 1373 K. The integral enthalpy of mixing obtained from experimental data at 1373 and 1823 K using the second law is compared with the model result.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

Generalized Burgers equations and Euler-Painleve transcendents. II

It was proposed earlier [P. L. Sachdev, K. R. C. Nair, and V. G. Tikekar, J. Math. Phys. 27, 1506 (1986)] that the Euler Painlevé equation yy[script `]+ay[script ']2+ f(x)yy[script ']+g(x) y2+by[script ']+c=0 represents the generalized Burgers equations (GBE's) in the same manner as Painlevé equations do the KdV type. The GBE was treated with a damping term in some detail. In this paper another GBE ut+uaux+Ju/2t =(gd/2)uxx (the nonplanar Burgers equation) is considered. It is found that its self-similar form is again governed by the Euler Painlevé equation. The ranges of the parameter alpha for which solutions of the connection problem to the self-similar equation exist are obtained numerically and confirmed via some integral relations derived from the ODE's. Special exact analytic solutions for the nonplanar Burgers equation are also obtained. These generalize the well-known single hump solutions for the Burgers equation to other geometries J=1,2; the nonlinear convection term, however, is not quadratic in these cases. This study fortifies the conjecture regarding the importance of the Euler Painlevé equation with respect to GBE's. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Dipole ordering in dilute solutions of ferroelectrics in antiferroelectric materials

The coefficients of thermal expansion reported by Worlton et al. [6] in the case of zircon are given in Table II along with the present data. Although Oql > or• in both cases, the anisotropy is more marked in the case of DyV04. From Table II, it is clear that the coefficient of volume expansion (,6) is almost the same for both compounds.

Bearing capacity factor N-c under phi=0 condition for piles in clays

Bearing capacity factor N-c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (phi=0) condition. The Study follows the lower bound limit analysis in conjunction With finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N-c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N-c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N-c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature.

Soft Functional Materials Induced by Fibrillar Networks of Small Molecular Photochromic Gelators

Low-molecular-mass organogelators (LMOGs) based on photochromic molecules aggregate in selected solvents to form gels through various spatio-temporal interactions. The factors that control the mode of aggregation of the chromophoric core in the LMOGs during gelation, gelation-induced changes in fluorescence, the formation of stacked superstructures of extended pi-conjugated systems, and so forth are discussed with selected examples. Possible ways of generating various light-harvesting assemblies are proposed, and some unresolved questions, future challenges, and their possible solutions on this topic are presented.

Synergistic Execution of Stream Programs on Multicores with Accelerators

The StreamIt programming model has been proposed to exploit parallelism in streaming applications oil general purpose multicore architectures. The StreamIt graphs describe task, data and pipeline parallelism which can be exploited on accelerators such as Graphics Processing Units (GPUs) or CellBE which support abundant parallelism in hardware. In this paper, we describe a novel method to orchestrate the execution of if StreamIt program oil a multicore platform equipped with an accelerator. The proposed approach identifies, using profiling, the relative benefits of executing a task oil the superscalar CPU cores and the accelerator. We formulate the problem of partitioning the work between the CPU cores and the GPU, taking into account the latencies for data transfers and the required buffer layout transformations associated with the partitioning, as all integrated Integer Linear Program (ILP) which can then be solved by an ILP solver. We also propose an efficient heuristic algorithm for the work-partitioning between the CPU and the GPU, which provides solutions which are within 9.05% of the optimal solution on an average across the benchmark Suite. The partitioned tasks are then software pipelined to execute oil the multiple CPU cores and the Streaming Multiprocessors (SMs) of the GPU. The software pipelining algorithm orchestrates the execution between CPU cores and the GPU by emitting the code for the CPU and the GPU, and the code for the required data transfers. Our experiments on a platform with 8 CPU cores and a GeForce 8800 GTS 512 GPU show a geometric mean speedup of 6.94X with it maximum of 51.96X over it single threaded CPU execution across the StreamIt benchmarks. This is a 18.9% improvement over it partitioning strategy that maps only the filters that cannot be executed oil the GPU - the filters with state that is persistent across firings - onto the CPU.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.

Improving Flow-Insensitive Solutions for Non-Separable Dataflow Problems

Flow-insensitive solutions to dataflow problems have been known to be highly scalable; however also hugely imprecise. For non-separable dataflow problems this solution is further degraded due to spurious facts generated as a result of dependence among the dataflow facts. We propose an improvement to the standard flow-insensitive analysis by creating a generalized version of the dominator relation that reduces the number of spurious facts generated. In addition, the solution obtained contains extra information to facilitate the extraction of a better solution at any program point, very close to the flow-sensitive solution. To improve the solution further, we propose the use of an intra-block variable renaming scheme. We illustrate these concepts using two classic non-separable dataflow problems --- points-to analysis and constant propagation.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.