The Lecanda-Roman-Roy geometric constraint algorithm for presymplectic Lagrangian systems is appl.ed to a mechanical model of singular field theories coupled to time independent external fields. The simple, yet intrin...
The Lecanda-Roman-Roy geometric constraint algorithm for presymplectic Lagrangian systems is appl.ed to a mechanical model of singular field theories coupled to time independent external fields. The simple, yet intrinsic structure of the algorithm allows the influence of the external field to be traced through the constraint analysis, showing clearly where pathologies arise-namely in the second generation non-dynamical constraints arising from the stability of the first generation compatibility constraints. Using a coordinate independent geometric algorithm provides a more systematic tool for investigating singular field theories than the usual ad hoc manipulation of the field equations;where the essential structure is often obscured by the details of the representation of the model and the complexity of the algebra.
For ill-posed initial value problems, step by step marching comput.tions are unconditionally unstable, and necessarily blow-up numerically as the mesh is refined. However, for the 1D nonlinear inverse heat conduction ...
For ill-posed initial value problems, step by step marching comput.tions are unconditionally unstable, and necessarily blow-up numerically as the mesh is refined. However, for the 1D nonlinear inverse heat conduction problem, we show how to construct consistent marching schemes that blow-up much more slowly than the counterpart analytical problem. Several new space marching finite difference schemes are formulated and compared with existing schemes relative to their error amplification properties. Using the Lax-Richtmyer theory, we evaluate the L2 norms of the linearized discrete solution operators mapping the sensor data into the desired temperature and gradient histories at the inaccessible active surface. Various combinations of space and time differencing are examined, leading to 18 different algorithms. A non-dimensional parameter-OMEGA, involving the time step DELTA-t, the effective thermal diffusivity-alpha, and the distance-iota from the sensor to the active surface, is shown to provide a measure of the numerical difficulty of the inverse calculation. All 18 schemes blow-up like 10-lambda-OMEGA, where the constant-lambda depends on the particular numerical method. There are substantial differences in the lambda's however, and some new algorithms, employing forward time differences at non-adjacent mesh points, are shown to produce relatively low values of lambda. Next, using synthetic noisy data, a nonlinear reconstruction problem is considered for which OMEGA = 25. This problem simulates heat transfer in gun barrels when a shell is fired. It is shown that while most of the 18 schemes cannot recover the thermal pulses at the gun tube wall, two of the new methods provide reasonably accurate results. A tendency to underestimate peak values in fast, narrow thermal pulses, is also noted.
The topics discussed here are network models of object recognition; a comput.tional theory of recognition; psychophysical support for a view-interpolation model: and an open issue, features of recognition. The authors...
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The topics discussed here are network models of object recognition; a comput.tional theory of recognition; psychophysical support for a view-interpolation model: and an open issue, features of recognition. The authors survey a successful replication of central characteristics of performance in 3-D object recognition by a comput.tional model based on interpolation among a number of stored views of each object. Network models of 3-D object recognition based on interpolation among specific stored views behave in several respects similarly to human observers in a number of recognition tasks. Even closer replication of human performance in recognition should be expected, once the issue of the features used to represent object views is resolved.< >
The energy spectrum and the eigenvectors of a charged particle in a uniform electric field with alternating site energies are studied for infinite systems. For the case of large energy mismatch, exact solutions are pr...
The energy spectrum and the eigenvectors of a charged particle in a uniform electric field with alternating site energies are studied for infinite systems. For the case of large energy mismatch, exact solutions are presented by using perturbation theory, from which it is found that the spectrum is that of two interspaced Stark ladders. The character of these Stark ladders is that the difference of the ratio of the energy and the field between two energies on a same rung is an even number.
In direct contrast to adaptive controllers the deterministic control of uncertain time-varying systems control is achieved using fixed nonlinear feedback control functions, which operate effectively over a specified m...
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In direct contrast to adaptive controllers the deterministic control of uncertain time-varying systems control is achieved using fixed nonlinear feedback control functions, which operate effectively over a specified magnitude range of a class of system parameter variations. There is no requirement for online identification of the values of the system parameters. Furthermore no statistical information of the system variations is required to yield the desired robust dynamic behaviour. If the parameter variations satisfy certain matching conditions, complete insensitivity to system variations can be achieved. The two main approaches, variable structure control (VSC) and Lyapunov control, are described.< >
Summary form only given, as follows. When a neural net is used to solve continuous problems, the learning environment, which may influence convergence and accuracy, differs from that for true-false problems. Based on ...
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Summary form only given, as follows. When a neural net is used to solve continuous problems, the learning environment, which may influence convergence and accuracy, differs from that for true-false problems. Based on the energy model for a neural net, different activity levels of the net are generalized to learn one selected continuous problem-polynomial function. The training results showed that there are some optimal activity levels that lead the net to obtain better accuracy than that from other levels. The concepts of maximum energy and minimum energy (or 'thermal noise') are proposed to explain why it is possible for a net to achieve a good learning environment to fit to the continuous problems.< >
The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector a...
The existence of Killing vectors in conformally flat perfect fluid spacetimes in general relativity is considered. In particular Killing vectors which are neither orthogonal nor parallel to the fluid velocity vector are considered and stationary fields in which the fluid velocity vector is not parallel to the timelike Killing vector field are shown to exist. This class of solutions is shown to include several stationary (but non-static) axisymmetric fields, thus providing counter-examples to a theorem of Collinson (1976). In the case when the fluid is non-expanding, the number of spacelike Killing vectors is shown to depend on the rank of four functions of time which appear in the metric. Some examples of stationary but non-static fields are presented in closed form.
The maximum anisotropic approximation for electron transport in an electric field is extended to the position-dependent case. Models utilising nonpolar optical, acoustic and piezoelectric phonon scattering processes a...
The maximum anisotropic approximation for electron transport in an electric field is extended to the position-dependent case. Models utilising nonpolar optical, acoustic and piezoelectric phonon scattering processes are constructed. The piezoelectric model produces the Euler-Darboux equation in the position-dependent case and an analytical solution is given. Analytical solutions are given for each of the models in the position-independent case.
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed tha...
All perfect fluid spacetimes with a purely electric Weyl tensor are shown to have an alignment between the fluid 4-velocity and a canonical null tetrad determined by the Weyl tensor. If, in addition, it is assumed that the flow is irrotational, the eigenframes of the shear and Weyl tensors coincide. In all but two rather special cases, it is proved that the vectors of this eigenframe are hypersurface orthogonal and consequently that a coordinate system exists in which the metric, shear and Eab(the electric part of the Weyl tensor) are all diagonal. Geodesic Petrov type D spacetimes are shown to be either Bianchi type 1 or to belong to the class of solutions considered by Szekeres (1975) and Szafron (1977). The Allnutt solutions (1982) are shown to be the only purely electric type D fields in which the shear is non-degenerate and in which the acceleration vector lies in the plane spanned by the principal null vectors. The field equations are partially integrated in two classes where no solutions are yet known.
The speed of a second-sound wave in liquid helium II is known to depend on amplitude, and thermal shocks may form. Prediction of the shock velocity depends on which conservation laws hold across the discontinuity. Whe...
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The speed of a second-sound wave in liquid helium II is known to depend on amplitude, and thermal shocks may form. Prediction of the shock velocity depends on which conservation laws hold across the discontinuity. When dissipation is taken into account a smooth but rapidly varying wave profile is predicted in place of a discontinuity. It is shown how waves of this kind may be used to resolve an uncertainty surrounding one of the conserved quantities across a shock. A number of wave profiles are also exhibited in the vicinity of a critical equilibrium temperature.
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