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.
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.
Thermal annealing of the E(c) - 0.18 eV level in Czochralski-grown silicon crystals irradiated by Co-60 gamma rays has been investigated using Hall effect measurements. An anomalous annealing kinetics has been found, ...
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Thermal annealing of the E(c) - 0.18 eV level in Czochralski-grown silicon crystals irradiated by Co-60 gamma rays has been investigated using Hall effect measurements. An anomalous annealing kinetics has been found, in which the centre disappearance probability is increased with isothermal annealing time. A tentative kinetic model of the process is proposed.
Previous results on nonlearnability of visual concepts relied on the assumption that such concepts are represented as sets of pixels [1]. This correspondence uses an approach developed by Haussler [2] to show that und...
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Previous results on nonlearnability of visual concepts relied on the assumption that such concepts are represented as sets of pixels [1]. This correspondence uses an approach developed by Haussler [2] to show that under an alternative, feature-based representation, recognition is PAC learnable from a feasible number of examples in a distribution-free manner.
N. Metropolis's (1953) algorithm has often been used for simulating physical systems that pass among a set of states, with the probabilities of the system being in such states distributed like the Boltzmann functi...
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N. Metropolis's (1953) algorithm has often been used for simulating physical systems that pass among a set of states, with the probabilities of the system being in such states distributed like the Boltzmann function. There are literally thousands of different appl.cations in the physical sciences and elsewhere. In this article, we explain how to reformulate the basic Metropolis algorithm so as to avoid the do-nothing steps and reduce the running time, while also keeping track of the simulated time as determined by the Metropolis algorithm. By the simulated time, we mean the number of Monte Carlo steps that would have been taken if the basic Metropolis algorithm had been used. This approach has already proved successful when used for parallel simulations of molecular beam epitaxy. We show an example.
The wavevector selection rules (WVSR) occurring in the reduction of Kronecker products of space group unirreps are classified, for convenience, into three types. For WVSR of type I, Dirl (1979) has shown that special ...
The wavevector selection rules (WVSR) occurring in the reduction of Kronecker products of space group unirreps are classified, for convenience, into three types. For WVSR of type I, Dirl (1979) has shown that special solutions of the multiplicity problem always exist. For WVSR of type II, Dirl has given a simple criterion for the existence for special solutions of the multiplicity problem and the authors show that, for all 230 (single and double) space groups, the Miller and Love matrix unirreps satisfy this criterion. WVSR of type III will be considered in a subsequent paper.
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.
Here we develop the Topological Approximation Method (TAM) which gives a new description of the mixing and transport processes in chaotic two-dimensional time-periodic Hamiltonian flows. It is based upon the structure...
Here we develop the Topological Approximation Method (TAM) which gives a new description of the mixing and transport processes in chaotic two-dimensional time-periodic Hamiltonian flows. It is based upon the structure of the homoclinic tangle, and supplies a detailed solution to a transport problem for this class of systems, the characteristics of which are typical to chaotic, yet not ergodic dynamical systems. These characteristics suggest some new criteria for quantifying transport and mixing-hence chaos-in such systems. The results depend on several parameters, which are found by perturbation analysis in the near integrable case, and numerically otherwise. The strength of the method is demonstrated on a simple model. We construct a bifurcation diagram describing the changes in the homoclinic tangle as the physical parameters are varied. From this diagram we find special regions in the parameter space in which we approximate the escape rates from the vicinity of the homoclinic tangle, finding non-trivial self-similar solutions as the forcing magnitude tends to zero. We compare the theoretical predictions with brute force calculations of the escape rates, and obtain satisfactory agreement.
For pt.I see ibid., vol.19, p.831-40, 1986. In paper I of this series, special solutions of the multiplicity problem were established for wavevector selection rules (WVSR) of types I and II occurring in the reduction ...
For pt.I see ibid., vol.19, p.831-40, 1986. In paper I of this series, special solutions of the multiplicity problem were established for wavevector selection rules (WVSR) of types I and II occurring in the reduction of Kronecker products of space group unirreps. A comput.r program based on Dirl's method is described which has been to show that special solutions of the multiplicity problem exist for all WVSR of type III in the reduction of Kronecker products of Miller and Love matrix unirreps in all 230 (single and double) space groups.
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