Considers the problem of lattice trails, introduced by Malakis (1975, 1976). The author proves the existence of a finite connective constant, and establishes a result for the growth of n-step trails tnanalogous to the...
Considers the problem of lattice trails, introduced by Malakis (1975, 1976). The author proves the existence of a finite connective constant, and establishes a result for the growth of n-step trails tnanalogous to the best known result for self-avoiding walks, tn= lambdanexpt(O(/n)). For the honeycomb (d=2) and Lave's lattice (d=3) the author establishes a counting theorem, from which one can deduce the exact value of the connective constant lambda for the honeycomb lattice, lambda2=2+ square root 2. Further, it follows that the trail problem is in the same universality class as the self-avoiding walk problem for those lattices. An exact amplitude relation between trails and self-avoiding walks, and between dumb-bells, and trails and self-avoiding walks is established. The non-existence of a counting theorem for arbitrary lattices is established. An inequality for the triangular lattice connective constant is proved. A high-density expansion for lambda for the d-dimensional hybercubic lattice is also obtained. The author argues that, contrary to recent suggestions, the model is in the same universality class as the self-avoiding walk model.
Spacetimes admitting a group of (local) projective collineations are considered. In an n-dimensional proper Einstein space it is shown that any vector field xi(i) generating a proper projective collineation (that is o...
Spacetimes admitting a group of (local) projective collineations are considered. In an n-dimensional proper Einstein space it is shown that any vector field xi(i) generating a proper projective collineation (that is one which is not an affine collineation) is the gradient of a scalar field phi (up to the addition of a Killing vector field). Then a four-dimensional Einstein spacetime admitting a proper projective collineation is shown to have constant curvature. For an n-dimensional space of non-zero constant curvature, the scalar field phi satisfies a system of third-order linear differential equations. The complete solution of this system is found in closed form and depends on (n + 1)(n + 2)/2 arbitrary constants. All gradient vector fields xi(i) generating projective collineations are found explicitly and together with the n(n + 1) /2 killing vector fields generate a Lie algebra of dimension n(n + 2).
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 configuration of self-avoiding polymer molecules terminally attached to a rigid boundary is resolved into loop, train and tail components on the basis of a convolution integral analysis. The expectation lengths (l...
The configuration of self-avoiding polymer molecules terminally attached to a rigid boundary is resolved into loop, train and tail components on the basis of a convolution integral analysis. The expectation lengths (lloop), (ltrain) and (ltail) and the component fractions are determined as functions of chain length and chain-plane interaction. In the case of zero chain-plane attraction thre is good quantitative agreement with Monte Carlo estimates, although the predicted dependence of (lloop) upon chain length appears too strong. Results are also presented for hard sphere sequences as a function of chain-plane attraction when it is found that there is a progressive redistribution amongst loop and tail states, the train exponent remaining essentially unmodified over the range of interactions investigated. Exponent representations are proposed and compared with earlier analyses. The various component structures are discussed in terms of the interplay of entropic and energetic processes at the boundary.
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.
The iterative convolution (IC) technique previously reported for linear self-avoiding sequences is extended to the description of nonintersecting rings of hard-sphere segments. The principal geometrical features of ri...
The iterative convolution (IC) technique previously reported for linear self-avoiding sequences is extended to the description of nonintersecting rings of hard-sphere segments. The principal geometrical features of rings of N=20, 40 and 62 segments are determined, including the intersegmental spatial distribution functions, the mean-square intersegmental separations, the radius of gyration, bond correlation function and segment density distribution function. These quantities are compared with independent Monte Carlo estimates, and the results are found to be generally in good quantitative agreement. A sum rule for the bond correlation function is proposed for rings, whilst the segment density distribution is found to exhibit serrations which are unresolved in the Monte Carlo data scatter. These serrations, moreover, occur at integral multiples of the segment diameter and are attributed to entropic processes associated with ring closure.
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.
The Letter describes how discrete Markov chains may be applied to speech recognition. In this application, a spectral vector is modelled by a state of a Markov chain, and an utterance is viewed as a sequence of observ...
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The Letter describes how discrete Markov chains may be applied to speech recognition. In this application, a spectral vector is modelled by a state of a Markov chain, and an utterance is viewed as a sequence of observed states. Experiment showed that a speech recogniser based on this Markov model not only outperforms the HMM recognisers tested for comparison, but also offers a saving in comput.tion time.
The Lecanda-Roman-Roy geometric constraint algorithm for presymplectic Lagrangian systems is applied 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 applied 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.
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