It is known that the direction of the magnetization vector of very fine single-domain ferromagnetic particles fluctuates under the influence of thermal agitation. Perturbation theory is applied rigorously to a singula...
It is known that the direction of the magnetization vector of very fine single-domain ferromagnetic particles fluctuates under the influence of thermal agitation. Perturbation theory is applied rigorously to a singular integral equation to derive an asymptotic formula for the relaxation time of the magnetization, for the case of uniaxial anisotropy and an applied magnetic field. The result agrees with that of Brown [Phys. Rev. 130, 1677 (1963)] as described succinctly by Aharoni [Phys. Rev. 177, 793 (1969)]. It should be emphasized that both Gilbert’s equation and the earlier Landau-Lifshitz equation are merely phenomenological equations, which are used to explain the time decay of the average magnetization. Brown suggested that the Gilbert equation should be augmented by a white-noise driving term in order to explain the effect of thermal fluctuations of the surroundings on the magnetization.
Ground based and satellite studies have indicated that, far from forming a steady state convection pattern, the electric field at high latitudes shows bursts of activity, particularly on the night-side, the bursts rep...
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Ground based and satellite studies have indicated that, far from forming a steady state convection pattern, the electric field at high latitudes shows bursts of activity, particularly on the night-side, the bursts repeating over time scales of less than an hour. Such dynamic fluctuations are thought to occur during intervals when the amount of energy input to the magnetosphere from the solar wind is large and there is evidence of an association with a southward turning of the IMF and magnetic reconnection in the magnetotail. The global coupled ionosphere/thermosphere model, developed in collaboration between Sheffield University and UCL, has been used to investigate the effects, both local and global, of such dynamic fluctuations in the high-latitude convection electric field.< >
A possible role for phonon excitations of the cytoskeleton in intraneuronal pattern recognition and learning is discussed. Biophysical support is presented for molecular implementation of adaptive resonant theory (ART...
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A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective...
A time-independent field theoretical framework for turbulence is suggested, based upon a variational principle for a stationary solution of the Fokker-Planck equation. We obtain a functional equation for the effective Action of this spatial field theory and investigate its general properties and some numerical solutions. The equation is completely universal, and allows for the scale invariant solutions in the inertial range. The critical indices are not fixed at the kinematical level, but rather should be found from certain eigenvalue conditions, as in the field theory of critical phenomena. Unlike the Wyld field theory, there are no divergences in our Feynman integrals, due to some magic cancellations. The simplest possible Gaussian approximation yields crude but still reasonable results (there are deviations from Kolmogorov scaling in 3 dimensions, but at 2.7544 dimensions it would be exact). Our approach allows us to study some new problems, such as spontaneous parity breaking in 3d turbulence. It turns out that with the appropriate helicity term added to the velocity correlation function, logarithmic infrared divergences arise in our field theory which effectively eliminates these terms. In order to build a quantitative theory of turbulence, one should consider more sophisticated Ansatz for the effective Action, which would require serious numerical work.
Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand trian...
Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand triangles. The grid Laplacian was inverted by means of the algebraic multi-grid solver. The free field model of the Quantum Gravity assumes the Gaussian behavior of Liouville field and curvature. We measured histograms as well as six momenta of these fields. Our results support the Gaussian assumption.
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical...
The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.
In this article we present a new formulation for coupling spectral element discretizations to finite difference and finite element discretizations addressing flow problems in very complicated geometries. A general ite...
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The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional general...
The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional generalization of the bonds flip, another is more sophisticated algorithm, based on Schwinger–Dyson equations. We found such care necessary, because our results appear to be quite unexpected. We simulated up to 60000 tetrahedra and observed none of the feared pathologies like factorial growth of the partition function with volume, or collapse to the branched polymer phase. The volume of the Universe grows exponentially when the bare cosmological constant λ approaches the critical value λ c from above, but the closed Universe exists and has peculiar continuum limit. The Universe compressibility diverges as (λ − λ c ) −2 and the bare Newton constant linearly approaches negative critical value as λ goes to λ c , provided the average curvature is kept at zero. The fractal properties turned out to be the same, as in two dimensions, namely the effective Hausdorff dimension grows logarithmically with the size of the test geodesic sphere.
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