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91.
A new trust-region and affine scaling algorithm for linearly constrained optimization is presented in this paper. Under no
nondegenerate assumption, we prove that any limit point of the sequence generated by the new algorithm satisfies the first
order necessary condition and there exists at least one limit point of the sequence which satisfies the second order necessary
condition. Some preliminary numerical experiments are reported.
The work was done while visiting Institute of Applied Mathematics, AMSS, CAS. 相似文献
92.
Using the Pirogov–Sinai theory, we study finite-size effects for the ferromagnetic q-state Potts model in a cube with boundary conditions that interpolate between free and constant boundary conditions. If the surface coupling is about half of the bulk coupling and q is sufficiently large, we show that only small perturbations of the ordered and disordered ground states are dominant contributions to the partition function in a finite but large volume. This allows a rigorous control of the finite-size effects for these weak boundary conditions. In particular, we give explicit formulæ for the rounding of the infinite-volume jumps of the internal energy and magnetization, as well as the position of the maximum of the finite-volume specific heat. While the width of the rounding window is of order L
–d
, the same as for periodic boundary conditions, the shift is much larger, of order L
–1. For strong boundary conditions—the surface coupling is either close to zero or close to the bulk coupling—the finite size effects at the transition point are shown to be dominated by either the disordered or the ordered phase, respectively. In particular, it means that sufficiently small boundary fields lead to the disordered, and not to the ordered Gibbs state. This gives an explicit proof of A. van Enter's result that the phase transition in the Potts model is not robust. 相似文献
93.
We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae
2
p
(1+a
1
e
–
+ ...) as , with p1. The staggered susceptibility behaves as
stagg
5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice. 相似文献
94.
C. Djurberg K. Jonason P. Nordblad 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(1):15-21
Experiments on the temperature and time dependence of the response function and the field cooled magnetisation of a Cu(Mn)
spin glass at temperatures below the zero field spin glass temperature are used to explore the non-equilibrium nature of the
underlying spin configuration. The results imply that a certain spin configuration is imprinted on the system as the temperature
is decreased at a constant cooling rate. The cooling rate governs the magnitude of the FC magnetisation ((H,T)). Any intermittent halt at a constant temperature, , imprints an extended spin configuration, a process that is reflected e.g. in a downward relaxation of . On continued cooling at the same rate, the magnitude of (T) remains at a lower level than that of a continuous cooling curve. These results are put into the context of the corresponding
behaviour of the response function as observed in measurements of the relaxation of the zero field cooled magnetisation.
Received 27 October 1998 and Received in final form 30 November 1998 相似文献
95.
Bernard Coupet Hervé Gaussier Alexandre Sukhov 《Proceedings of the American Mathematical Society》1999,127(11):3191-3200
We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in
96.
We consider an extension of the affine scaling algorithm for linear programming problems with free variables to problems having infinitely many constraints, and explore the relationship between this algorithm and the finite affine scaling method applied to a discretization of the problem.This material is based on research supported by Air Force Office of Scientific Research Grant AFOSR 89-0410. 相似文献
97.
Asymptotic normality of the solutions of the initial-value problems for multidimensional Burgers' equation with weakly dependent possible non-Gaussian initial condition is proved. 相似文献
98.
J. D. Gunton 《Journal of statistical physics》1984,34(5-6):1019-1037
A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ
N
models.Work supported by NSF grant No. DMR-8013700. 相似文献
99.
Che-Chian Ko Thein Kyu Steven D. Smith 《Journal of Polymer Science.Polymer Physics》1995,33(3):517-525
Dynamics of phase separation in bisphenol-A polycarbonate (PC)/syndiotactic polymethyl methacrylate (sPMMA) blends has been investigated by means of time-resolved light scattering. Solvent-cast films of the PC/sPMMA blends were transparent, suggestive of miscible character. Several temperature jumps were carried out at a 50/50 PC/sPMMA composition from a homogeneous state (room temperature) into a two-phase regime. The process of phase separation first occurred for some considerable period, then it was followed by phase dissolution driven by chemical reaction. The thermodegradative reaction of sPMMA triggered the dissolution process by probably forming PC/sPMMA graft or random copolymers at the interface, which eventually resulted in a single phase. However, annealing at elevated temperatures for an extended period could lead to cross-linking, and thus a two-phase structure could be fixed permanently. The early stage of spinodal decomposition was interpreted in terms of the linearized Cahn-Hilliard theory. In the late stages of spinodal decomposition, the relationship between scattering peak wavenumber and time was found to obey a power law, but the exponents showed a strong dependence on temperature jumps. The temporal universal scaling failed due to the influence of the chemical reaction. © 1995 John Wiley & Sons, Inc. 相似文献
100.
M. R. Koblischka S. L. Huang K. Fossheim T. H. Johansen H. Bratsberg 《Physica C: Superconductivity and its Applications》1998,300(3-4):207-211
Flux distributions of partial-melting processed Bi2Sr2CaCu2O8+δ ceramics are obtained using magneto-optic imaging. In remanent states (μ0Ha=0 T), large amounts of trapped flux are observed along (Sr,Ca)2CuOy particles embedded in the Bi2Sr2CaCu2O8+δ matrix. Despite the relatively large size of these particles (up to 30 μm), the pinning effect is similar to that of Y2BaCuO5 particles in melt-processed YBa2Cu3O7−δ. Furthermore, we discuss how the pinning capability of non-superconducting particles of different sizes and densities will show up in magneto-optic images. 相似文献