Fractal structure of high-temperature graphs of O(N) models in two dimensions

The critical behavior of the two-dimensional O(N) model close to criticality is shown to be encoded in the fractal structure of the high-temperature graphs of the model. Based on Monte Carlo simulations and with the help of percolation theory, de Gennes' results for polymer rings, corresponding to the limit N-->0, are generalized to random loops for arbitrary -2相似文献   

Continuity of eigenvalues for Schrödinger operators, $L^p$-properties of Kato type integral operators

Given an arbitrary relatively compact (finely) open subset of -eigenvalues of are studied where is the Dirichlet Laplacian on D and are measures on such that is continuous and is bounded for every ball X in being Green's function for X). Moreover, it is shown that these eigenvalues depend continuously on D and . The results are based on very general compactness and convergence properties of integral operators of Kato type which are developed before. Received: 9 November 2000 / Published online: 24 September 2001     

Global comparison of perturbed Green functions

Given a Green function G (e.g. with respect to (−Δ)^α/2, 0<α≤2) on a region X where G has a generalized triangle property and given a (G-bounded) signed measure μ on X, necessary and sufficient conditions are given for the existence of a perturbed Green function which is comparable with G. This is done in the general setting of measurable spaces. Applications to C^1,1-regions in R^d and, for the classical case α=2, to finitely connected regions in ℝ² are given.     

Preconcentration methods for the determination of trace elements in water by x-ray fluorescence spectrometry: Part 2. Interference studies

Seven methods for the preconcentration of fifteen elements for their subsequent measurement by x-ray fluorescence spectrometry have been evaluated for their susceptibility to interferences. A two-level factorial experimental design has been used, enabling an economical and meaningful comparison of the seven methods to be made. A scheme for rating the methods on the basis of the effect of several interfering species is proposed. Use of such a scheme has enabled an objective comparison of the methods considered to yield their relative ranks. It is also shown that spectral and chemical interferences can be discerned to some extent. Combination of the response rating proposed earlier and the interference rating schemes reported here gives rise to an overall comparison and rank for the methods, allowing an objective choice of the optimal method(s) to be made.     

Intrinsic Hölder Continuity of Harmonic Functions

We consider the stochastic differential equation (SDE) of the form

$$\begin{array}{@{}rcl@{}} \left\{\begin{array}{rcl} dX^ x(t) &=& \sigma(X(t-)) dL(t) \\ X^ x(0)&=&x,\quad x\in{\mathbb{R}}^ d, \end{array}\right. \end{array} $$

where \(\sigma :{\mathbb {R}}^ d\to {\mathbb {R}}^ d\) is globally Lipschitz continuous and L={L(t):t≥0} is a Lévy process. Under this condition on σ it is well known that the above problem has a unique solution X. Let \((\mathcal {P}_{t})_{t\ge 0}\) be the Markovian semigroup associated to X defined by \(\left ({\mathcal {P}}_{t} f\right ) (x) := \mathbb {E} \left [ f(X^ x(t))\right ]\), t≥0, \(x\in {\mathbb {R}}^{d}\), \(f\in \mathcal {B}_{b}({\mathbb {R}}^{d})\). Let B be a pseudo–differential operator characterized by its symbol q. Fix \(\rho \in \mathbb {R}\). In this article we investigate under which conditions on σ, L and q there exist two constants γ>0 and C>0 such that

$$\left| B {\mathcal{P}}_{t} u \right|_{H^{\rho}_{2}} \le C \, t^{-\gamma} \,\left| u \right|_{H^{\rho}_{2}}, \quad \forall u \in {H^{\rho}_{2}}(\mathbb{R}^{d} ),\, t>0. $$

     

Wang-Landau multibondic cluster simulations for second-order phase transitions

For a second-order phase transition the critical energy range of interest is larger than the energy range covered by a canonical Monte Carlo simulation at the critical temperature. Such an extended energy range can be covered by performing a Wang-Landau recursion for the spectral density followed by a multicanonical simulation with fixed weights. But in the conventional approach one loses the advantage due to cluster algorithms. A cluster version of the Wang-Landau recursion together with a subsequent multibondic simulation improves for 2D and 3D Ising models the efficiency of the conventional Wang-Landau or multicanonical approach by power laws in the lattice size. In our simulations real gains in CPU time reach 2 orders of magnitude.