Showing papers by "Michael E. Fisher published in 1989"

The three-dimensional Ising model revisited numerically

Abstract: Several basic universal amplitude ratios are studied afresh for three-dimensional nearest-neighbor Ising models. In revising earlier work, modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes: C± for the susceptibility χ; ƒ1± for the correlation length ζ1; A± for the specific heat C(T); and B for the spontaneous magnetization M0. We find C + C - = 4.95±0.15 , ƒ 1 + ƒ 1 - = 1.960±0.01 , A + A - = 0.523±0.009 , αA + C + B + = 0.0581±0.0010 , while αA+ (ƒ1+)3 verifies hyperuniversality to within ±0.8%. A method for calculating amplitude ratios which allows for corrections to scaling yields estimates for C + C - and ƒ 1 + ƒ 1 - in excellent agreement with those derived from the individual amplitudes. Finally, explicit formulae are given for the numerical evaluation of χ(T), ζ1(T), C(T) and M0(T) over the full temperature range from criticality to T=0 and ∞; corresponding plots and convenient near-critical representations are also presented.

Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics

Abstract: The application of mathematical optimization techniques to a simplified mathematical model of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals is discussed. Two particular cases are discussed: first, that of the insulin infusion program which results in an initially high blood glucose level being reduced to acceptable levels; secondly, that of the control of blood glucose levels following a meal, prior to which blood glucose and net blood-glycemic hormone were at their fasting levels. >

Universal critical adsorption profile from optical experiments

Abstract: The analysis of optical data for critical adsorption from a fluid (or fluid mixture) onto a wall or interface is discussed theoretically with emphasis on elucidating the universal, scaled adsorption profile P(z/\ensuremath{\xi}), where \ensuremath{\xi}(T) is the correlation length and z is the distance from the interface. A novel strategy, which embodies theoretically well-established features, is applied to recent reflectivity and ellipsometry experiments on binary mixtures against glass and vapor substrates. Overall, the data indicate relatively strong surface fields and clearly reveal crossover from a power-law regime, P(x)\ensuremath{\approxeq}${P}_{0}$/${x}^{\ensuremath{\beta}/\ensuremath{ u}}$, as x-g0, to P(x)\ensuremath{\approxeq}${P}_{\ensuremath{\infty}}$${e}^{\mathrm{\ensuremath{-}}x}$, as x-g\ensuremath{\infty}, occurring around x\ensuremath{\simeq}1.4 with ${P}_{\ensuremath{\infty}}$/${P}_{0}$\ensuremath{\simeq}0.85. The relative merits of reflectivity and ellipsometry techniques are assessed (the latter currently proving more definitive) and various experimental issues are identified which must be resolved before more details of the adsorption profile could be extracted from further observations.

Spin-(1/2 antiferromagnetic XXZ chain: New results and insights.

Abstract: We study the criticality at the isotropic limit of the S=(1/2, antiferromagnetic, XXZ chain on approach from the Ising side. Long series are developed for the longitudinal and transverse correlation sums or structure factors ${S}_{\mathrm{zz}}$ and ${S}_{+\mathrm{\ensuremath{-}}}$ around the Ising limit. Their extrapolation indicates a divergence as the critical point is approached, with two different powers, a result quite unexpected if one employs a naive scaling argument since the critical correlations are isotropic and there is only one correlation length, \ensuremath{\xi}. An analytical calculation is presented, in which this paradox is resolved and the numerical results are confirmed.

Wetting in a two-dimensional random-bond Ising model

Abstract: We analyze a square-lattice random-bond Ising model using a numerical transfer-matrix technique to test the theory proposed by Lipowsky and Fisher for the complete wetting transition of a wall by one of two phases which coexist in a random medium. The theoretical scaling arguments are checked in detail. The transverse and longitudinal correlation lengths, a h ) and C$h), are found to be related by ~ i ~ ~ with 6=0.65*0.02 as the external field, or chemical potential deviation, h, approaches 0: the theoretical expectation is S , = + The mean wetting layer thickness diverges as l(h)-h-*while&-hvlas h-0with $=vi=^.

Optimal feedback control for linear stochastic systems driven by counting processes

Abstract: A new formulation is presented for a class of partially observed linear stochastic control problems described by three sets of stochaslic differential expressions: one for the system to be controlled, one for the observer (measurement) channel and one for the control channel driven by the observed process. The noise processes perturbing the system and observer dynamics are vector-valued counting processes (in particular Poisson processes) with time varying intensities. The approach is constructive, determining the optimal linear feedback control law subject to constraints on control (gain) matrices and closed loop system uncertainly. This makes the approach directly appealing to control system design. For illustration, numerical examples are solved using the proposed approach.

Single input-output systems containing a small parameter

Abstract: Some of the solution properties of an nth order single input-output system with bounded control in which the coefficient of the highest order derivative is a small parameter e are discussed. In particular, the reachable set from the origin for this system can be approximated to within O(e), as e → 0 by reachable sets constructed from either of two (n — l)-dimensional systems. These approximating systems arise in a natural way, the first by a natural partitioning of the original system matrix and the second by setting e = 0. The results have particular significance in the case n = 3.