Virial coefficients and equations of state for mixtures of hard discs,hard spheres and hard hyperspheres

The composition-independent virial coefficients of a d-dimensional binary mixture of (additive) hard hyperspheres following from a recent proposal for the equation of state of the mixture (Santos, A., Yuste, S. B., and López de Haro, M., 1999, Molec. Phys., 96, 1) are examined. Good agreement between theoretical estimates and available exact or numerical results is found for d = 2, 3, 4 and 5, except for mixtures whose components are very disparate in size. A slight modification that remedies this deficiency is introduced and the resummation of the associated virial series is carried out, leading to a new proposal for the equation of state. The case of binary hard sphere mixtures (d = 3) is analysed in some detail.     

Ferrimagnetic coupling in oxamido-bridged Mn(II)Cu(II) compounds: a combined CASPT2 and DDCI study

Multiconfigurational perturbation theory (CASPT2) and difference dedicated configuration interaction (DDCI) are applied to study the ferrimagnetic coupling in an oxamido-bridged Mn(II)Cu(II) molecular species. CASPT2 reproduces the experimental coupling very well. From the partition of the CASPT2 energy, the most important contributions to the coupling are established. Spin populations are calculated with DDCI. The successive improvement of the N-electron wave function allows us to analyse the contributions to the spin delocalization.     

A Popov-theory-based survey on digital control of infinite-dimensional systems with unboundedness

This paper represents a Popov-theory-based assessment of thecurrent status of the digital control of infinite–dimensionalsystems with certain unboundedness in control and/or observation,summarizing some results and indicating which, in the authors'opinion, would be the promising directions for future research.     

An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

Pionization effects in nucleon-nucleus scattering

A simple unitary model for meson production in nucleon-nucleon scattering is extended to nucleon-nucleus scattering. In the high energy limit the produced mesons remain coherent with the projectile over the entire depth of the nucleus and tend to increase the total cross sections. A crude estimate of the size of the effect gives an increase of the total cross section for proton-deuteron scattering of 13 mb at NAL energies.     

Spin-orbit and Pauli-correlation effects in intermediate-energy proton-nucleus inelastic scattering

The excitation of the 3^? (6.13 MeV) state of ¹⁶O by 0.8 GeV protons is studied using Glauber theory with a spin-orbit NN amplitude. Two previously suggested approaches for handling the z-ordered non-commuting NN profile functions, γ, are compared and found to give nearly identical results for the usual observables. Transitions to certain LM substates which are forbidden in one approach are allowed in the other, but their cross sections are proportional to the fourth power of the strength of the NN spin-orbit amplitude and thus quite small. It is also shown that, in this energy region, an expansion in powers of the strength of the spin-orbit interaction converges rapidly and consequently any convenient ordering of the γ's can be used without serious errors. Using this result an estimate of the effects of Pauli correlations on the cross section and the polarization is given.     

Renormalization point invariance,twisted fans,and critical exponents at finite ϵ in the reggeon calculus.

A procedure for calculating critical exponents directly at finite ? is proposed. It relies on the invariance of the critical exponents at the critical coupling g^c of the full theory with respect to finite changes in the renormalization point. This is expressed as the coincidence of curves at the point β = 0 in the plane of β versus a critical exponent parametrically described by the renormalized coupling for various values of the renormalization point (the “twisted fan”). If more than one critical exponent is present the fan is a set of curves in a multidimensional space with the twist at β = 0 and the exact values of the critical exponents. In perturbative approximations, an approximate invariance may result whether or not a zero of β exists to that order. We show that in the one and two loop approximations to the Reggeon calculus this approximate invariance does occur. The values of the critical exponents at the approximate twists show remarkable stability properties. We obtain σ_tot ≈ (lns)^?γ where ?γ ≈ 0.11 and 0.17 for one and two loops respectively.