OPTIMAL REGULATION OF NATURAL RESOURCES IN THE PRESENCE OF IRREVERSIBLE THRESHOLD EFFECTS

ABSTRACT. Thresholds are an important physical consideration in the regulation of natural resources. This paper is the first to present a complete analytical framework in which to evaluate optimal regulation of a natural resource in the presence of irreversible threshold effects. Necessary conditions are presented for optimal regulation of these problems both for when the threshold has a known location in state‐space and for when the location of the threshold is unknown. In the case where the location is known, the literature is corrected on a seemingly minor technical point regarding the behavior of the co‐state variables that turns out to be of considerable importance. For the case when the location of the threshold is not known, it is shown that thresholds in state‐space implies a nonstandard risk structure.     

Brownian dynamics simulation of gelation in soft sphere systems with irreversible bond formation

Brownian dynamics simulation is used to study the structure and small-deformation shear rheology of three-dimensional particle gels formed from a model of soft spherical particles incorporating a combination of flexible, irreversible bond formation and non-bonded interparticle interactions. An essential feature of the model is the restriction of angular reorganization of cross-linked aggregates during and after gelation. Numerical data relating to the fractal structure and porosity of the gels are compared with those from some related particle gel simulation models in two and three dimensions. Stress relaxation and frequency dependent rheological properties are determined as a function of the strength and nature of the interparticle interactions, and the results are discussed in relation to structural properties. A linear relationship is demonstrated between the high-frequency modulus and the number of bonds in the gel network.     

Calculation of the vapour-liquid coexistence curve for a fluctuating point charge water model

Recent studies of the phase behaviour of several polarizable water models have shown that typically the inclusion of polarizability into current non-polarizable, rigid models of water actually decreases the accuracy of their predictions of the liquid-vapour coexistence curve. Most of the polarizable models examined so far have been shown to characteristically over-predict the saturation pressure and correspondingly under-predict the critical temperature. It is the purpose of this Research Note to report the results of a Gibbs—Duhem integration of the liquid—vapour coexistence curve for the TIP4P-FQ water model and to discuss the possible reasons behind the lack of improvement of polarizable water models over their non-polarizable counterparts.     

Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n^? with maximal quantum-classical distance; the value n^? decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.     

Computation of Flashing Flows In Variable Cross-Section Ducts

A Finite-Volume scheme which enables computing fast transient single phase and two phase flows in variable cross section ducts is presented. The physical modelling relies on the Homogeneous Relaxation Model. The theoretical framework is briefly presented, together with the main ideas of a new approximate Riemann solver. Numerical results confirm the suitability of the present approach.     

Configuration interaction of Er3+ with a charge transfer configuration in the elpasolite compound Cs2NaErCl6

The discrepancies of the crystal-field analysis in Cs₂NaErCl₆ are lowered by letting the 4f¹¹ configuration interact with a charge transfer configuration enclosing a p electron. 75 levels with a total degeneracy equal to 130 were fitted with a mean deviation of 10.5 cm^?1, compared with 21.4 cm^?1 in the standard model. It is found that: (i) the p electrons involved in the process originate most probably from the six Cl^? ligands; (ii) 14% of the 3p⁶ orbitals are projected onto the central ion coordinate system as an unique orbital with p angular character; (iii) this projected orbital can be coupled with 4fⁿ configurations and handled by tensorial methods; and (iv) the most probable mechanism responsible for the improvement of the crystal-field analysis is a 4f¹¹ 3p⁶-4f¹²3p⁵ interaction. The first configuration represents Er³⁺ surrounded by six Cl^? ligands, whereas in the second one, the rare-earth ion and the ligands have gained and lost one electron respectively. The crystal-field analysis enables the estimation of the location of the charge transfer band.     

Order Reduction of Parametrically Excited Nonlinear Systems: Techniques and Applications

The basic problem of order reduction of nonlinear systems with time periodic coefficients is considered in state space and in direct second order (structural) form. In state space order reduction methods, the equations of motion are expressed as a set of first order equations and transformed using the Lyapunov–Floquet (L–F) transformation such that the linear parts of new set of equations are time invariant. At this stage, four order reduction methodologies, namely linear, nonlinear projection via singular perturbation, post-processing approach and invariant manifold technique, are suggested. The invariant manifold technique yields a unique ‘reducibility condition’ that provides the conditions under which an accurate nonlinear order reduction is possible. Unlike perturbation or averaging type approaches, the parametric excitation term is not assumed to be small. An alternate approach of deriving reduced order models in direct second order form is also presented. Here the system is converted into an equivalent second order nonlinear system with time invariant linear system matrices and periodically modulated nonlinearities via the L–F and other canonical transformations. Then a master-slave separation of degrees of freedom is used and a nonlinear relation between the slave coordinates and the master coordinates is constructed. This method yields the same ‘reducibility conditions’ obtained by invariant manifold approach in state space. Some examples are given to show potential applications to real problems using above mentioned methodologies. Order reduction possibilities and results for various cases including ‘parametric’, ‘internal’, ‘true internal’ and ‘true combination resonances’ are discussed. A generalization of these ideas to periodic-quasiperiodic systems is included and demonstrated by means of an example.     

Structure indices for multidimensional systems

The structure indices of a one-dimensional system are an importantset of invariants. In this paper we examine a generalizationof this concept to multidimensional linear systems, which correspondsto the algebraic concept of a Hilbert series. We use the standardtheory of the Hilbert series to explain some of the previousID system-theoretic results. We discuss the computation of nDstructure indices from an initial condition set, and the invariantswhich can be derived from these indices.