ENVIRONMENTAL DAMAGES AND OPTION VALUES

The purpose of this paper is to clarify a concept — option value — that has arisen in environmental literature, to illustrate how it might be measured, and to indicate its potential importance. Option value arises when failure to control environmental disruption leads to irreversible losses of uncertain magnitude. We show that, even in the absence of risk aversion, replacing random variables representing benefits of control with their expected values results in an underestimate of benefits and that the required “correction factor” is option value. An example shows that option value can be substantial relative to conventionally estimated benefits (from 10 percent to over 50 percent in the example).     

The free energy of a macroscopic system

The statistical mechanics of classical and quantum mechanical systems interacting with many-body forces are investigated in the canonical and grand canonical ensembles. Under various general conditions on the attractive and repulsive parts of the potential energy and on the shapes of the domains _k confining the system, it is shown that the canonical free energy per particle and the grand canonical pressure have unique limits for infinite systems which are convex monotonie functions of the specific volume and chemical potential respectively, and satisfy the expected thermodynamic relations.For pure pair forces with potential (r) sufficient conditions are: (r)D ₁/r³⁺ as r0, |(r)|D ₂/r³⁺ as r (>0), and (r)-w₀ all r; the domains _k may be constructed from a finite set of bounded domains of arbitrary shape by any sequence of isotropic expansions such that the volume V(_k) approaches infinity with k.The work reported here was done while the author was on leave of absence from The Wheatstone Physics Laboratory, King's College, London W. C. 2, England.     

Asymptotic behavior of Toeplitz matrices and determinants

We consider the inverse X _N and determinant D_N(c) of an N×N Toeplitz matrix C_N=[c_i?j] ₀ ^N?1 as N ar∞. Under the condition that there exists a monotonic decreasing summable bound b _n ≧|c _n |+|c _?n |, and that the generating function \(c(\theta ) = \sum\limits_{n = - \infty }^\infty {c_n e^{i{\text{ }}n{\text{ }}\theta } }\) does not vanish, we construct a matrix iterative process which yields (i) explicit asymptotic formulae for the elements of X_N when v(c) = (2π)^?1 [arg{c(2π)}?arg{c(0)}] is zero. Thence we obtain (ii) expressions for the constants, and bounds on the remainder, in the asymptotic formula $$\ln D_N (c) = N{\text{ }}k_0 (c) + E_0 (c) + E_{1,N} (c) + \mathcal{R}_N (c),$$ and (iii) the extension of this formula to the case of general integral v(c). Under certain further conditions the monotonicity of E_1,N+?_N is proved. We discuss various identities for D_N which apply when c(θ) is a rational function of e^iθ and mention a conjecture for D _N when c(θ) has zeros, and is discontinuous with arbitrary v(c).     

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.     

Selective incorporation of functional dicarboxylates into zinc metal-organic frameworks

Zinc(II) nitrate reacts with different ratios of 1,4-benzenedicarboxylic acid (H(2)bdc) and 2-halo-1,4-benzenedicarboxylic acid (H(2)bdc-X, X = Br or I) to give [Zn(4)O(bdc)(3-x)(bdc-X)(x)], in which preferential incorporation of bdc is observed. The selective incorporation is related to crystal growth rates, and the proportion of incorporated bdc-X rises with increasing reaction time.     

Stars at infinity in Teichmüller space

Geometriae Dedicata - We investigate a metric structure on the Thurston boundary of  Teichmüller space. To do this, we develop tools in sup metrics and apply Minsky’s...     

Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Effect of oxygen content on the specific heat and magnetic susceptibility of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript>

The specific heat and magnetic susceptibility of a sample of YBa₂Cu₃O_7?δ (YBCO) was measured for 0≤δ≤0.85, 0.8≤T≤120K, and H=0, 3, 5, 7, 9T. The data show the existence of both S=1/2 and S=2 paramagnetic centers, consistent with EPR results. The δ dependences of their concentrations and of other parameters are reported.     

Enthalpies of solution and crystallization of ammonium aluminum sulphate dodecahydrate in water at 25°C

Enthalpies of crystallization of NH₄Al(SO₄)₂·12H₂O from aqueous solutions at 25°C, measured using a calorimetric method and determined from previously published data on the concentration dependence of the enthalpy of solution, are reported. The results are compared with the values obtained from the temperature dependence of solubility and from vapor pressure data by using the Williamson equation. The integral and partial molar enthalpies of solution in concentrated and diluted solutions are given.     

Differentiable rigidity for hyperbolic toral actions

Our aim is to extend existing results about differentiable rigidity of higher rank abelian actions by automorphisms of a torus. Previous proofs have required an assumption of semisimplicity, that is, that the action is by commuting diagonalizable matrices. Here we introduce a technique that utilizes the unipotent part of a non-semisimple action, which allows us to discard the semisimplicity assumption. In its place we will make a technical assumption that the spectrum of the action restricted to leaves of the coarse Lyapunov decomposition is sufficiently narrow.