Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I(t) = I0(t−t0)q for t greater-or-equal, slanted t0, I(t) = 0 for t < t0; and (ii) I(t) = I0tq for t greater-or-equal, slanted t0, I(t) = 0 for t < t0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

World parliament – fact or fiction? On the feasibility of world parliamentary models

Cosmopolitan ideals have been on the philosophical agenda for several millennia but the end of the Cold War started a new discussion on state sovereignty, global democracy, the role of international law and global institutions. The Westphalian state system in practice since the 17th century is transforming and the democracy deficit needs new solutions. An impetus has been the fact that in the present world, an international body representing global citizens does not exist. In this Master’s thesis, the possibility of establishing a world parliament is examined. In a case analysis, 17 models on world parliament from two journals, a volume of essays and two other publications are discussed. Based on general observations, the models are divided into four thematic groups. The models are analyzed with an emphasis on feasible and probable elements. Further, a new scenario with a time frame of thirty years is proposed based on the methodology of normative futures studies, taking special interest in causal relationships and actions leading to change. The scenario presents three gradual steps that each need to be realized before a sustainable world parliament is established. The theoretical framework is based on social constructivism, and changes in international and multi-level governance are examined with the concepts of globalization, democracy and sovereignty. A feasible, desirable and credible world parliament is constituted gradually by implying electoral, democratic and legal measures for members initially from exclusively democratic states, parliamentarians, non-governmental organizations and other groups. The parliament should be located outside the United Nations context, since a new body avoids the problem of inefficiency currently prevailing in the UN. The main objectives of the world parliament are to safeguard peace and international law and to offer legal advice in cases when international law has been violated. A feasible world parliament is advisory in the beginning but it is granted legislative powers in the future. The number of members in the world parliament could also be extended following the example of the EU enlargement process.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.