A model for time-dependent grain boundary diffusion of ions and electrons through a film or scale, with an application to alumina

A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern. Reactions with the environment constitute the boundary conditions and drive the transport between the surfaces. Time-dependent simulations solving the Poisson equation self-consistently with the Nernst-Planck flux equations for the mobile species are performed. In the resulting Poisson-Nernst-Planck system of equations, the electrostatic potential is obtained from the Poisson equation in its integral form by summation. The model is used to interpret alumina membrane oxygen permeation experiments, in which different oxygen gas pressures are applied at opposite membrane surfaces and the resulting flux of oxygen molecules through the membrane is measured. Simulation results involving four mobile species, charged aluminum and oxygen vacancies, electrons, and holes, provide a complete description of the measurements and insight into the microscopic processes underpinning the oxygen permeation of the membrane. Most notably, the hypothesized transition between p-type and n-type ionic conductivity of the alumina grain boundaries as a function of the applied oxygen gas pressure is observed in the simulations. The range of validity of a simple analytic model for the oxygen permeation rate, similar to the Wagner theory of metal oxidation, is quantified by comparison to the numeric simulations. The three-dimensional model we develop here is readily adaptable to problems such as transport in a solid state electrode, or corrosion scale growth

Legal Enforcement of Duties to Oneself : Kant vs. Neo-Kantians

This Article considers writings by modern scholars including Rawls, Dworkin, and D.A.J. Richards on the topic of Kant\u27s discussion of the neutrality principle and the harm principle

Law as Fact and as Reason for Action: A Response to Robert Alexy on Law\u27s \u27Ideal Dimension\u27

Robert Alexy’s 2013 Natural Law Lecture, published in vol. 58 of the American Journal of Jurisprudence, presents law as having two dimensions, ideal and real, and thus a dual nature, to be elucidated by a conceptual analysis distinguishing between the observer’s and the participant’s perspective. It argues on this basis for a “non-positivist” theory of law that is “inclusive” in that it classifies some unjust laws as laws, but not all (and is thus not “super-inclusive”); it rejects the “exclusive non-positivism” that would treat every injustice in a law’s making or content as excluding it from the class of valid laws. Gustav Radbruch’s famous post-War formula -- extreme injustice invalidates law -- adopted in the jurisprudence of Germany’s higher courts, is thus to be defended as expressing the inclusive non-positivism that articulates the best concept of law that can be constructed and defended as expedient. Alexy’s 2013 article classifies the theory in Natural Law and Natural Rights as super-inclusive, but sees hopeful signs of inclusive non-positivism in some recent writings of its author. The present article, which is published in Am. J. Juris. 59 (2014), argues that Natural Law and Natural Rights defends, in a sense, all three “non-positivist” positions, each in its proper place as a truth about unjust law: it is (from an observer’s perspective) a fact; it is (from a participant’s perspective) deprived by any significant injustice of law’s generic and presumptive status (legal-moral validity) as a reason for action; and it is (from the perspective of particular participants in their circumstances) sometimes, despite its injustice and legal-moral invalidity, a source (by virtue of both the foregoing truths taken with other moral responsibilities and needs) of collateral obligations the extent of which is likely, often, to track, approximately, the results of applying the Radbruch formula. The article argues against Alexy’s theoretical procedures both of conceptual analysis and of concept construction, regrets the “non-positivist/positivist” labeling, raises doubts about speaking of duality of dimensions and nature, and notes the significance of the 2013 article’s further thesis that any injustice in a law impairs (“qualifies”) its legal status

On The Critical Legal Studies Movement

The present study critically examines the account of legal thought developed in Roberto Unger\u27s very long article, The Critical Legal Studies Movement (1983), and tests it against Unger\u27s own account of certain exemplary difficulties in the Anglo-American law of Contract. These scrutinies reveal that Unger\u27s account fundamentally misunderstands the ways of legal thought, and disguises its misunderstanding behind equivocations on (in)determinate and (un)justified

Law, Morality, and Sexual Orientation

During the past thirty years there has emerged in Europe a standard form of legal regulation of sexual conduct. This standard form or scheme, which I shall call the standard modem [European] position, is accepted by the European Court of Human Rights and the European Commission of Human Rights (the two supra-national judicial and quasijudicial institutions of the European Convention for the Protection of Human Rights and Fundamental Freedoms (1950), to which almost all European states are party, whether or not they are also party to the European [Economic] Community now known as the European Union). The standard modem European position has two limbs. On the one hand, the state is not authorized to, and does not, make it a punishable offence for adult consenting persons to engage, in private, in immoral sexual acts (for example, homosexual acts). On the other hand, states do have the authority to discourage, say, homosexual conduct and orientation (i.e. overtly manifested active willingness to engage in homosexual conduct). And typically, though not universally, they do so. That is to say, they maintain various criminal and administrative laws and policies which have as part of their purpose the discouraging of such conduct. Many of these laws, regulations, and policies discriminate (i.e. distinguish) between heterosexual and homosexual conduct adversely to the latter

On the Practical Meaning of Secularism

The secularism I consider in this Article is a public reality, the secularism which shapes public debate, deliberation, dispositions, and action, and dominates our education and culture. I shall be considering the ideas, not the people; and people are often less consistent, and better, than their theories. There is no profit in estimating whether secularism\u27s dominance now is greater than in Plato\u27s Athens or lesser than in Stalin\u27s Leningrad. There is certainly a rich field for historical investigation of the particular and often peculiar forms taken by western secularism under the influence of the faith it supplants. But I shall not try to resume or repeat the illuminating investigations carried forward by De Lubac, Voegelin, Fabro, Maclntyre, Chadwick, and many others. Still less do I join in the game of declaring this a post-modem, or post-baroque, or post-Christian, or historically-minded and post-classicist era, period, age or epoch. Instead I want to explore secularism\u27s practical significance, as it can be illuminated by understanding practical reason itself. We try to carry forward that understanding when we reflect on the basic reasons for action, the first principles (as Aquinas calls them) of natural law, on the choices, intentions, and commitments they guide and shape, and on the personal dignity of a being who can respond either integrally and reasonably or arbitrarily and deviantly to their intelligibility and directiveness

Law as Fact and as Reason for Action: A Response to Robert Alexy on Law\u27s \u27Ideal Dimension\u27

Robert Alexy’s 2013 Natural Law Lecture, published in vol. 58 of the American Journal of Jurisprudence, presents law as having two dimensions, ideal and real, and thus a dual nature, to be elucidated by a conceptual analysis distinguishing between the observer’s and the participant’s perspective. It argues on this basis for a “non-positivist” theory of law that is “inclusive” in that it classifies some unjust laws as laws, but not all (and is thus not “super-inclusive”); it rejects the “exclusive non-positivism” that would treat every injustice in a law’s making or content as excluding it from the class of valid laws. Gustav Radbruch’s famous post-War formula -- extreme injustice invalidates law -- adopted in the jurisprudence of Germany’s higher courts, is thus to be defended as expressing the inclusive non-positivism that articulates the best concept of law that can be constructed and defended as expedient. Alexy’s 2013 article classifies the theory in Natural Law and Natural Rights as super-inclusive, but sees hopeful signs of inclusive non-positivism in some recent writings of its author. The present article, which is published in Am. J. Juris. 59 (2014), argues that Natural Law and Natural Rights defends, in a sense, all three “non-positivist” positions, each in its proper place as a truth about unjust law: it is (from an observer’s perspective) a fact; it is (from a participant’s perspective) deprived by any significant injustice of law’s generic and presumptive status (legal-moral validity) as a reason for action; and it is (from the perspective of particular participants in their circumstances) sometimes, despite its injustice and legal-moral invalidity, a source (by virtue of both the foregoing truths taken with other moral responsibilities and needs) of collateral obligations the extent of which is likely, often, to track, approximately, the results of applying the Radbruch formula. The article argues against Alexy’s theoretical procedures both of conceptual analysis and of concept construction, regrets the “non-positivist/positivist” labeling, raises doubts about speaking of duality of dimensions and nature, and notes the significance of the 2013 article’s further thesis that any injustice in a law impairs (“qualifies”) its legal status