Dying and Rising As We Grow Up: Lifelong Baptismal Formation

(Excerpt) In honor of David Truemper, who taught me the Lutheran Confessions, I want to begin with a quotation from the Large Catechism. Luther writes: Thus we see what a great and excellent thing baptism is, which snatches us from the jaws of the devil and makes God our own, overcomes and takes away sin and daily strengthens the new man, always remains until we pass from this present misery to eternal glory. Therefore let everybody regard his baptism as the daily garment which he is to wear all the time. Every day he should be found in faith and amid its fruits, every day he should be suppressing the old man and growing up in the new

The Language of the Psalter and Sunday Worship

(Excerpt) Which words shall we use on Sunday morning? Shall we speak Aramaic or Greek, Latin or German, seventeenth-century British English or twenty first- century American English? Shall our scriptural translation be as literal as possible or as accessible as possible? Shall we concur with the editors of our denominational news magazines and employ a sixth grade vocabulary, or can we hope to engage the brains of also our learned members? Who decides which words we speak or sing: the organist, the pastor, a congregational committee, a national staff of liturgical experts, or an international theological bureaucracy? We are alive in a time of some considerable debate about the words of our worship. Not since the Reformation, and probably never before then, has there been such rapid and continuing changes, such creativity, indeed such rancor, over the language of our praise and petition

The Word in the world

Holy Innocents and the Lutheran Book of Worship

Nonlinear Ordinary Differential Equations in Fluid Dynamics

The equivalence between nonlinear ordinary differential equations (ODEs) and linear partial differential equations (PDEs) was recently revisited by Smith, who used the equivalence to transform the ODEs of Newtonian dynamics into equivalent PDEs, from which analytical solutions to several simple dynamical problems were derived. We show how this equivalence can be used to derive a variety of exact solutions to the PDEs describing advection in fluid dynamics in terms of solutions to the equivalent ODEs for the trajectories of Lagrangian fluid particles. The PDEs that we consider describe the time evolution of non-diffusive scalars, conserved densities, and Lagrangian surfaces advected by an arbitrary compressible fluid velocity field u(x, t). By virtue of their arbitrary initial conditions, the analytical solutions are asymmetric and three-dimensional even when the velocity field is one-dimensional or symmetrical. Such solutions are useful for verifying multidimensional numerical algorithms and computer codes for simulating advection and interfacial dynamics in fluids. Illustrative examples are discussed

Microscopic Irreversibility and Gibbs Entropy

In a recent paper of the same title [J. Non-Equilib. Thermodyn., 15 (1990), 151], Liboff observed that the fine-grained Gibbs entropy of a canonical Hamiltonian system remains constant in time even for Hamiltonians that are not even in momenta and consequently violate time-reversal invariance (TRI). Here we extend this observation to non-canonical Hamiltonian systems, including systems with singular Poisson tensors and pseudo-Hamiltonian systems that violate the Jacobi identity. Necessary and sufficient conditions are given for the Gibbs entropy to be constant in such systems. The concept of TRI is not in general meaningful for such systems, but it is shown that systems with constant entropy are always microscopically reversible in the Poincare recurrence sense, which implies that H- (Lyapunov) functions do not exist. This result applies as a special case to canonical systems, regardless of whether or not they obey TRI. A distinction should therefore be drawn between microscopic reversibility and TRI

Existence of the Dielectric Constant in Fluids of Classical Deformable Molecules

The existence of the dielectric constant epsilon is investigated for fluids composed of classical deformable (polarizable) molecules. The development is based upon generalized functional-derivative relations which involve joint distributions in molecular positions r/sub k/ and dipole moments ..mu../sub k/. Sufficient conditions for the existence of epsilon are expressed in terms of the generalized direct correlation function c(12) = c(r/sub 1/, ..mu../sub 1/; r/sub 2/, ..mu../sub 2/). It is found that epsilon exists if -kTc(12) depends only on relative positions and dipole moment directions (in addition to Vertical Bar..mu../sub 1/Vertical Bar and Vertical Bar..mu../sub 2/Vertical Bar), and becomes asymptotic to the dipole--dipole potential at long range. An expression for epsilon in terms of a short-ranged total correlation function h/sub 0/(12) emerges automatically from the development. An expression for epsilon in terms of c(12) is also derived. The latter expression involves an inverse kernel in (Vertical Bar..mu../sub 1/Vertical Bar, Vertical Bar..mu../sub 2/Vertical Bar) space. The case of rigid polar molecules is reconsidered as a special case of the present formulation