Religion, Nationalism, and American Identity: Reflections on Mark Noll’s America’s God

Historian Mark Noll’s magisterial America’s God: From Jonathan Edwards to Abraham Lincoln was an immediate sensation when it appeared in 2002. Jon Butler, the Howard R. Lamar Professor of American Studies, History, and Religious Studies at Yale University, declared “America’s God delineates the Americanization of an Old World Protestantism with a breadth, learning, and sophistication unmatched by any other historian.” Noll describes this process of “Americanization” as consisting of a “shift away from European theological traditions, descended directly from the Protestant Reformation, toward a Protestant evangelical theology decisively shaped by its engagement with Revolutionary and post-Revolutionary America.” And Noll concludes that this American “Protestant evangelicalism differed from the religion of the Protestant Reformation as much as sixteenth-century Reformation Protestantism differed from the Roman Catholic theology from which it emerged.” This paper will argue that, notwithstanding Noll’s considerable achievement, his identification of an “American” synthesis minimizes (although it never denies) the profound sectional variations of that synthesis. In doing so, Noll downplays the ways in which two competing social formations, grounded in fundamentally different systems of social relations, prevented the synthesis from fully uniting “Americans.” The different understandings of the synthesis, like the different understandings of its central texts – the Bible, the Declaration of Independence, and the Constitution – reflected the chasm that separated white Northerners and white Southerners and made both groups see themselves as the true defenders of “America’s God.” Noll’s work thus both enriches our understanding of the how most white Americans differed from their European contemporaries, and simultaneously demonstrates the fundamental divide within American national identity, a divide so pronounced that only a long and bloody war could settle the question of which of the two competing national projects was “God’s America.

Dispersion vs. anti-diffusion: well-posedness in variable coefficient and quasilinear equations of KdV-type

We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition between the dispersive effects which stem from the leading-order term, and anti-diffusion which stems from the lower-order terms with two spatial derivatives. We show that the dispersive effects can dominate the backwards diffusion: we find a condition which guarantees well-posedness of the initial value problem for linear, variable coefficient equations of this kind, even when such anti-diffusion is present. In fact, we show that even in the presence of localized backwards diffusion, the dispersion will in some cases lead to an overall effect of parabolic smoothing. By contrast, we also show that when our condition is violated, the backwards diffusion can dominate the dispersive effects, leading to an ill-posed initial value problem. We use these results on linear evolution equations as a guide when proving well-posedness of the initial value problem for some quasilinear equations which also exhibit this competition between dispersion and anti-diffusion: a Rosenau-Hyman compacton equation, the Harry Dym equation, and equations which arise in the numerical analysis of finite difference schemes for dispersive equations. For these quasilinear equations, the well-posedness theorem requires that the initial data be uniformly bounded away from zero

Global bifurcation theory for periodic traveling interfacial gravity-capillary waves

We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can be positive, negative, or zero, and the surface tension parameter is positive. Thus, included in the parameter set are the cases of pure capillary water waves and gravity-capillary water waves. Our choice of coordinates allows for the possibility that the fluid interface is not a graph over the horizontal. We use a technical reformulation which converts the traveling wave equations into a system of the form "identity plus compact." Rabinowitz' global bifurcation theorem is applied and the final conclusion is the existence of either a closed loop of solutions, or an unbounded set of nontrivial traveling wave solutions which contains waves which may move arbitrarily fast, become arbitrarily long, form singularities in the vorticity or curvature, or whose interfaces self-intersect.Comment: Corrected a typ

Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

Non-existence of small-amplitude doubly periodic waves for dispersive equations

Abstract. We formulate the question of existence of spatially periodic, time-periodic solutions for evolution equations as a fixed point problem, for certain temporal periods. We prove that if a certain estimate applies for the Duhamel integral, then time-periodic solutions cannot be arbitrarily small. This provides a partial analogue in the spatially periodic case of scattering results for dispersive equations on the real line, as scattering implies the non-existence of small-amplitude traveling waves. Furthermore, it also complements small-divisor methods (e.g, the Craig-Wayne-Bourgain method) for proving the existence of small-amplitude time-periodic solutions (again, for frequencies in certain set). Non-existence d’onde de petites amplitudes doublement périodiques pour les équations dispersives Résumé: Nous exprimons le problème d’existence de solutions périodiques en temps et en espace d’opérateurs d’évolution sous forme de problèmes de points fixes, pour certaines périodes de temps. Nous prouvons que si une certaine estimation pour l’integrale de Duhamel existe, alors les solutions périodiques en temps ne peuvent etre arbi-trairement petites. Cela donne des résultats analogues pour le cas de la diffusion d’ondes périodiques dans l’espace sur la droite réelle, puisque la diffusion implique la non-existence d’onde de petites amplitudes. De plus, nos résultats vi-ennent compléter les méthodes des petits diviseurs (comme par exemple la méthode de Craig-Wayne-Bourgain) pour prouver l’existence de solutions périodiques en temps de petites amplitudes (pour des frequences dans un certain ensemble). 1

Thrombin generation in human coronary arteries after percutaneous transluminal balloon angioplasty

AbstractObjectives. The aim of this study was to investigate the relation between coronary atherosclerotic plaque injury and activation of the coagulation cascade.Background. Thrombus formation after atherosclerotic plaque disruption has been implicated in the pathogenesis of atherosclerosis, unstable angina and myocardial infarction.Methods. Biochemical markers of thrombin generation (prothrombin fragment F1+2) and thrombin activity (fibrinopeptide A) were measured in coronary blood before, during and immediately after percutaneous transluminal coronary angioplasty. After demonstrating that blood withdrawal through an angioplasty catheter does not artifactually elevate the plasma levels of these markers in patients after heparinization, coronary artery samples ware collected proximal and distal to the lesion before and distal to the lesion after baltoon inflation in 26 patients.Results. Plasma levels of F1+2measured proximal to the lesion before angioplasty (median 0.47 nmol/liter, 95% confidence interval [CI] 0.40 to 0.50) were significantly elevated after angioplasty (median 0.55 nmol/liter, 95% CI 0.46 to 0.72, p = 0.001). In contrast, plasma fibrinopeptide A levels measured proximal to the lesion before angioplasty (median 2.0 ng/ml, 95% CI 1.3 to 22) were similar to those measured after angioplasty (median 1.8 ng/ml, 95% CI 1.3 to 3.0, p = NS). After we defined a normal range of interassay variability on the basis of values obtained from samples drawn proximal and distal to the lesion before angioplasty, seven patients (27%) had a significant increase in F1+2plasma levels. A significant increase in plasma fibrinopeptide A occurred in five of these seven patients. Lesions with dissection, filling defects or haziness on postangioplasty angiography were associated with more thrombin generation than lesions without these features.Conclusions. Markers of thrombio generation and activity can be collected safely and assayed accurately in heparinized blood withdrawn through aa angioplasty catheter. Balloon dilation of coronary stenoses increases thrombin generation and activity within the coronary artery in a substantial subgroup of patients undergoing angioplasty