Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

Using the uncertainty principle to design simple interactions for targeted self-assembly

We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed self-assembling materials

Oral Argument in the Time of COVID: The Chief Justice Plays Calvinball

In this Article, we empirically assess the Supreme Court’s experiment in hearing telephonic oral arguments. We compare the telephonic hearings to those heard in person by the current Court and examine whether the Justices followed norms of fairness and equality. We show that the telephonic forum changed the dynamics of oral argument in a way that gave the Chief Justice new power, and that Chief Justice Roberts, knowingly or unknowingly, used that new power to benefit his ideological allies. We also show that the Chief interrupted the female Justices disproportionately more than the male Justices and gave the male Justices more substantive opportunities to have their questions answered. This analysis transcends the significance of individual cases. The fact that the Court experimented with telephonic oral argument, the way it did so, and how the practice could be improved are all issues of profound national importance. The new format had the potential to influence the outcome of cases that have broad national significance, to shift norms of equality and transparency in the Court, and more generally to affect judicial legitimacy. If the Court favors certain parties or certain ideological camps by its choice of forum in a time of crisis, then that will undermine not only the Court’s legitimacy but also raise doubts as to whether any of our national institutions have the capacity to adapt to crises

Cytomegalovirus myelitis in perinatally acquired HIV

A 7 year old child perinatally infected with HIV who died from progressive muscular paralysis and central nervous respiratory failure is described. Cytomegalovirus (CMV) prophylaxis with a special intravenous CMV hyper-immunoglobulin had been successfully conducted for more than four years. Macroscopic and microscopic immunohistochemical examination of the spinal cord revealed a diffuse CMV infiltration of the entire myelon. CMV infected cells were identified as astrocytes, oligodendrocytes, neurons, macrophages, ependymal, endothelial, and Schwann cells. Other organs had no signs of CMV infection. Central nervous spinal CMV infection was most probably due to insufficient penetration of the blood-brain barrier by the CMV hyper-immunoglobulin. In suspicious cases early spinal magnetic resonance imaging (1.5 tesla) combined with an examination of urine and cerebrospinal fluid for CMV is recommended

On uniformization of Burnside's curve y2=x5−xy^2=x^5-x

Main objects of uniformization of the curve $y^2=x^5-x$ are studied: its Burnside's parametrization, corresponding Schwarz's equation, and accessory parameters. As a result we obtain the first examples of solvable Fuchsian equations on torus and exhibit number-theoretic integer $q$-series for uniformizing functions, relevant modular forms, and analytic series for holomorphic Abelian integrals. A conjecture of Whittaker for hyperelliptic curves and its hypergeometric reducibility are discussed. We also consider the conversion between Burnside's and Whittaker's uniformizations.Comment: Final version. LaTeX, 23 pages, 1 figure. The handbook for elliptic functions has been moved to arXiv:0808.348

General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

Facilitation shifts paradigms and can amplify coastal restoration efforts

Restoration has been elevated as an important strategy to reversethe decline of coastal wetlands worldwide. Current practice in restorationscience emphasizes minimizing competition between outplantedpropagules to maximize planting success. This paradigmpersists despite the fact that foundational theory in ecology demonstratesthat positive species interactions are key to organism successunder high physical stress, such as recolonization of bare substrate. Asevidence of how entrenched this restoration paradigm is, our surveyof 25 restoration organizations in 14 states in the United States revealedthat >95% of these agencies assume minimizing negative interactions(i.e., competition) between outplants will maximize propagulegrowth. Restoration experiments in both Western and Eastern Atlanticsalt marshes demonstrate, however, that a simple change in plantingconfiguration (placing propagules next to, rather than at adistance from, each other) results in harnessing facilitation and increasedyields by 107% on average. Thus, small adjustments in restorationdesign may catalyze untapped positive species interactions,resulting in significantly higher restoration success with no addedcost. As positive interactions between organisms commonly occur incoastal ecosystems (especially in more physically stressful areas likeuncolonized substrate) and conservation resources are limited, transformationof the coastal restoration paradigm to incorporate facilitationtheory may enhance conservation efforts, shoreline defense, andprovisioning of ecosystem services such as fisheries production