Novel Methods to Determine and Use the Magnetic Vector Potential in Numerical General Relativistic Magnetohydrodynamics

Many codes have been developed to study highly relativistic, magnetized flows around and inside compact objects. Depending on the adopted formalisms, some of these codes evolve the vector potential A, and others evolve the magnetic field B = curl(A) directly. Given that these codes possess unique strengths, it is sometimes desirable to start a simulation using a code that evolves B and complete it using a code that evolves A. Transferring data from one code to another requires an inverse curl algorithm. This dissertation describes two new inverse curl techniques in the context of Cartesian numerical grids: a cell-by-cell method, which scales approximately linearly with the size of the numerical grid, and a global linear algebra approach, which lacks those ideal scaling properties but is generally more robust, e.g., in the context of a magnetic field possessing some nonzero divergence. We demonstrate that these algorithms successfully generate smooth vector potential configurations in challenging special and general relativistic contexts. In addition, we examine the magnetic helicity, which is a measure of the overall twist of a magnetic field configuration. It is defined as the integral of the dot product of A and B over the volume, and it should be conserved as a system evolves. By examining this quantity, we can put further constraints on the physical accuracy of numerical codes

A Different Challenge for the ALI: Herein of Foreign Country Judgments, an International Treaty, and an American Statute

Symposium: Preparing for the Next Century-A New Restatement of Conflicts

A Different Challenge for the ALI: Herein of Foreign Country Judgments, an International Treaty, and an American Statute

Symposium: Preparing for the Next Century-A New Restatement of Conflicts

Nonparty Jurisdiction

The Supreme Court\u27s recent decisions on personal jurisdiction, including its 2021 decision in Ford Motor Co. v. Montana Eighth Judicial District Court, have all focused on the adjudication of plenary claims. In seven years, the Court has decided six major cases on personal jurisdiction in that context. However, these precedents also appear to guide lower courts in areas outside the traditional focus of personal jurisdiction doctrine but where personal jurisdiction is nonetheless necessary. For example, a court must have personal jurisdiction over a nonparty witness in order to compel the witness to testify or to produce documents. A court must have personal jurisdiction over a person in order to obtain preliminary relief, and a court must have jurisdiction, either personal jurisdiction or attachment jurisdiction, in order to recognize and enforce a foreign country judgment or arbitral award. In the development of its jurisdictional jurisprudence, the Supreme Court has never paused to consider the implications of its decisions on these other applications of personal jurisdiction. This Article attempts to chart a path by examining these other forms of personal jurisdiction that arise, often in connection with the assertion of jurisdiction over a nonparty to the initial litigation. This Article presents a coherent approach to the power of courts over nonparties that is consistent with the prevailing constitutional doctrine on personal jurisdiction developed in the context of traditional plenary claims. This Article offers a comprehensive consideration of how courts should approach the question of their authority over nonparties-a theory of nonparty or discovery jurisdiction that fits comfortably with the Court\u27s present jurisprudence