Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems

We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations. We can compute branches of solutions with limit points, bifurcation points, etc. Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations

Parametric Manifolds I: Extrinsic Approach

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss-Codazzi formalism. We generalize this formalism to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface-forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed.Comment: Plain TeX, 21 pages, no figure

The Aftermath of Mexico\u27s Fuel-Theft Epidemic: Examining the Texas Black Market and the Conspiracy to Trade in Stolen Condensate.

Organized crime has infiltrated the oil patch, creating a theft network with an annual value of $2–$4 billion. Over the past decade, Mexican drug cartels have plundered mass amounts of natural gas condensate produced by Petróleos Mexicanos (Pemex)—the governing Mexican agency for production and export of hydrocarbons. The Mexican government has not sat by idly. Pemex’s production losses have skyrocketed from $300 million, between 2006 and 2011, to an estimated$585 million in 2013 alone. Considering derivative costs associated with these thefts, Pemex’s annual losses reach into the billions. Diversified and driven by profits derived from the United States black market for stolen fuel, the cartels have remained undeterred despite Mexico’s equally diversified efforts to defend its “national patrimony.” Pemex has turned to United States courts for recourse, bringing with it theories of conspiracy and conversion. Pemex has filed three actions in the United States District Court for the Southern District of Texas since 2006, naming several oil and gas tycoons as defendants and alleging an overarching conspiracy to purchase $300 million in stolen condensate. Mexico’s financial struggles and inability to guard against fuel theft pose a direct threat to United States economic stability and national security, increase risks associated with United States investment, and spawn liability exposure for United States refineries as innocent end-users of stolen fuel. Given the growing trends in fuel theft and the Mexican government’s inability to reverse that trend in its own fields, there is no foreseeably effective stopgap on the horizon. Refineries located in targeted states, including Texas, face significant financial liabilities associated with purchasing stolen condensate. Without sufficient protective measures end-users could potentially forfeit multi-million-dollar purchases or damages mirroring those purchases

The Aftermath of Mexico\u27s Fuel-Theft Epidemic: Examining the Texas Black Market and the Conspiracy to Trade in Stolen Condensate.

Organized crime has infiltrated the oil patch, creating a theft network with an annual value of $2–$4 billion. Over the past decade, Mexican drug cartels have plundered mass amounts of natural gas condensate produced by Petróleos Mexicanos (Pemex)—the governing Mexican agency for production and export of hydrocarbons. The Mexican government has not sat by idly. Pemex’s production losses have skyrocketed from $300 million, between 2006 and 2011, to an estimated$585 million in 2013 alone. Considering derivative costs associated with these thefts, Pemex’s annual losses reach into the billions. Diversified and driven by profits derived from the United States black market for stolen fuel, the cartels have remained undeterred despite Mexico’s equally diversified efforts to defend its “national patrimony.” Pemex has turned to United States courts for recourse, bringing with it theories of conspiracy and conversion. Pemex has filed three actions in the United States District Court for the Southern District of Texas since 2006, naming several oil and gas tycoons as defendants and alleging an overarching conspiracy to purchase $300 million in stolen condensate. Mexico’s financial struggles and inability to guard against fuel theft pose a direct threat to United States economic stability and national security, increase risks associated with United States investment, and spawn liability exposure for United States refineries as innocent end-users of stolen fuel. Given the growing trends in fuel theft and the Mexican government’s inability to reverse that trend in its own fields, there is no foreseeably effective stopgap on the horizon. Refineries located in targeted states, including Texas, face significant financial liabilities associated with purchasing stolen condensate. Without sufficient protective measures end-users could potentially forfeit multi-million-dollar purchases or damages mirroring those purchases

Application of Statistical Quality Control to the Destructive Testing of Cement in the Control Laboratory

Industrial Engineering and managemen

Simulasi Penanganan Potensi Aliran Debris di Gunung Sago (Studi Kasus di Batang Lakin, Kecamatan Lareh Sago Halaban, Kabupaten Lima Puluh Kota)

The regions in foothills of Sago mountain are flood-prone area due to debris flow. As occurred on March 22, 2010, there has been a catastrophic overflow of debris flow from Sago mountain. The disaster resulted in severe damage around the rivers downstream Sago mountains, including Batang Lakin river. This research study debris flow potential and how to mitigate it in Batang Lakin river, West Sumatra. Analysis of potential debris flow hazard of Batang Lakin river and alternative debris mitigation is simulated using the debris flow simulator Kanako 2D version 2.051. Simulation is important for verifying effect of controlling flow of debris prior to construction work carried out. Rain data input was calculated based on fifty years time period and one hundred years time period Research findings show that at Batang Lakin river, debris flow occurred and overflowing river channel. Alternative countermeasure chosen is sabo dam. For fifty years period when debris flow peak discharge of 59.50 m3/second required 2 units of sabo dams (closed type) with positions at Sta 0 +200 (Sabo height 6 m) and at Sta 0 +450 (Sabo height 4 m). For one hundred years period when debris flow peak discharge of 62.66 m3/second required 2 units of sabo dams (closed type) with positions at Sta 0 +200 (Sabo height 6 m) and at Sta 0 +450 (Sabo height 5 m) to prevent overflow of debris flow to the settlement. Thus, the right efforts to control debris flow on Batang Lakin is the sabo dam

The Topology of Branching Universes

The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology

On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-existence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein-Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner-Nordstr\"{o}m metric is accomplished.Comment: 29 pages, 0 figure