State-of-the-art survey of dissimilar metal joining by solid state welding

State-of-the-art of dissimilar metal joining by solid state diffusion bonding and roll and press welding, emphasizing stainless steel and aluminum allo

Precedents, Variables, and Options in Planning a U.S. Military Disengagement Strategy from Iraq

The questions of how to empower the Iraqis most effectively and then progressively withdraw non-Iraqi forces from that country is one of the most important policy problems currently facing the United States. The authors seek to present the U.S. situation in Iraq in all of its complexity and ambiguity, with policy recommendations for how that withdrawal strategy might be most effectively implemented. They consider previous instances of U.S. military occupation of foreign countries and the difficulty of maintaining domestic support for such operations. The authors view the empowerment of a viable Iraqi central government and a security force to defend its authority as vital to the future of that country, but also suggest that there are severe constraints on the potential for the United States to sustain its military presence in that country at the current level. They conclude that the United States must be prepared to withdraw from Iraq under non-optimal conditions and that the chief U.S. goals should be to devise an exit strategy for Iraq that focuses on bolstering Iraqi government legitimacy even if this does not involve creating a Western style democracy. The authors strongly reject the idea withdrawing from Iraq by the use of a formal timetable, and call for the U.S. to continue its policy of renouncing permanent Iraqi bases.https://press.armywarcollege.edu/monographs/1731/thumbnail.jp

Reconstructing Iraq: Insights, Challenges, and Missions for Military Forces in a Post-Conflict Scenario

In October 2002, the U.S. Army War College\u27s Strategic Studies Institute, in coordination with the Office of the Army Deputy Chief of Staff/G-3, initiated a study to analyze how American and coalition forces can best address the requirements that will necessarily follow operational victory in a war with Iraq. The objectives of the project were to determine and analyze probable missions for military forces in a post-Saddam Iraq; examine associated challenges; and formulate strategic recommendations for transferring responsibilities to coalition partners or civilian organizations, mitigating local animosity, and facilitating overall mission accomplishment in the war against terrorism. The study has much to offer planners and executors of operations to occupy and reconstruct Iraq, but also has many insights that will apply to achieving strategic objectives in any conflict after hostilities are concluded. The current war against terrorism has highlighted the danger posed by failed and struggling states. If this nation and its coalition partners decide to undertake the mission to remove Saddam Hussein, they will also have to be prepared to dedicate considerable time, manpower, and money to the effort to reconstruct Iraq after the fighting is over. Otherwise, the success of military operations will be ephemeral, and the problems they were designed to eliminate could return or be replaced by new and more virulent difficulties.https://press.armywarcollege.edu/monographs/1806/thumbnail.jp

3+1 spinfoam model of quantum gravity with spacelike and timelike components

We present a spinfoam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. The model is an extension of a recently introduced Lorentzian model, in which both timelike and spacelike components are included. The spinfoams in the model, corresponding to quantized 4-geometries, carry a natural non-perturbative local causal structure induced by the geometry of the algebra of the internal gauge (sl(2,C)). Amplitudes can be expressed as integrals over the spacelike unit-vectors hyperboloid in Minkowski space, or the imaginary Lobachevskian space.Comment: 16 pages, 1 figur

Spin foam model for Lorentzian General Relativity

We present a spin foam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. Its vertex amplitude turns out to be the one recently introduced by Barrett and Crane. As in the case of its Euclidean relatives, the model fully implements the desired sum over 2-complexes which encodes the local degrees of freedom of the theory.Comment: 8 pages, 1 figur

Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity

The Barrett-Crane models of Lorentzian quantum gravity are a family of spin foam models based on the Lorentz group. We show that for various choices of edge and face amplitudes, including the Perez-Rovelli normalization, the amplitude for every triangulated closed 4-manifold is a non-negative real number. Roughly speaking, this means that if one sums over triangulations, there is no interference between the different triangulations. We prove non-negativity by transforming the model into a ``dual variables'' formulation in which the amplitude for a given triangulation is expressed as an integral over three copies of hyperbolic space for each tetrahedron. Then we prove that, expressed in this way, the integrand is non-negative. In addition to implying that the amplitude is non-negative, the non-negativity of the integrand is highly significant from the point of view of numerical computations, as it allows statistical methods such as the Metropolis algorithm to be used for efficient computation of expectation values of observables.Comment: 13 page

Positivity of Spin Foam Amplitudes

The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (e^{iS}) rather than imaginary-time (e^{-S}) path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model.Comment: 15 pages LaTeX. v3: Final version, with updated conclusions and other minor changes. To appear in Classical and Quantum Gravity. v4: corrects # of samples in Lorentzian tabl

Spin Foam Models of Yang-Mills Theory Coupled to Gravity

We construct a spin foam model of Yang-Mills theory coupled to gravity by using a discretized path integral of the BF theory with polynomial interactions and the Barret-Crane ansatz. In the Euclidian gravity case we obtain a vertex amplitude which is determined by a vertex operator acting on a simple spin network function. The Euclidian gravity results can be straightforwardly extended to the Lorentzian case, so that we propose a Lorentzian spin foam model of Yang-Mills theory coupled to gravity.Comment: 10 page

Finite Number of States, de Sitter Space and Quantum Groups at Roots of Unity

This paper explores the use of a deformation by a root of unity as a tool to build models with a finite number of states for applications to quantum gravity. The initial motivation for this work was cosmological breaking of supersymmetry. We explain why the project was unsuccessful. What is left are some observations on supersymmetry for q-bosons, an analogy between black holes in de Sitter and properties of quantum groups, and an observation on a noncommutative quantum mechanics model with two degrees of freedom, depending on one parameter. When this parameter is positive, the spectrum has a finite number of states; when it is negative or zero, the spectrum has an infinite number of states. This exhibits a desirable feature of quantum physics in de Sitter space, albeit in a very simple, non-gravitational context.Comment: 25 pages, 5 figure

Finiteness and Dual Variables for Lorentzian Spin Foam Models

We describe here some new results concerning the Lorentzian Barrett-Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a ``dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.Comment: 15 pages, 1 figur