Graphical Evolution of Spin Network States

The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution, and evaluate its action both on edges and on vertices of the spin network states. The analytical computations are carried out completely to yield a finite, diffeomorphism invariant result. We use techniques from the recoupling theory of colored graphs with trivalent vertices to evaluate the graphical part of the Hamiltonian action. We show that the action on edges is equivalent to a diffeomorphism transformation, while the action on vertices adds new edges and re-routes the loops through the vertices.Comment: 24 pages, 21 PostScript figures, uses epsfig.sty, Minor corrections in the final formula in the main body of the paper and in the formula for the Tetrahedral net in the Appendi

Microstructural development during the quenching and partitioning process in a newly designed low-carbon steel

This paper presents a detailed characterization of the microstructural development of a new quenching and partitioning (Q&P) steel. Q&P treatments, starting from full austenitization, were applied to the developed steel, leading to microstructures containing volume fractions of retained austenite of up to 0.15. The austenite was distributed as films in between the martensite laths. Analysis demonstrates that, in this material, stabilization of austenite can be achieved at significantly shorter time scales via the Q&P route than is possible via a bainitic isothermal holding. The results showed that the thermal stabilization of austenite during the partitioning step is not necessarily accompanied by a significant expansion of the material. This implies that the process of carbon partitioning from martensite to austenite occurs across low-mobility martensite–austenite interfaces. The amount of martensite formed during the first quench has been quantified. Unlike martensite formed in the final quench, this martensite was found to be tempered during partitioning. Measured volume fractions of retained austenite after different treatments were compared with simulations using model descriptions for carbon partitioning from martensite to austenite. Simulation results confirmed that the carbon partitioning takes place at low-mobility martensite–austenite interfaces.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.OLD Metals Processing, Microstructures and PropertiesOLD Surface and Interface Engineerin

Regularization of the Hamiltonian constraint and the closure of the constraint algebra

In the paper we discuss the process of regularization of the Hamiltonian constraint in the Ashtekar approach to quantizing gravity. We show in detail the calculation of the action of the regulated Hamiltonian constraint on Wilson loops. An important issue considered in the paper is the closure of the constraint algebra. The main result we obtain is that the Poisson bracket between the regulated Hamiltonian constraint and the Diffeomorphism constraint is equal to a sum of regulated Hamiltonian constraints with appropriately redefined regulating functions.Comment: 23 pages, epsfig.st

Linear Contraction Behavior of Low-Carbon, Low-Alloy Steels During and After Solidification Using Real-Time Measurements

A technique for measuring the linear contraction during and after solidification of low-alloy steel was developed and used for examination of two commercial low-carbon and low-alloy steel grades. The effects of several experimental parameters on the contraction were studied. The solidification contraction behavior was described using the concept of rigidity in a solidifying alloy, evolution of the solid fraction, and the microstructure development during solidification. A correlation between the linear contraction properties in the solidification range and the hot crack susceptibility was proposed and used for the estimation of hot cracking susceptibility for two studied alloys and verified with the real casting practice. The technique allows estimation of the contraction coefficient of commercial steels in a wide range of temperatures and could be helpful for computer simulation and process optimization during continuous casting. © 2013 The Minerals, Metals & Materials Society and ASM International

Topos quantum theory with short posets

Topos quantum mechanics, developed by Isham et. al., creates a topos of presheaves over the poset V(N) of abelian von Neumann subalgebras of the von Neumann algebra N of bounded operators associated to a physical system, and established several results, including: (a) a connection between the Kochen-Specker theorem and the non-existence of a global section of the spectral presheaf; (b) a version of the spectral theorem for self-adjoint operators; (c) a connection between states of N and measures on the spectral presheaf; and (d) a model of dynamics in terms of V(N). We consider a modification to this approach using not the whole of the poset V(N), but only its elements of height at most two. This produces a different topos with different internal logic. However, the core results (a)--(d) established using the full poset V(N) are also established for the topos over the smaller poset, and some aspects simplify considerably. Additionally, this smaller poset has appealing aspects reminiscent of projective geometry.Comment: 14 page

Clinical management of women with metastatic breast cancer: a descriptive study according to age group

BACKGROUND: The primary aim of treatment of a patient who has developed metastatic disease is palliation. The objectives of the current study are to describe and quantify the clinical management of women with metastatic breast cancer from the diagnosis of metastatic disease until death and to analyze differences between age groups. METHODS: Data were collected from the medical files of all patients (n = 116) who had died after December 31, 1999, after a diagnosis of metastatic breast cancer in two teaching hospitals in the south of the Netherlands. RESULTS: Of the 116 patients included in our study, 10 (9%) already had metastatic disease at diagnosis and 106 developed distant disease after the diagnosis of localized breast cancer. Before they died, 70% of the 116 patients developed metastases in one or more bones, 50% in the lung and/or pleura, 50% in the abdominal viscera, 23% in the central nervous system, and 19% in the skin. Patients younger than 50 years were much more likely to develop metastases in the central nervous system than patients 50 years and older. Seventy-seven (66%) of the 116 patients with metastatic breast cancer received chemotherapy. This proportion decreased with age (p = 0.005), as did the number of schemes per patient. Together, they received 132 chemotherapy schemes, of which 35 (27%) resulted in partial remission or stabilization of the disease process. Ninety-eight patients (84%) received hormonal treatment. This proportion did not differ between the three age groups. Together, they received 216 hormonal treatments, 38 (16%) of which resulted in partial remission or stabilization of the disease process. Seventy-nine patients (68%) received palliative radiotherapy. This proportion decreased with age (p = 0.03). Together, they underwent 216 courses, 176 (77%) of which resulted in relief of the complaints. CONCLUSION: Patients aged 70 years and older are less likely to receive chemotherapy or radiotherapy. Part of this difference could be explained by their shorter survival time after the diagnosis of metastatic disease and their lower risk of developing brain and bone metastases. However, more research is needed to understand the age-related differences in the treatment of metastatic breast cancer, and especially how comorbidity and frailty limit therapeutic choices

Matrix Elements of Thiemann's Hamiltonian Constraint in Loop Quantum Gravity

We present an explicit computation of matrix elements of the hamiltonian constraint operator in non-perturbative quantum gravity. In particular, we consider the euclidean term of Thiemann's version of the constraint and compute its action on trivalent states, for all its natural orderings. The calculation is performed using graphical techniques from the recoupling theory of colored knots and links. We exhibit the matrix elements of the hamiltonian constraint operator in the spin network basis in compact algebraic form.Comment: 32 pages, 22 eps figures. LaTeX (Using epsfig.sty,ioplppt.sty and bezier.sty). Submited to Classical and Quantum Gravit