Precision heat forming of tetrafluoroethylene tubing

An invention that provides a method of altering the size of tetrafluoroethylene tubing which is only available in limited combination of wall thicknesses and diameter are discussed. The method includes the steps of sliding the tetrafluoroethylene tubing onto an aluminum mandrel and clamping the ends of the tubing to the mandrel by means of clamps. The tetrafluorethylene tubing and mandrel are then placed in a supporting coil which with the mandrel and tetrafluorethylene tubing are then positioned in a insulated steel pipe which is normally covered with a fiber glass insulator to smooth out temperature distribution therein. The entire structure is then placed in an event which heats the tetrafluorethylene tubing which is then shrunk by the heat to the outer dimension of the aluminum mandrel. After cooling the aluminum mandrel is removed from the newly sized tetrafluorethylene tubing by a conventional chemical milling process

Directed Random Markets: Connectivity determines Money

Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this work, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.Comment: 14 pages, 6 figure

Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem

We study chaotic orbits of conservative low--dimensional maps and present numerical results showing that the probability density functions (pdfs) of the sum of $N$ iterates in the large $N$ limit exhibit very interesting time-evolving statistics. In some cases where the chaotic layers are thin and the (positive) maximal Lyapunov exponent is small, long--lasting quasi--stationary states (QSS) are found, whose pdfs appear to converge to $q$--Gaussians associated with nonextensive statistical mechanics. More generally, however, as $N$ increases, the pdfs describe a sequence of QSS that pass from a $q$--Gaussian to an exponential shape and ultimately tend to a true Gaussian, as orbits diffuse to larger chaotic domains and the phase space dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in the International Journal of Bifurcation and Chaos, on Jun 21, 201

Non-Canonical Perturbation Theory of Non-Linear Sigma Models

We explore the O(N)-invariant Non-Linear Sigma Model (NLSM) in a different perturbative regime from the usual relativistic-free-field one, by using non-canonical basic commutation relations adapted to the underlying O(N) symmetry of the system, which also account for the non-trivial (non-flat) geometry and topology of the target manifold.Comment: 11 pages, 1 figure, LaTe

D-branes with Lorentzian signature in the Nappi-Witten model

Lorentzian signature D-branes of all dimensions for the Nappi-Witten string are constructed. This is done by rewriting the gluing condition $J_+=FJ_-$ for the model chiral currents on the brane as a well posed first order differential problem and by solving it for Lie algebra isometries $F$ other than Lie algebra automorphisms. By construction, these D-branes are not twined conjugacy classes. Metrically degenerate D-branes are also obtained.Comment: 22 page

Physical interpretation of NUT solution

We show that the well-known NUT solution can be correctly interpreted as describing the exterior field of two counter-rotating semi-infinite sources possessing negative masses and infinite angular momenta which are attached to the poles of a static finite rod of positive mass.Comment: 7 pages, 1 figure, submitted to Classical and Quantum Gravit

Households’ Financial Vulnerability

Households’ financial vulnerability determines households’ default risk. Financial stability could be affected by households’ behavior under stressful macroeconomic conditions. Households’ financial vulnerability depends on their indebtedness levels and on the fragility of their income sources to be able to fulfill their obligations. The main source of households’ uncertainty comes from labor income generation, which is critically determined by unemployment. Heterogeneity of indebtedness levels and of income uncertainty calls for microeconomic analysis. This paper uses panel data survival analysis to estimate the probability of job loss at the individual level. Using semi-parametric methods, a significant heterogeneity is found for the impact of aggregate unemployment among individuals. Monte Carlo simulations are run to assess households financial stress and then to estimate aggregate debt at risk under high unemployment rate scenarios. Since the majority of debt is held by those with lower levels of income vulnerability, it is found that financial stability is not significantly affected by high unemployment levels.

Stabilized mixed approximation of axisymmetric Brinkman flows

This paper is devoted to the numerical analysis of an augmented finite element approximation of the axisymmetric Brinkman equations. Stabilization of the variational formulation is achieved by adding suitable Galerkin least-squares terms, allowing us to transform the original problem into a formulation better suited for performing its stability analysis. The sought quantities (here velocity, vorticity, and pressure) are approximated by Raviart−Thomas elements of arbitrary order k ≥ 0, piecewise continuous polynomials of degree k + 1, and piecewise polynomials of degree k, respectively. The well-posedness of the resulting continuous and discrete variational problems is rigorously derived by virtue of the classical Babuška–Brezzi theory. We further establish a priori error estimates in the natural norms, and we provide a few numerical tests illustrating the behavior of the proposed augmented scheme and confirming our theoretical findings regarding optimal convergence of the approximate solutions

Polyakov loop in chiral quark models at finite temperature

We describe how the inclusion of the gluonic Polyakov loop incorporates large gauge invariance and drastically modifies finite temperature calculations in chiral quark models after color neutral states are singled out. This generates an effective theory of quarks and Polyakov loops as basic degrees of freedom. We find a strong suppression of finite temperature effects in hadronic observables triggered by approximate triality conservation (Polyakov cooling), so that while the center symmetry breaking is exponentially small with the constituent quark mass, chiral symmetry restoration is exponentially small with the pion mass. To illustrate the point we compute some low energy observables at finite temperature and show that the finite temperature corrections to the low energy coefficients are $N_c$ suppressed due to color average of the Polyakov loop. Our analysis also shows how the phenomenology of chiral quark models at finite temperature can be made compatible with the expectations of chiral perturbation theory. The implications for the simultaneous center symmetry breaking-chiral symmetry restoration phase transition are also discussed.Comment: 24 pages, 8 ps figures. Figure and appendix added. To appear in Physical Review