Towards robust aero-thermodynamic predictions for re-usable single-stage to orbit vehicles

Re-usable single stage to orbit launch vehicles promise to reduce the cost of access to space, but their success will be particularly reliant on accurate and robust modelling of their aero-thermodynamic characteristics. For preliminary design and optimization studies, relatively simple numerical prediction techniques must perforce be used, but it is important that the uncertainty that is inherent in the predictions of these models be understood. Predictions of surface pressure and heat transfer obtained using a new reduced-order model that is based on the Newtonian flow assumption and the Reynolds analogy for heating are compared against those of a more physically-sophisticated Direct Simulation Monte Carlo method in order to determine the ability of the model to capture the aero-thermodynamics of vehicles with very complex configuration even when run at low enough resolution to be practical in the context of design optimization studies. Attention is focused on the high-altitude regime where lifting re-usable Single-Stage to Orbit configurations will experience their greatest thermal load during re-entry, but where non-continuum effects within the gas of the atmosphere might be important. It is shown that the reduced-order model is capable of reproducing the results of the more complex Monte Carlo formalism with surprising fidelity, but that residual uncertainties exist, particularly in the behaviour of the heating models and in the applicability of the continuum assumption given the onset of finite slip velocity on surface of vehicle. The results suggest thus that, if used with care, reduced-order models such as those described here can be used very effectively in the design and optimization of space-access vehicles with very complex configuration, as long as their predictions are adequately supported by the use of more sophisticated computational techniques

Entanglement between a qubit and the environment in the spin-boson model

The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of $\alpha$, the strength of the ohmic coupling to the environment, and $\epsilon$, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For $\epsilon=0$, the entanglement increases monotonically with $\alpha$, until it becomes maximal for $\alpha \lim 1^-$. For fixed $\epsilon>0$, the entanglement is a maximum as a function of $\alpha$ for a value, $\alpha = \alpha_M < 1$.Comment: 4 pages, 3 figures. Shortened version restricted to groundstate entanglemen

Deformation of the Planetary Orbits Caused by the Time Dependent Gravitational Potential in the Universe

In the paper are studied the deformations of the planetary orbits caused by the time dependent gravitational potential in the universe. It is shown that the orbits are not axially symmetric and the time dependent potential does not cause perihelion precession. It is found a simple formula for the change of the orbit period caused by the time dependent gravitational potential and it is tested for two binary pulsars.Comment: 7 page

Flow equation analysis of the anisotropic Kondo model

We use the new method of infinitesimal unitary transformations to calculate zero temperature correlation functions in the strong-coupling phase of the anisotropic Kondo model. We find the dynamics on all energy scales including the crossover behaviour from weak to strong coupling. The integrable structure of the Hamiltonian is not used in our approach. Our method should also be useful in other strong-coupling models since few other analytical methods allow the evaluation of their correlation functions on all energy scales.Comment: 4 pages RevTeX, 2 eps figures include

Understanding High-Temperature Superconductors with Quantum Cluster Theories

Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding (dynamical) mean-field approximation when the cluster size becomes one. Here we will review systematic dynamical cluster simulations of the two-dimensional Hubbard model, that display phenomena remarkably similar to those found in the cuprates, including antiferromagnetism, superconductivity and pseudogap behavior. We will then discuss results for the structure of the pairing mechanism in this model, obtained from a combination of dynamical cluster results and diagrammatic techniques.Comment: 8 pages, 12 figures; submitted to proceedings of M2S-HTSC VIII, Dresden 200

Small pipe characterization system (SPCS) conceptual design

Throughout the Department of Energy (DOE) complex there are many facilities that have been identified for Decontamination and Decommissioning (D&D). As processes are terminated or brought off-line, facilities are placed on the inactive list, and facility managers and site contractors are required to assure a safe and reliable decommissioning and transition of these facilities to a clean final state. Decommissioning of facilities requires extensive reliable characterization, decontamination and in some cases dismantlement. Characterization of piping systems throughout the DOE complex is becoming more and more necessary. In addition to decommissioning activities, characterization activities are performed as part of surveillance and maintenance (S&M). Because of the extent of contamination, all inactive facilities require some type of S&M. These S&M activities include visual assessment, equipment and material accounting, and maintenance. The majority of the inactive facilities have piping systems 3 inches or smaller that are inaccessible because they are contaminated, imbedded in concrete, or run through hot cells. Many of these piping systems have been inactive for a number of years and there exists no current system condition information or the historical records are poor and/or missing altogether. Many of these piping systems are placed on the contaminated list, not because of known contamination, but because of the risk of internal contamination. Many of the piping systems placed on the contamination list may not have internal contamination. Because there is a potential however, they are treated as such. The cost of D&D can be greatly reduced by identifying and removing hot spot contamination, leaving clean piping to be removed using conventional methods. Accurate characterization of these piping systems is essential before, during and after all D&D activities

Oscillations of the magnetic polarization in a Kondo impurity at finite magnetic fields

The electronic properties of a Kondo impurity are investigated in a magnetic field using linear response theory. The distribution of electrical charge and magnetic polarization are calculated in real space. The (small) magnetic field does not change the charge distribution. However, it unmasks the Kondo cloud. The (equal) weight of the d-electron components with their magnetic moment up and down is shifted and the compensating s-electron clouds don't cancel any longer (a requirement for an experimental detection of the Kondo cloud). In addition to the net magnetic polarization of the conduction electrons an oscillating magnetic polarization with a period of half the Fermi wave length is observed. However, this oscillating magnetic polarization does not show the long range behavior of Rudermann-Kittel-Kasuya-Yosida oscillations because the oscillations don't extend beyond the Kondo radius. They represent an internal electronic structure of the Kondo impurity in a magnetic field. PACS: 75.20.Hr, 71.23.An, 71.27.+

Exact perturbative solution of the Kondo problem

We explicitly evaluate the infinite series of integrals that appears in the "Anderson-Yuval" reformulation of the anisotropic Kondo problem in terms of a one-dimensional Coulomb gas. We do this by developing a general approach relating the anisotropic Kondo problem of arbitrary spin with the boundary sine-Gordon model, which describes impurity tunneling in a Luttinger liquid and in the fractional quantum Hall effect. The Kondo solution then follows from the exact perturbative solution of the latter model in terms of Jack polynomials.Comment: 4 pages in revtex two-colum

The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram

One central challenge in high-$T_c$ superconductivity (SC) is to derive a detailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and $O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-$T_c$ cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single- and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low- to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH- and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences - and thus, the material dependence to show up in the "non-universal" finite-T phase diagram ($T_c$-values).Comment: 17 pages, 9 figure

Kondo effect induced by a magnetic field

We study peculiarities of transport through a Coulomb blockade system tuned to the vicinity of the spin transition in its ground state. Such transitions can be induced in practice by application of a magnetic field. Tunneling of electrons between the dot and leads mixes the states belonging to the ground state manifold of the dot. Remarkably, both the orbital and spin degrees of freedom of the electrons are engaged in the mixing at the singlet-triplet transition point. We present a model which provides an adequate theoretical description of recent experiments with semiconductor quantum dots and carbon nanotubes