Thermal modeling of a metallic thermal protection tile for entry vehicles

The thermal Energy Flow Simulation (TEFS) computer program was developed to simulate transient heat transfer through composite solids and predict interfacial temperatures. The program and its usage are described. A simulation of the thermal response of a new thermal protection tile design for the Space Shuttle Orbiter is presented and graphically compared with actual data. An example is also provided which shows the program's usage as a design tool for theoretical models

When is the deconfinement phase transition universal?

Pure Yang-Mills theory has a finite-temperature phase transition, separating the confined and deconfined bulk phases. Svetitsky and Yaffe conjectured that if this phase transition is of second order, it belongs to the universality class of transitions for particular scalar field theories in one lower dimension. We examine Yang-Mills theory with the symplectic gauge groups Sp(N). We find new evidence supporting the Svetitsky-Yaffe conjecture and make our own conjecture as to which gauge theories have a universal second order deconfinement phase transition.Comment: 5 pages, 4 figures; Contribution to Confinement 2003, Tokyo, Japan, July 21-24, 200

Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states lo calized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge-Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r potential.Comment: 22 pages, 9 Figure

Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the δ\delta-Function Potential in 1-dimensional Relativistic Quantum Mechanics

We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudo-differential operator $H = \sqrt{p^2 + m^2}$. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics

Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity

The non-relativistic hydrogen atom enjoys an accidental $SO(4)$ symmetry, that enlarges the rotational $SO(3)$ symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius $R$ with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter $\gamma$, in general the accidental $SO(4)$ symmetry is lifted. However, for $R = (l+1)(l+2) a$ (where $a$ is the Bohr radius and $l$ is the orbital angular momentum) some degeneracy remains when $\gamma = \infty$ or $\gamma = \frac{2}{R}$. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of $R$ and $\gamma$.Comment: 27 pages, 7 figure

Majorana Fermions in a Box

Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $\lambda = - \lambda^*$, of self-adjoint extensions, for Majorana fermions $\lambda$ is restricted to $\pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schr\"odinger equation that does not suffer from these problems.Comment: 23 pages, 2 figure

The Freezing of Random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.Comment: 4 pages, 8 figures. v2: presentation improve