FORTRAN subroutines for out-of-core solutions of large complex linear systems

The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems

Symmetry and inert states of spin Bose Condensates

We construct the list of all possible inert states of spin Bose condensates for $S \le 4$. In doing so, we also obtain their symmetry properties. These results are applied to classify line defects of these spin condensates at zero magnetic field.Comment: an error in Sec III C correcte

Signature of superconducting states in cubic crystal without inversion symmetry

The effects of absence of inversion symmetry on superconducting states are investigated theoretically. In particular we focus on the noncentrosymmetric compounds which have the cubic symmetry $O$ like Li$_2$Pt$_3$B. An appropriate and isotropic spin-orbital interaction is added in the Hamiltonian and it acts like a magnetic monopole in the momentum space. The consequent pairing wavefunction has an additional triplet component in the pseudospin space, and a Zeeman magnetic field $\bf{B}$ can induce a collinear supercurrent $\bf{J}$ with a coefficient $\kappa(T)$. The effects of anisotropy embedded in the cubic symmetry and the nodal superconducting gap function on $\kappa(T)$ are also considered. From the macroscopic perspectives, the pair of mutually induced $\bf{J}$ and magnetization ${\bf{M}}$ can affect the distribution of magnetic field in such noncentrosymmetric superconductors, which is studied through solving the Maxwell equation in the Meissner geometry as well as the case of a single vortex line. In both cases, magnetic fields perpendicular to the external ones emerge as a signature of the broken symmetry.Comment: 16 pages in pre-print forma

Josephson Current between Triplet and Singlet Superconductors

The Josephson effect between triplet and singlet superconductors is studied. Josephson current can flow between triplet and singlet superconductors due to the spin-orbit coupling in the spin-triplet superconductor but it is finite only when triplet superconductor has $L_z=-S_z=\pm 1$, where $L_z$ and $S_z$ are the perpendicular components of orbital angular momentum and spin angular momentum of the triplet Cooper pairs, respectively. The recently observed temperature and orientational dependence of the critical current through a Josephson junction between UPt$_3$ and Nb is investigated by considering a non-unitary triplet state.Comment: 4 pages, no figure

Asymmetric Fermi superfluid in a harmonic trap

We consider a dilute two-component atomic fermion gas with unequal populations in a harmonic trap potential using the mean field theory and the local density approximation. We show that the system is phase separated into concentric shells with the superfluid in the core surrounded by the normal fermion gas in both the weak-coupling BCS side and near the Feshbach resonance. In the strong-coupling BEC side, the composite bosons and left-over fermions can be mixed. We calculate the cloud radii and compare axial density profiles systemically for the BCS, near resonance and BEC regimes.Comment: 15 pages, 5 figure

Center of mass and relative motion in time dependent density functional theory

It is shown that the exchange-correlation part of the action functional $A_{xc}[\rho (\vec r,t)]$ in time-dependent density functional theory , where $\rho (\vec r,t)$ is the time-dependent density, is invariant under the transformation to an accelerated frame of reference $\rho (\vec r,t) \to \rho ' (\vec r,t) = \rho (\vec r + \vec x (t),t)$, where $\vec x (t)$ is an arbitrary function of time. This invariance implies that the exchange-correlation potential in the Kohn-Sham equation transforms in the following manner: $V_{xc}[\rho '; \vec r, t] = V_{xc}[\rho; \vec r + \vec x (t),t]$. Some of the approximate formulas that have been proposed for $V_{xc}$ satisfy this exact transformation property, others do not. Those which transform in the correct manner automatically satisfy the ``harmonic potential theorem", i.e. the separation of the center of mass motion for a system of interacting particles in the presence of a harmonic external potential. A general method to generate functionals which possess the correct symmetry is proposed

Feeling (Mis)Understood and Intergroup Friendships in Interracial Interactions

The present research investigated whether having out-group friends serves as a buffer for feeling misunderstood in interracial interactions. Across three experience sampling studies, we found that among ethnic minorities who have few White friends or are not interacting with White friends, daily interracial interactions are associated with feeling less understood. By contrast, we found that among ethnic minorities who have more White friends or are interacting with White friends, the relationship between daily interracial interactions and feeling understood is not significant. We did not find similar results for Whites; that is, having ethnic minority friends did not play a role in the relationship between daily interracial interactions and feeling understood. Together, these studies demonstrate the beneficial effects of intergroup friendships for ethnic minorities

Pinhole calculations of the Josephson effect in 3He-B

We study theoretically the dc Josephson effect between two volumes of superfluid 3He-B. We first discuss how the calculation of the current-phase relationships is divided into a mesoscopic and a macroscopic problem. We then analyze mass and spin currents and the symmetry of weak links. In quantitative calculations the weak link is assumed to be a pinhole, whose size is small in comparison to the coherence length. We derive a quasiclassical expression for the coupling energy of a pinhole, allowing also for scattering in the hole. Using a selfconsistent order parameter near a wall, we calculate the current-phase relationships in several cases. In the isotextural case, the current-phase relations are plotted assuming a constant spin-orbit texture. In the opposite anisotextural case the texture changes as a function of the phase difference. For that we have to consider the stiffness of the macroscopic texture, and we also calculate some surface interaction parameters. We analyze the experiments by Marchenkov et al. We find that the observed pi states and bistability hardly can be explained with the isotextural pinhole model, but a good quantitative agreement is achieved with the anisotextural model.Comment: 20 pages, 21 figures, revtex

Sensitivity-analysis method for inverse simulation application

An important criticism of traditional methods of inverse simulation that are based on the Newton–Raphson algorithm is that they suffer from numerical problems. In this paper these problems are discussed and a new method based on sensitivity-analysis theory is developed and evaluated. The Jacobian matrix may be calculated by solving a sensitivity equation and this has advantages over the approximation methods that are usually applied when the derivatives of output variables with respect to inputs cannot be found analytically. The methodology also overcomes problems of input-output redundancy that arise in the traditional approaches to inverse simulation. The sensitivity- analysis approach makes full use of information within the time interval over which key quantities are compared, such as the difference between calculated values and the given ideal maneuver after each integration step. Applications to nonlinear HS125 aircraft and Lynx helicopter models show that, for this sensitivity-analysis method, more stable and accurate results are obtained than from use of the traditional Newton–Raphson approach