Metastability of R-Charged Black Holes

The global stability of R-charged AdS black holes in a grand canonical ensemble is examined by eliminating the constraints from the action, but without solving the equations of motion, thereby constructing the reduced action of the system. The metastability of the system is found to set in at a critical value of the chemical potential which is conjugate to the R-charge. The relation among the small black hole, large black hole and the instability is discussed. The result is consistent with the metastability found in the AdS/CFT-conjectured dual field theory. The "renormalized" temperature of AdS black holes, which has been rather ad hoc, is suggested to be the boundary temperature in the sense of AdS/CFT correspondence. As a byproduct of the analysis, we find a more general solution of the theory and its properties are briefly discussed.Comment: 36 pages, 7 figures, v2 is the published version. the exposition is made slightly shorter and hopefully cleare

Effect of the spin-orbit interaction and the electron phonon coupling on the electronic state in a silicon vacancy

The electronic state around a single vacancy in silicon crystal is investigated by using the Green's function approach. The triply degenerate charge states are found to be widely extended and account for extremely large elastic softening at low temperature as observed in recent ultrasonic experiments. When we include the LS coupling $\lambda_{\rm Si}$ on each Si atom, the 6-fold spin-orbital degeneracy for the $V^{+}$ state with the valence +1 and spin 1/2 splits into $\Gamma_{7}$ doublet groundstates and $\Gamma_{8}$ quartet excited states with a reduced excited energy of $O(\lambda_{\rm Si}/10)$. We also consider the effect of couplings between electrons and Jahn-Teller phonons in the dangling bonds within the second order perturbation and find that the groundstate becomes $\Gamma_{8}$ quartet which is responsible for the magnetic-field suppression of the softening in B-doped silicon.Comment: 4 pages, 2 figure

Global-in-time behavior of the solution to a Gierer-Meinhardt system

Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition. The long-time behavior of the solution, however, has not yet been clarified mathematically. In this paper, we study the case when its ODE part takes periodic-in-time solutions, that is, $\tau=s+1$. Under some additional assumptions on parameters, we show that the solution exists global-in-time and absorbed into one of these ODE orbits. Thus spatial patterns eventually dis- appear if those parameters are in a region without local self-enhancement or long-range inhibition

On existence of matter outside a static black hole

It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of matter composed of a perfect fluid in static black hole spacetimes under certain conditions, which can be interpreted as a relation between the stellar mass and the black hole mass.Comment: 4pages, final version accepted for publication in Journal of Mathematical Physic

Adhesion between polymers and evaporated gold and nickel films

To obtain information on the adhesion between metal films and polymeric solids, the adhesion force was measured by means of a tensile pull test. It was found that the adhesion strengths between polymeric solids and gold films evaporated on polymer substrates were (1.11 + or - 0.53) multiplied by 10(6) N/M(2) on PTFE, about 5.49 multiplied by 10(6) N/m(2) on UHMWPE, and 6.54x10(6) on 6/6 nylon. The adhesion strengths for nickel films evaporated on PTFE, UHMWPE, and 6/6 nylon were found to be a factor of 1.7 higher than those for the gold coated PTFE, UHMWPE, and 6/6 nylon. To confirm quantitatively the effect of electron irradiation on the adhesion strength between a PTFE solid and metal films, a tensile pull test was performed on the irradiated PTFE specimens, which were prepared by evaporating nickel or gold on PTFE surfaces irradiated by 2-keV electrons for various times. After irradiation, the adhesion strength increased to (4.92 + or - 0.92)x10(6) N/m(2) for nickel coated PTFE and (1.82 + or - 0.48)x10(6) N/m(2) for gold coated PTFE. The improvement in adhesion for nickel is higher than that for gold

Lens space surgeries on A'Campo's divide knots

It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parameters, the corresponding plane curve is constructed. The surgery coefficients are also considered. Such presentations support us to study each knot itself, and the relationship among the knots in the set of lens space surgeries.Comment: 26 pages, 19 figures. The proofs of Theorem 1.3 and Lemma 3.5 are written down by braid calculus. Section 4 (on the operation Adding squares) is revised and improved the most. Section 5 is adde

Localization Properties of Electronic States in Polaron Model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling are completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.Comment: 6 pages, 6 figure

Emergence of noncollinear magnetic ordering in small magnetic clusters: Mnn_n and As@Mnn_n

Using first-principles density functional calculations, we have studied the magnetic ordering in pure Mn$_n$ ($n=2-$10, 13, 15, 19) and As@Mn$_n$ ($n=1-$10) clusters. Although, for both pure and doped manganese clusters, there exists many collinear and noncollinear isomers close in energy, the smaller clusters with $n\leqslant$5 have collinear magnetic ground state and the emergence of noncollinear ground states is seen for $n\geqslant$6 clusters. Due to strong $p-d$ hybridization in As@Mn$_n$ clusters, the binding energy is substantially enhanced and the magnetic moment is reduced compared to the corresponding pure Mn$_n$ clusters.Comment: 10 Pages and 5 Figure