Cap Omega Research Articles

Interior dynamics of fatou sets

In this paper, we investigate the precise behavior of orbits inside attracting basins. Let f be a holomorphic polynomial of degree mge 2 in mathbb {C}, mathcal {A}(p) be the basin of attraction of an attracting fixed point p of f, and Omega _i (i=1, 2, cdots ) be the connected components of mathcal {A}(p). Assume Omega _1 contains p and {f^{-1}(p)}cap Omega _1ne {p}. Then there is a constant C so that for every point z_0 inside any Omega _i, there exists a point qin cup _k f^{-k}(p) inside Omega _i such that d_{Omega _i}(z_0, q)le C, where d_{Omega _i} is the Kobayashi distance on Omega _i. In paper Hu (Dynamics inside parabolic basins, 2022), we proved that this result is not valid for parabolic basins.

Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant

Let Omega subset {mathbb {R}}^d be a C^1 domain or, more generally, a Lipschitz domain with small Lipschitz constant and A(x) be a d times d uniformly elliptic, symmetric matrix with Lipschitz coefficients. Assume u is harmonic in Omega , or with greater generality u solves {text {div}}(A(x)nabla u)=0 in Omega , and u vanishes on Sigma = partial Omega cap B for some ball B. We study the dimension of the singular set of u in Sigma , in particular we show that there is a countable family of open balls (B_i)_i such that u|_{B_i cap Omega } does not change sign and K backslash bigcup _i B_i has Minkowski dimension smaller than d-1-epsilon for any compact K subset Sigma . We also find upper bounds for the (d-1)-dimensional Hausdorff measure of the zero set of u in balls intersecting Sigma in terms of the frequency. As a consequence, we prove a new unique continuation principle at the boundary for this class of functions and show that the order of vanishing at all points of Sigma is bounded except for a set of Hausdorff dimension at most d-1-epsilon .

An exterior overdetermined problem for Finsler N-Laplacian in convex cones

We consider a partially overdetermined problem for anisotropic N-Laplace equations in a convex cone Sigma intersected with the exterior of a bounded domain Omega in {mathbb {R}}^N, Nge 2. Under a prescribed logarithmic condition at infinity, we prove a rigidity result by showing that the existence of a solution implies that Sigma cap Omega must be the intersection of the Wulff shape and Sigma . Our approach is based on a Pohozaev-type identity and the characterization of minimizers of the anisotropic isoperimetric inequality inside convex cones.

Nonlinear microwave absorption in ceramic superconducting Y-Ba-Cu-O.

Novel microwave measurements in ceramic YBa/sub 2/Cu/sub 3/O/sub 7-//sub delta/ reveal that in the superconducting phase the absorption is highly nonlinear in the microwave power. At T = 80 K the surface resistance increases with dc field at a rate of 0.0025 ..cap omega../Oe, and with the microwave rf field at 0.07 ..cap omega../Oe, resulting in an absorption that can be substantial in the absence of an applied dc field.

Subthreshold antiproton production in 28Si+28Si collisions at 2.1 GeV/nucleon.

We report on the first observation of subthreshold antiproton production in nucleus-nucleus collisions. This measurement was made for the system /sup 28/Si+/sup 28/Si at a bombarding energy of 2.1 GeV/nucleon (kinetic energy per NN pair in the c.m. frame /similar to/850 MeV). A differential cross section d/sup 2/sigma/dP d ..cap omega.. of 80 +- 40 nb/sr (GeV/c) was measured for p-bar production at 1.9 GeV/c and 0/sup 0/. This result is 3 orders of magnitude larger than that predicted by a calculation incorporating internal motion of the nucleons in the colliding nuclei.

Gaussian and 1/N approximations in semiclassical cosmology.

We study the lambdaphi/sup 4/ theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field ..cap omega..(x) = (lambda)/sup 1/2/ and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation.

Properties of shape-driving orbitals: Rotational bands in 131La.

Several rotational bands have been populated in /sup 131/La via the /sup 116/Cd(/sup 19/F, 4n..gamma..) fusion-evaporation reaction. Bands built on low-lying h/sub 11/2/, g/sub 7/2/, and d/sub 5/2/ proton states have been identified. At higher spins, both proton and neutron (h/sub 11/2/)/sup 2/ alignments have been observed. While the proton alignment from low-..cap omega.. orbitals maintains a prolate nuclear shape, the alignment of high-..cap omega.. neutrons drives the nucleus to a collectively rotating oblate shape (..gamma..approx.-60/sup 0/). The results are interpreted in the framework of the cranked shell model. In addition, B(M1;I..-->..I-1)/B(E2;I..-->..I-2) ratios have been extracted for several of the bands and the results compared to a semiclassical model to identify the detailed structure.

Semidecoupling in doubly odd deformed nuclei.

Structures in which a neutron occupies an ..cap omega.. = (1/2 with decoupling parameter a/sub n/approx. =1 and a proton is in an ..cap omega..not =(1/2 orbit have been found in a doubly odd deformed nucleus. These bands are almost identical to the ..cap omega..not =(1/2 bands in neighboring odd proton nuclei. This behavior is reproduced analytically within the two-quasiparticle-plus-rotor model.

Rf surface resistance of Y-Ba-Cu-O thin films.

The rf surface resistance of superconducting Y-Ba-Cu-O thin films has been measured using a stripline resonator technique. The electron-beam-evaporated films have been measured from 0.6 to 17.4 GHz and from 4.2 to 8 K. The surface resistance reaches as low as 3.9 x 10/sup -4/ ..cap omega.. at the lowest frequency, and is expected to improve significantly as the film quality is optimized.

Radiative pion capture and pion photoproduction in a chiral bag model.

Radiative pion capture on nucleons is studied in a chiral bag model at pion laboratory momenta in the range q/sub L/approx.300--500 MeV. We calculate dsigma/d..cap omega.. and L-R asymmetry. Through detailed balance and time reversal invariance we also calculate dsigma/d..cap omega.. and P(theta) (nucleon recoil polarization) for pion photoproduction at equivalent photon laboratory momenta. A detailed comparison is made with the data.

Measurement of pion-proton bremsstrahlung for pions at 299 MeV.

We have measured the fivefold differential cross section ${d}^{5}$\ensuremath{\sigma}/d${\ensuremath{\Omega}}_{\ensuremath{\pi}}$d${\ensuremath{\Omega}}_{\ensuremath{\gamma}}$${\mathrm{dE}}_{\ensuremath{\gamma}}$ for the process ${\ensuremath{\pi}}^{+}$p\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$p\ensuremath{\gamma} with incident pions of energy 299 MeV. The angular regions for the outgoing pions (55\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\ensuremath{\theta}}_{\mathrm{lab}{}^{\ensuremath{\pi}}\mathrm{\ensuremath{\le}}95}$\ifmmode^\circ\else\textdegree\fi{}), and photons (${\ensuremath{\theta}}_{\mathrm{lab}{}^{\ensuremath{\gamma}}=241\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\ifmmode\pm\else\textpm\fi{}10}$\ifmmode^\circ\else\textdegree\fi{}) in coplanar geometry are selected to maximize the sensitivity to the radiation from the magnetic dipole moment of the ${\ensuremath{\Delta}}^{++}$(1232) resonance. At low photon energies, the data agree with the soft-photon approximation to pion-proton bremsstrahlung. At forward pion angles the data agree with older data and with the latest theoretical calculations for 2.3${\ensuremath{\mu}}_{p}$\ensuremath{\le}${\ensuremath{\mu}}_{\ensuremath{\Delta}}$\ensuremath{\le}3.3${\ensuremath{\mu}}_{p}$. However at more backward pion angles where no data existed, the predictions fail.

Quantum effects and the resistive transition in superconducting granular films

Static and dynamic properties of an array of Josephson junctions shunted by Ohmic resistors are discussed within a quantum Ginzburg-Landau theory. The phase diagram at zero temperature is calculated in mean field approximation. It shows that global superconductivity at T = 0 is possible only if the normal-state film resistance R/sub n/ is smaller than a critical value R/sub n//sup c/ which depends only logarithmically on the Josephson coupling and charging energies. The particular value R/sub n//sup c/ = 6.5 k..cap omega.. found in recent experiments on granular films is in reasonable agreement with estimates for these parameters. A phenomenological order parameter relaxation mechanism is introduced and the associated fluctuation-induced conductivity and diamagnetic susceptibility above T/sub c/ are determined. The resulting precursor conductivity does not explain the observed exponential decrease with R/sub n/-R/sub n//sup c/ of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thouless picture, is in good agreement with the experimental data.

Entropy generation, particle creation, and quantum field theory in a cosmological spacetime: When do number and entropy increase?

This paper reexamines the statistical quantum field theory of a free, minimally coupled, real scalar field Phi in a statically bounded, classical Friedmann cosmology, where the time-dependent scale factor ..cap omega..(t) tends to constant values ..cap omega../sub 1/ and ..cap omega../sub 2/ for tt/sub 2/. The principal objective is to investigate the intuition that ''entropy'' S correlates with average particle number , so that increases in induced by parametric amplification manifest a one-to-one connection with increases in S. The definition of particle number N/sub k/ becomes unambiguous for t>t/sub 2/ and t

Solution of the horizon and flatness problems by multiple inflations.

A simple treatment is developed to describe a universe that has undergone successive generic inflations of the type described by us in a previous work. By comparing general expressions for the horizon and flatness problems it is shown that allowing ''failed'' inflationary bubbles within the visible universe results in values of ..cap omega.. that may depart logarithmically from unity. An exact relationship between a scale and which period of inflation determined its density perturbation amplitude is derived. Restricting attention to the case of double inflation, it is shown that many visible scales today fell within the event horizons of both de Sitter phases. It is assumed that the later inflation will set the density perturbation amplitude of such scales when they reenter the post-inflation horizon. The relative values of the amplitudes are examined and it is shown that the amplitudes created by earlier inflations will tend to be higher than that of later epochs. The relative values of the number of e-folds of the two inflations give rise to four combinations that solve the horizon problem. Treating all values as equally likely, a double-valued spectrum is obtained in only one, and not a preferred one, of those combinations.

Upper critical field and resistivity of single-crystal EuBa2Cu

A wide-temperature-range profile of the H/sub c//sub 2/-T curve for the superconducting 1:2:3 compound is presented. The data were obtained from a EuBa/sub 2/Cu/sub 3/O/sub y/ single crystal under a pulsed magnetic field up to 50 T along the c axis. H/sub c//sub 2/ at 4.2 K is 27.5 +- 2.5 T for the onset of the resistivity. The residual resistivity is roughly estimated to be about 50 ..mu cap omega.. cm. The magnetoresistance is positive and the general features of the superconducting properties except T/sub c/ are well sketched by the Bardeen-Cooper-Schrieffer dirty-limit model. The anisotropies in H/sub c//sub 2/ and the resistivity are also discussed

Discrete Angle Biasing in Monte Carlo Radiation Transport

An angular biasing procedure is presented for use in Monte Carlo radiation transport with discretized scattering angle data. As in more general studies, the method is shown to reduce statistical weight fluctuations when it is combined with the exponential transformation. This discrete data application has a simple analytic form that is problem independent. The results from a sample problem illustrate the variance reduction and efficiency characteristics of the combined biasing procedures, and a large neutron and gamma-ray integral experiment is also calculated. A proposal is given for the possible code generation of the biasing parameter rho and the preferential direction ..cap omega../sub 0/ used in the combined biasing schemes.

Electron cyclotron current drive at the second harmonic in the WT-3 tokamak.

Electron cyclotron current drive (ECCD) at the second harmonic (..omega.. = 2..cap omega../sub e/) is demonstrated for two types of plasma in the WT-3 tokamak. When microwave power P/sub EC/ is injected into a plasma after Ohmic heating (OH) power is shut down, the plasma current is sustained and ramped up by the EC wave only. Here 2..cap omega../sub e/ EC-driven current is generated by 2..cap omega../sub e/ EC heating of an energetic electron tail existing in the OH plasma. Further, when P/sub EC/ is injected into a microwave discharge plasma, 2..cap omega../sub e/ EC-driven plasma current is started up and 2..cap omega../sub 3/ ECCD plasma is formed without OH power. The 2..cap omega../sub e/ ECCD efficiency is the same order as that at ..omega.. = ..cap omega../sub e/, but the 3..cap omega../sub e/ EC-driven current is not generated, in contrast with the theoretical prediction.

Omega ---> Xi - gamma and Omega ---> Xi -l+l- decays and the single-quark-transition model.

It is shown that the QCD-corrected single-quark transition s..-->..d..gamma.. is likely to be the dominant mechanism for ..cap omega../sup -/..--> gamma../sup -/..gamma.. decay. Various phenomenological implications of this dominance in ..cap omega../sup -/..--> gamma../sup -/..gamma.. and ..cap omega../sup -/..--> gamma../sup -/l/sup +/l/sup -/ transitions are presented in detail and compared with predictions of other possible mechanisms. In particular, the single-quark-dominance model gives branching ratios of 1.65 x 10/sup -4/, 1.4 x 10/sup -6/, and 6.6 x 10/sup -8/ for ..cap omega../sup -/..--> gamma../sup -/..gamma.., ..cap omega../sup -/..--> gamma../sup -/e/sup +/e/sup -/, and ..cap omega../sup -/..--> gamma../sup -/..mu../sup +/..mu../sup -/, respectively. The determination of both the radiative and the Dalitz-pair decays has the potential of revealing the full structure of the flavor-changing sd..gamma.. vertex, as well as exploring deviations from the standard model.

Strong monopole electron-collisional excitation in highly stripped ions.

The collision strengths for electric monopole collisional excitation of the outermost subshell of highly stripped closed-shell ions are examined and found to scale nearly hydrogenically. The collision strength near threshold for the principal monopole excitation process (in the distorted-wave approximation) is written as ..cap omega..(Z) = xi/sub n//sub l/(Z)eta/sub nl/(Z)N/sub nl/I/sub H//..delta..E(Z), where xi/sub n//sub l/(Z) is near 0.3, 0.5, and 0.6 for the He-like (1s--2s), Ne-like (2p--3p), and Ni-like (3d--4d) sequences, respectively, and where eta/sub n//sub l/(Z) accounts for mixing effects and is near unity at low Z. The excitation process in nickel-like ions is more effective per electron than for neonlike ions and is favorable to the development of x-ray lasers below 44 A. The extension of the monopole excitation scheme to Nd-like ions appears very attractive for longer wavelengths.

Effects of high-power ion Bernstein waves on a tokamak plasma.

Ion Bernstein wave heating (IBWH) has been investigated on PLT with up to 650 kW of rf power coupled to the plasma, exceeding the ohmic power of 550 kW. Plasma antenna loading of 2 ..cap omega.. has been observed, resulting in 80 to 90% of the rf power being coupled to the plasma. An ion heating efficiency of ..delta..T/sub i/(0)n/sub e//P/sub rf/ = 6 x 10/sup 13/ eV cm/sup -3//kW, without high energy tail ions, has been observed up to the maximum rf power. The deuterium particle confinement during high power IBWH increases significantly (as much as 300%). Associated with it, a longer injected impurity confinement time, reduced drift wave turbulence activity, frequency shifts of drfit wave turbulence, and development of a large negative edge potential were observed. The energy confinement time, however, shows some degradation from the ohmic value, which can be attributed to the enhanced radiation loss observed during IBWH. The ion heating and energy confinement time are relatively independent of plasma current.