Crossover from high-temperature vortex-liquid to low-temperature vortex-glass behavior in single phase HgBa2Ca2Cu3O8+δ superconductor

The ρ-T curves in our single phase HgBa₂Ca₂Cu₃O_8+δ superconductor were measured as a function of temperature and magnetic field, ρ=ρ₀exp(−U_eff/κ_BT). It can be transformed to another form d(lnρ)/d(1/T)=−U_eff+TdU_eff/dT, then this becomes a plot of the activation energy U_eff as a function of temperature. Our data plotted in these ways show a clear crossover from high-temperature two-dimensional vortex-liquid to a critical region associated with the low-temperature three-dimensional vortex-glass phase transition. The critical exponents v(z−1)=3.9±1.9 in this system are little different with previous measurements in BSCCO and YBCO systems.     

Single-electron charging spectra: from natural to artificial atoms

We present a theoretical study of the charging spectra in natural and artificial atoms. We apply a model electrostatic potential created by a homogenously charged sphere. This model potential allows for a continuous passage from the Coulomb potential of the nucleus to parabolic confinement potential of quantum dots. We consider electron systems with N=1,…,10 electrons with the use of the Hartree–Fock method. We discuss the qualitative similarities and differences between the chemical potential spectrum of electron systems bound to nucleus and confined in quantum dots.     

Digital Sums and Divide-and-Conquer Recurrences: Fourier Expansions and Absolute Convergence

We propose means for computing the Fourier expansions of periodic functions appearing in higher moments of the sum-of-digits function and in the solutions of some divide-and-conquer recurrences. The expansions are shown to be absolutely convergent. We also give a new approach to efficiently compute numerically the coefficients involved to high precision.     

On theL p-bounds for maximal functions associated to convex bodies inR n

The dimension-freeL ²-maximal inequality for convex symmetric bodies obtained in [2] is extended forp>3/2.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

The accurate dimensional measurements within small internal structures

This paper shows that the dimension of internal structure of a component can be measured remotely to a resolution better than 5 μm by use of the combination of high resolution optical microscopy and image processing.A specialised high resolution, long working distance and diffraction limited lens was used to image within the component. A series of digital images were made to map spatially the interior of the component. An edge detector was then used to localise the specific location of features in order that an accurate internal measurement could be made. A visualisation of the internal surface finish was also achieved.     

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators