F2-laser patterning of GaPO4 resonators for humidity sensing

Piezoelectric gallium orthophosphate (GaPO₄) thickness – shear mode resonators were patterned by F₂-laser ablation and employed for gas sensing. The thickness of GaPO₄ crystals was reduced from 215 m to 115 m by laser ablation and the piezoelectric fundamental resonance frequency in the thinned region increased thereby from 6 MHz to 12 MHz. The Q values of laser-thinned and pristine resonators in air were Q7000 and Q95000, respectively. The GaPO₄ crystals were coated by thin polyimide layers that served as receptor for water vapour. The resonance frequency of coated crystals decreased linearly with increasing level of relative humidity (RH) and the sensitivity for laser-patterned 12 MHz GaPO₄ resonators, S_RH-98 Hz/%RH, was much larger than for the pristine 6 MHz GaPO₄ resonators. PACS 61.10.-i; 68.37.-d; 81.15.Fg     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Energy relaxation in disordered charge and spin density waves

We investigate collective effects in the strong pinning model of disordered charge and spin density waves (CDWs and SDWs) in connection with heat relaxation experiments. We discuss the classical and quantum limits that contribute to two distinct contribution to the specific heat (a Cv T-2 contribution and a Cv T contribution respectively), with two different types of disorder (strong pinning versus substitutional impurities). From the calculation of the two level system energy splitting distribution in the classical limit we find no slow relaxation in the commensurate case and a broad spectrum of relaxation times in the incommensurate case. In the commensurate case quantum effects restore a non vanishing energy relaxation, and generate stronger disorder effects in incommensurate systems. For substitutional disorder we obtain Friedel oscillations of bound states close to the Fermi energy. With negligible interchain couplings this explains the power-law specific heat Cv T observed in experiments on CDWs and SDWs combined to the power-law susceptibility (T)T-1+ observed in the CDW o-TaS3.     

Onset of superconductivity at 107K in YBa2Cu3O7 − δ at high pressure

Electrical resistivity measurements under pressure have been carried out on the high-temperature superconductor YBa₂Cu₃O_{7 –} as a function of temperature T between 1 and 300 K at various pressures between 8 kbar and 149 kbar. The superconducting transition temperature T_c increases almost linearly with pressure at the rate dT_c/dP - 0.13 K/kbar. The onset of T_c, defined as the temperature at which(T) drops to 90% of its extrapolated normal state value, increases from 95 K at 8 kbar to 107 K at 149 kbar. These results suggest that higher pressures will yield yet higher values of T_c.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Primes in Short Intervals

Contrary to what would be predicted on the basis of Cramérs model concerning the distribution of prime numbers, we develop evidence that the distribution of (x+H)–(x), for 0xN, is approximately normal with mean H and variance HlogN/H, when NHN^1–.Dedicated to Freeman Dyson, with best wishes on the occasion of his eightieth birthdayResearch supported by NSF grants DMS–0070720 and DMS–0244660.Research supported by the American Institute of Mathematics and NSF grants.     

Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).     

Nonlocal Monte Carlo algorithm for self-avoiding walks with fixed endpoints

We study a new Monte Carlo algorithm for generating self-avoiding walks with variable length (controlled by a fugacity) and fixed endpoints. The algorithm is a hybrid of local (BFACF) and nonlocal (cut-and-paste) moves. We find that the critical slowing-down, measured in units of computer time, is reduced compared to the pure BFACF algorithm: _CPU N^2.3 versus N^3.0. We also prove some rigorous bounds on the autocorrelation time for these and related Monte Carlo algorithms.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

A characterization of Robertson-Walker spaces by null sectional curvature

ForN a null vector andA a vector perpendicular toN, define the null sectional curvature, with respect to TV, of the planeN A ask _N(N A) = R(N,A)A,N<A,A.Then Robertson-Walker metrics can be locally characterized as those for whichk _n at each point is a constant for all the null plans at that point (in each null direction,N must be appropriately chosen). A global characterization of Robertson-Walker spaces is achieved by adding completeness and causality hypotheses.     

Polarization Characteristics of He–Ne Laser Radiation Reflected by Glass‐Reinforced Plastic

We have measured the Stokes parameters of the He–Ne laser radiation ( = 0.63 m) reflected at angles of incidence from 5 to 70° by glassreinforced plastic based on a siliconorganic polymer binder before and after its heating to 1200 K by CO₂ laser radiation. The probe radiation from the He–Ne laser is linearly polarized parallel or perpendicular to the incidence plane. It is shown that the flux reflected in the mirror direction by samples illuminated at a Brewster angle ( 56°) by He–Ne laser radiation linearly polarized in the plane of incidence contains a component with elliptical polarization.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

A Low-Noise 230 GHz SIS Receiver for Radio Astronomy Employing Untuned Nb/AlOx/Nb Tunnel Junctions

A heterodyne receiver based on a 1/3 reduced height rectangular waveguide SIS mixer with two mechanical tuners has been built for astronomical observations of molecular transitions in the 230 GHz frequency band. The mixer used an untuned array (R_nC_j3, R_n70 ) of four Nb/AIOx/Nb tunnel junctions in series as a nonlinear mixing element. A reasonable balance between the input and output coupling efficiencies has been obtained by choosing the junction number N=4. The receiver exhibits DSB (Double Side Band) noise temperature around 50 K over a frequency range of more than 10 GHz centered at 230 GHz. The lowest system noise temperature of 38 K has been recorded at 232.5 GHz. Mainly by adjusting the subwaveguide backshort, the SSB (Single Side Band) operation with image rejection of 15 dB is obtained with the noise temperature as low as 50 K. In addition, the noise contribution from each receiver component has been studied further. The minimum SIS mixer noise temperature is estimated as 15 K, pretty close to the quantum limit v/k11 K at 230 GHz. It is believed that the receiver noise temperatures presented are the lowest yet reported for a 230 GHz receiver using untuned junctions.     

Spin fluctuations in both the ordered and paramagnetic phases of MnSi! MnSi a heavy Fermi liquid?

Polarised neutrons and polarisation analysis have been used to determine the diffuse magnetic scattering from MnSi as a function of temperature. Measurements at 50 K (1.72T _c) and 100 K (3.45T _c) in the paramagnetic phase confirmed the presence of strong spatial correlations previously reported at 300 K (10T _c) and 580 K (20T _c). The spatial correlations between regions of spin density separated by 12 Å are of a ferromagnetic nature and determine the static susceptibility. Integration of the paramagnetic response over an inverse atomic volume yields a moment per manganese atom of 1.2 _B , a value considerably larger than the 0.4 _B observed in Bragg scattering and magnetisation measurements at 4.2 K. Measurements made at 11 K in the ordered magnetic phase reveal strong diffuse scattering corresponding to 0.8 _B per Mn atom. The increase in the diffuse scattering observed in the paramagnetic phase corresponds to the passage of the Bragg component into the background.The presence of significant scattering in the ordered phase and the very unusual wave vector dependence of the diffuse scattering observed at 11 K has been interpreted assuming MnSi to be a heavy Fermi liquid. Furthermore we believe these measurements give the first direct observation of the exchange hole.     

Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential

We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essential-spectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V L ^m/2( ^m ) for m 3) and arbitrary A, or slowly decaying V (i.e. V(x |x|^– , (0,2), as |x| ) and magnetic potentials A corresponding to constant magnetic fields B = curl A.Partially supported by the Ministry of Culture, Science and Education under Grant No. 52.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

Self-consistent large-signal calculation on the gyrotron-TWA

By means of a ballistic method a self-consistent large-signal calculation on the gyrotron traveling wave amplifier (gyrotron-TWA) with uniform waveguide and magnetic field has been accomplished. The theory is valid for arbitrary harmonics of the cyclotron frequency and arbitrary TEmn modes.Computer simulation shows that under defined conditions a beam efficiency 50 %, an output power 300 kW and a gain28 dB at a central frequency of 35 GHz with a 3 dB bandwidth of 2,7 % could be obtained. This method will be effective for the theoretical analysis and the parameter-optimization on the gyrotron-TWA.     

Experimental investigation of the 2.1-μm single-mode Tm-Ho:KYF laser

We report on the development and comprehensive characterization of a room-temperature single-mode 2-m Tm-Ho:KYF laser. A maximum CW output power of 70 mW at the central wavelength of 2.078 m has been obtained. Using a 5-mm long intracavity birefringent filter the single-mode emission wavelength can be tuned over a range of 40 nm. Both frequency and relative intensity noise have been investigated showing a 1-ms emission linewidth of 600 kHz and an intensity noise spectrum that is quantum-noise limited for Fourier frequencies higher than 1 MHz. PACS 42.55Xi; 42.55Rz; 42.60Pk; 42.70Hj; 42.60Lh     

On the variation of hopping transport in amorphous silicon with preparation conditions

Thedc conductivity of amorphous silicon prepared by two successive ion bombardments at different temperatures has been measured as a function of temperature. The results may be expressed in terms of a generalized hopping formula =₀ exp [–(T ₀/T) ⁿ where the parameter set {n,T ₀, ₀} varies with the irradiation conditions. In particular, the hopping exponent has been found to assume the limiting values ofn1/4 at irradiation temperatures ofT _i100 K and ofn1/2 atT _i500 K, whereas intermediate values ofn have been observed for temperatures inbetween. It is concluded that thermally activated redistribution processes of radiation defects control the final state of disorder in the irradiated samples, which in turn determines the particular hopping characteristics. Within the framework of existing theories the two limiting cases can be explained to be due to a disordered solid of homogeneous and granular structure, respectively.