Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Isotone policies for the value iteration method for Markov decision processes

Summary This paper considers the value iteration process for countable state discounted Markov decision processes and shows that under certain conditions there will exist anN-isotone sequence of optimal decision rules and value functions, whereN-isotonicity of a sequence of decision rules { _n }, n {1,2,...}=N requires that, for a specified partial order overK=UK(i) (K(i) being the feasible action space fori) then _n–1(i) _n (i), n2 and alli I, with a similar definition ofN-isotonic for the value functions {v _n },n1.

---

Zusammenfassung Wir betrachten die Wertiteration bei diskontierten Markovschen Entscheidungsprozessen mit abzählbarem Zustandsraum. Wir zeigen, daß unter gewissen Bedingungen eineN-isotone Folge von optimalen Entscheidungsregeln und Wertfunktionen existiert.N-isoton heißt eine Folge von Entscheidungsregeln { _n },n {1,2,...}=N, dann, wenn für eine Halbordnung überK=UK(i) gilt _n–1 (i) _n–1(i) _n (i) für allen2 undi I. (K(i is die Menge der zulässigen Aktionen im Zustandi). Eine analoge Definition derN-Isotonie gilt für die Wertfunktionen {v_n},n1.

     

γ ? α2 Phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%)

The ₂ phase transformation in fractured high temperature stress rupture Ti-48Al-2Nb(at.%) alloy has been studied by analytical electron microscopy. ₂ and phases were found at grain boundaries. ₂ layers that suspended in layers and interfacial ledge higher than 2d ₍₁₁₁₎ at /₂ interfaces were observed in the lamellar grains. These facts indicated that ₂ phase transformation and dynamic recrystallization have occurred during high temperature stress rupture deformation. It can be concluded that deformation induced ₂ phase transformation and dynamic recrystallization resulted in the presence of particles at grain boundaries. A structural and compositional transition area between deformation-induced ₂(or ) and its adjacently original (or ₂) phases was found by HREM and EDS and is suggested as a way to transform between and ₂ phase during high temperature stress rupture deformation. The transition area was formed by slide of partial dislocations on close-packed planes and diffusion of atoms.     

Geometrical factors for parts of an infinite cylindrical surface

A method is described for calculating geometrical factors, allowing for attenuation of radiation by the medium, and computing radiative heat transfer between coaxial strips forming part of a cylinder.Notation mean generalized geometrical factor - local generalized geometrical factor for a closed infinite cylindrical surface - F surface area - l length of ray between elements dF_m - D and H diameter and length of cylinder - k ray attenuation coefficient - equivalent solid angle [1] determined from the condition _mm=1 at =0 for a closed surface - f () indicatrix of the specific radiation intensity (a quantity analogous to the specific luminous intensity [1]) - angle between the normal to an element of surface and the ray linking the surface elements - and angles in a section of the surface - angle between the radius and the chord subtending the projections of dF_mon the section - angle between the radius and the chord subtending the projection of element dF_mon the section and the edge of the surface - acute angle between rayl and the generator of the cylinder - ₀ half subtended angle for the arc of a section of the surface - S₂ and M generalized local geometrical factors in the notation of [2] (s₂ and is shown in Table 2 - M local factor for an infinite cylinder with a semicircular cross section for a point in the middle of the plane part of the surface; a table of values of M is given in [2]) - n number of strips     

Preparation of lanthanide orthophosphates by crystallisation from phosphoric acid solution

Highly crystalline solids of the composition of LnPO₄ · nH₂O (Ln = La, Ce, Pr, Nd. Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu and Y) were prepared by crystallisation from boiling phosphoric acid solution with the initial concentration 2 M/1 of H₃PO₄ and 0.02 M/1 of Ln. The number of molecules of water (n) was close to 1. The crystallisation process was completed within two hours. Scanning electron micrographs showed that the diameter of the LnPO₄ · H₂O crystalline particles was increasing within the group of elements from below 1 m (LaPO₄ · H₂O) to above 5 m (TmPO₄ · H₂O). Such large crystals of lanthanide phosphates cannot be obtained by usually applied precipitation methods. The light lanthanides (La Sm) formed clusters of shapeless particles with the tendency to form rod-like crystals. The heavy lanthanides (Ho Lu, and YPO₄ · H₂O) consisted of spherical globules. The TbPO₄ · H₂O and DyPO₄ · H₂O, formed a mixture of the spherical and rod-like crystals.     

The microstructure of sintered Si-Al-O-N ceramics

Fine-grained ceramics, based on the substituted -Si₃N₄ crystal structure, have been prepared with near theoretical densities by pressureless sintering of compacts containing a large Y₂O₃ additive concentration. The microstructure contains two phases, and an Y/Al rich silicate glassy matrix, in the as-sintered condition. The matrix may be crystallized on heat treatment to a Si-substituted yttrium-aluminium garnet phase. The phase compositions and transformation mechanisms have been analysed by X-ray microanalysis, electron diffraction and imaging of thin sections.A preliminary survey of mechanical properties of these sintered ceramics shows that they are comparable with commercial hot-pressed silicon nitrides, particularly at high temperatures. The possibility of development of a range of ceramic alloys, dependent on their chemical environment and temperature of application, is discussed.     

Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Catalytic decomposition of hydrazine in weakly alkaline solutions on platinum nanoparticles

The kinetics and stoichiometry of catalytic decomposition of hydrazine in 0.01 M NaOH solutions in the presence of unstabilized (gray colloid) and stabilized with sodium polyacrylate (brown colloid) platinum nanoparticles were studied. The main decomposition products are ammonia and N₂ with H₂ impurity (up to 1.5%), i.e., hydrazine decomposition predominantly follows the stoichiometric equation 3N₂H₄ = 4NH₃ + N₂. The catalytic activity was studied as influenced by nanoparticle size distribution. Despite higher nanoparticle dispersion, the catalytic activity of the stabilized brown colloid is lower than that of the gray colloid. The reaction mechanism is discussed.Translated from Radiokhimiya, Vol. 46, No. 6, 2004, pp. 531–535.Original Russian Text Copyright © 2004 by Ananev, Boltoeva, Sukhov, Bykov, Ershov.     

Hall-Effect study of YNi2B2C superconductor

Hall-effect and critical magnetic fields H_c2(T) have been studied for YNi₂B₂C (prepared using high pressure technique) at H130 kOe and 1.6T300K. The normal state Hall coefficient R_H was found to be negative (R_H=–1.43.10^–11 cm/Oe at T=4.2 K and H=130 kOe) and slightly growing in absolute value with increase of temperature. The dependence of the Hall voltage on magnetic field in the mixed superconducting state shows no sign reversal as was observed earlier for some high-T_c systems. The values of ¦H_c2/ T¦and H_c2(0) are found to be 4.8 kOe/K and 47 kOe respectively.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

The thermal conductivity and Lorenz function of the tin-lead alloy system Sn x Pb1 − x (x = 0.85, 0.7 0.5 0.3)

The thermal conductivity and electrical resistivity of the tin-lead alloy system Sn _x Pb_{1 – x} (x = 0.85, 0.7 0.5 0.3) were measured in the temperature range 7–300 K. The thermal conductivity was analyzed at temperature T 20K, assuming 1//T+Tⁿ, where , , and n are constants. The analysis shows that n < 2, and not n 2, which would be expected for a normal pure metal. The electrical resistivities could be represented by a T ⁵ relation for temperatures up to about 60 K. The characteristic temperature _R appears to decrease with increasing weight percent of lead. The total Lorenz functions were high, indicating the presence of phonon conductivity. The phonon conductivity _g appears to vary with T, and can be represented by _g=a/Tⁿ (a > 0) and n2.Work supported by the Universiti Sains Malaysia.     

Superfluid density in the presence of persistent current in superfluid4He

The superfluid density _s in the presence of persistent current(v _n –v _s 0) is investigated using the Doppler-shifted fourth-sound technique. In the vortex-free Landau state, _s remains constant within our experimental resolution of two parts in 10 ⁵ . This is not inconsistent with a theoretical prediction by Khalatnikov. Where vortices are present outside the Landau region, a fractional change in _s becomes as large as 1.2%, depending on rotation velocity and temperature, and shows a relatively complex hysteresis behavior.This research is supported by NSF and ONR.     

On strong Dickson pseudoprimes

It is known that the Lucas sequenceV _n(,c)=aⁿ + bⁿ,a, b being the roots ofx ² – x + c=0 equals the Dickson polynomial .^n–2i Lidl, Müller and Oswald recently defined a number b to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [itg_n(b, c)b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined.     

Reissner-Sagoci problem for a non-homogeneous half-space with surface constraint

This paper deals with the problem of twisting of a non-homogeneous, isotropic, half-space by rotating a circular part of its boundary surface (0ra, z = 0) through a given angle. A ring (a<r<b, z = 0) outside this circle is stress-free and the remaining part (r>b, z = 0) is rigidly clamped. The shear modulus is assumed to vary with the cylindrical coordinates r, z by the power law ( = _, r z ). Such a dependence is of practical interest in the context of Soil Mechanics. The problem leads to a Fredholm integral equation of the second kind which is solved numerically, giving an evaluation of the influence of non-homogeneity on the torque at the surface and the stress intensity factor. The homogeneous case studied in [16] is recovered. Expressions for some quantities of physical importance such as the torque applied at the surface and stress intensity factor are obtained. It appears from our investigation that the influence of clamping dies out with increasing and . Quantitative evaluations are given and some curves for the relative increase, due to clamping, in the torque and in the stress intensity factor are presented.     

Evaporation of liquids from cylindrical vessels under conditions of free concentrational convection in a gas phase

An analytical solution is obtained for the axisymmetric problem of free concentrational convection in a vapor-gas mixture with isothermal evaporation of liquids from open cylindrical vessels. Formulas are derived to calculate concentration fields, local and integral mass fluxes of vapor. A comparative analysis of the results of analytical and numerical simulation is carried out for the processes of the evaporation of liquids under the conditions of convective mass transfer.Notation p pressure, Pa - density, kg/m³ - v velocity, m/sec - , dynamic and kinematic viscosity, Pa·sec, m²/sec - D diffusion coefficient, m²/sec - ₁, ₂ mass fractions of vapor and gas in a mixture - g free fall acceleration, m/sec² - M ₁,M ₂ molar masses of vapor and gas, kg/kmole - _r , _z radial and axial components of the velocity of a gas-vapor mixture, m/sec - r, z cylindrical coordinates, m - R, H radius and height of vessel, m - j local mass flux of vapor, kg/(m²·sec) - j vessel cross-sectional area-averaged mass flux of vapor, kg/(m²·sec) - j vessel cross-sectional area-averaged mass flux Chelyabinsk State Technical University, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 403–407, May–June, 1995.     

Elastic energy of the vortex state in type II superconductors. I. High inductions

The elastic properties of the flux line lattice (FLL) in type II superconductors are calculated from the linearized Ginzburg-Landau (GL) theory for large inductionsBH _c2 . They appear to be strongly nonlocal, i.e., the elastic modulic ₁₁ andc ₄₄ for homogeneous deformations do not apply if the strain field varies over distances /(1–B/H _c2 )^1/2 d ( is the penetration depth,d is the FL distance). For smaller strain wavelength,c ₁₁ andc ₄₄ are smaller by factors (1–B/H _c2 )²/2 ² and (1–B/H _c2 )/ 2 ² , respectively. The order parameter and local field of a deformed FLL exhibit the expected spatial frequency modulation, but also a pronounced amplitude modulation whose degree of modulation increases with the strain wavelength. The results of further calculations avoiding the linearization of the GL theory are given.     

Non fermi liquid ground states in strongly correlated f-electron materials

Experimental efforts to characterize and develop an understanding of non Fermi liquid (NFL) behavior at low temperature in f-electron materials are reviewed for three f-electron systems: M_1–xU_xPd₃ (M = Sc, Y), U_1–xTh_xPd₂Al₃, and UCu_5–xPd_x. The emerging systematics of NFL behavior in f-electron systems, based on the present sample of nearly ten f-electron systems, is updated. Many of the f-electron systems exhibit the following temperature dependences of the electrical resistivity p, specific heat C, and magnetic susceptibility for T T₀, where T_o is a characteristic temperature: P(T) 1 –aT/T ₀, where a < 0 or > 0, C(T)/T (-1/T _o) In (T/bT ₀), and (T) 1 –c(T/T_o)^1/2. In several of the f-electron systems, the characteristic temperature T_o can be identified with the Kondo temperature T_k.     

Conditions for existence of exact solutions of the problem of a fusing wedge

A well-defined condition, determining the values of the aperture angles of a fusing wedge, is presented for exact solutions of the single-phase problem of a fusing wedge that were obtained earlier and are written for these values. The critical orientation of the fusing wedge to the axis of fusion when the written solution degenerates is indicated.Notation , , _n , _n , _n A ₁,A ₂,B auxiliary variables - P _n ,Q _n ,S _n ,T _n polynomials - k, m, n, i natural numbers - , _k angles between the normals to the surfaces forming the fusing wedge - z the axis in a Cartesian coordinate system - U temperature at points of the body infinitely remote from the fusing boundary Voronezh Institute of Technology, Voronezh, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 750–753, June, 1994.     

A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for 4n ² where n is integer. This implies that the instability area which is emanating from =4n ² in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands