Effect of vacuum magnetic field on the gravitodynamic stability of liquid jet

Summary  The MHD stability of a liquid jet (radiusR ₀ and density ϱ) under the influence of self-gravitating force has traditionally been studied using a normal-mode type of analysis. The dispersion relation is obtained and studied analytically and numerically. The axial magnetic fields inside and outside the jet have always stabilizing effects. The transverse magnetic field has a destabilizing effect. It is found that the largest doman of instability is fastly shrinking (as α> ?) with increasingH ₀ /H _G values,H _G 4(4πGϱ² R ² ₀ μ)^1/2, whereG is the gravitational constant. Some reported works are recovered as limiting cases from the present work.     

Radiative corrections to the Coulomb energy levels and emission of a hydrogen-like atom in a superstrong magnetic field

The probability and intensity of hydrogen-like atom emission in strong magnetic field В >> Z ^2α2 B ₀, α = e ²/cħ = 1/137, and B ₀ = m ² c ³ /eħ = 4.41⋅10¹³ G is calculated. The role of electron-positron vacuum polarization is discussed.     

Absorption spectra and magneto-optic figures of merit in the Bi x Sm3-x Fe5-y Ga y O12 system

The absorption (α) and Faraday rotation (θ) spectra of 14 garnets belonging to the series Bi _x Sm_3-x Fe_5-y Ga _y O₁₂ (0<x<1.05, 0.8<y<1.15) have been measured between 15 000 cm⁻¹ and 19 000 cm⁻¹. The figure of merit (θ/α) at 17 850 cm⁻¹ (560 nm) increases linearly with increasing bismuth concentration up tox∼0.6 where it begins to increase less rapidly. For operation of magneto-optic display devices at 17 850 cm⁻¹ there is no advantage in using garnets in this series withx>0.8. The Faraday rotation at 17 850 cm⁻¹ increases linearly with bismuth concentration whereas the absorption coefficient increases more rapidly. The presence of Bi³⁺ increases the intensity of all Fe³⁺ pair transitions in the garnet system as a result of the increased superexchange induced by Bi³⁺. This is in keeping with the observation that the intensity of the⁶A_1g (S)→⁴T_1g (G) transition in (RE)₃Fe₅O₁₂ (RE=Er, Y, Dy, Gd, Eu) increases on traversing the above RE series as do the Curie temperatures of these iron garnets.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

The Primakoff reaction study for pion polarizability measurement at COMPASS

The electromagnetic structure of charged pions can be described by the electric (α_π) and magnetic (β_π) polarizabilities that depend on the rigidity of pion’s internal structure as a composite particle. It is shown that the values of α_π and β_π can be precisely measured via the Primakoff reaction π⁻ + (A, Z) → π⁻ + (A, Z) + γ in the COMPASS experiment at CERN.     

C*-Algebras associated with one dimensional almost periodic tilings

For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX _α with an equivalence relationR _α. OnR _α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C^*-algebra of this groupoid and show that it is the irrational rotation C^*-algebra,A _α. Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.     

Superdiffusion and stable laws

The superdiffusion equation with a fractional Laplacian Δ ^α/2 in _N-dimensional space describes the asymptotic (t→∞) behavior of a generalized Poisson process with the range (discontinuity) distribution density ∼|x|−α−1. The solutions of this equation belong to a class of spherically symmetric stable distributions. The main properties of these solutions are given together with their representations in the form of integrals and series and the results of numerical calculations. It is shown that allowance for the finite velocity of free particle motion for α>1 merely amounts to a reduction in the diffusion coefficient with the form of the distribution remaining stable. For α<1 the situation changes radically: the expansion velocity of the diffusion packet exceeds the velocity of free particle motion and the superdiffusion equation becomes physically meaningless. Zh. éksp. Teor. Fiz. 115, 1411–1425 (April 1999)     

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.      

Complexation of Dimethyl 2,3-Naphthalenedicarboxylate with 2-hydroxypropyl-α-, -β- and -γ-cyclodextrins in Aqueous Solution by Fluorescence,Circular Dichroism and Molecular Mechanics

Fluorescence, circular dichroism and molecular mechanics have been used to study the complexation of 2,3-dimethyl naphthalenedicarboxylate with 2-hydroxypropyl-α-, -β and -γ-cyclodextrins (HPCDs) in aqueous solution. Emission spectra upon excitation of the naphthalenedicarboxylate group show two bands whose intensity ratio R is quite sensitive to polarity. From the change of R and lifetimes averages <τ> with HPCD concentration and temperature were obtained the stoichiometry, the association constants and the enthalpy and entropy changes during the complexation. R, <τ> and the fluorescence anisotropies (r) extrapolated at [HPCD]→∞ allows us to estimate the polarity and microviscosity of the media surrounding the guest when complexed. In addition, the analysis of quenching and induced circular dichroism experiments and molecular mechanics calculations in the presence of water, provide information about the forces responsible for the complexation and the geometry of the complexes.     

Interaction of Anderson impurities with high orbital angular momenta: Non-RKKY behavior and instability of Kondo lattice

The hybridization-induced interaction of Anderson impurities with orbital angular momentum l is revisited. At short distances R<R _c ∝(l+1)/k _F the interaction has antiferromagnetic sign and decays as (R _c /R)^4l . At larger distances R>R _c the RKKY-like oscillatory interaction sets in. As l increases, the system will sooner or later enter the “short-distance” domain, where the intersite magnetic interaction dominates over the screening processes. This means that, contrary to previous expectations, the nonmagnetic state of the Anderson lattice is unstable at l→∞. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 76–81 (10 January 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Kinetic phenomena in zero-gap semiconductors CuFeS<Subscript>2</Subscript> and CuFeTe<Subscript>2</Subscript>: Effect of pressure and heat treatment

Electrical resistivity ρ and Hal coefficient R are measured as a function of the temperature (T = 1.7−310 K) and the magnetic field (up to H = 28 kOe) in zero-gap semiconductor CuFeS₂ samples subjected to hydrostatic compression and under various heat-treatment conditions. At low temperatures, anomalies are observed in the kinetic effects related to the presence of ferromagnetic clusters: the magnetoresistance at T = 4.2 K and T = 20.4 K acquires a hysteretic character and thermopower α changes its sign at T < 15 K. The temperature dependence of conduction-electron concentration n in CuFeS₂ has a power form in the temperature range T = 14−300 K, which is characteristic of the intrinsic conductivity in zero-gap semiconductors. In CuFeS₂, we have n(T) ∝ T ^1.2; in isoelectron compound Cu_1.13Fe_1.22Te₂, we have n(T) ∝ T ^1.93. Heat treatment is found to affect the intrinsic conductivity of CuFeS₂, as the action of hydrostatic compression (carrier concentration changes); that is, the carrier concentration changes. However, a power form of the n(T) and ρ(T) dependences is retained.     

Connectivity of growing networks with link constraints

We propose a growing network model with link constraint, in which new nodes are continuously introduced into the system and immediately connected to preexisting nodes, and any arbitrary node cannot receive new links when it reaches a maximum number of links k_m. The connectivity of the network model is then investigated by means of the rate equation approach. For the connection kernel A(k)=k^γ, the degree distribution n_k takes a power law if γ≥1 and decays stretched exponentially if 0≤γ< 1. We also consider a network system with the connection kernel A(k)=k^α(k_m-k)^β. It is found that n_k approaches a power law in the α> 1 case and has a stretched exponential decay in the 0≤α< 1 case, while it can take a power law with exponential truncation in the special α=β=1 case. Moreover, n_k may have a U-type structure if α> β.     

On Minimal Eigenvalues¶of Schrödinger Operators on Manifolds

We consider the problem of minimizing the eigenvalues of the Schr?dinger operator H=−Δ+αF(κ) (α>0) on a compact n-manifold subject to the restriction that κ has a given fixed average κ₀. In the one-dimensional case our results imply in particular that for F(κ)=κ² the constant potential fails to minimize the principal eigenvalue for α>α_c=μ₁/(4κ₀ ²), where μ₁ is the first nonzero eigenvalue of −Δ. This complements a result by Exner, Harrell and Loss, showing that the critical value where the constant potential stops being a minimizer for a class of Schr?dinger operators penalized by curvature is given by α _c . Furthermore, we show that the value of μ₁/4 remains the infimum for all α >α _c . Using these results, we obtain a sharp lower bound for the principal eigenvalue for a general potential. In higher dimensions we prove a (weak) local version of these results for a general class of potentials F(κ), and then show that globally the infimum for the first and also for higher eigenvalues is actually given by the corresponding eigenvalues of the Laplace–Beltrami operator and is never attained. Received: 17 July 2000 / Accepted: 11 October 2000     

A Replica-Coupling Approach to Disordered Pinning Models

We consider a renewal process τ = {τ ₀, τ ₁,...} on the integers, where the law of τ _i − τ _i-1 has a power-like tail P(τ _i − τ _i-1 = n) = n ^−(α+1) L(n) with α ≥ 0 and L(·) slowly varying. We then assign a random, n-dependent reward/penalty to the occurrence of the event that the site n belongs to τ. In such generality this class of problems includes, among others, (1 + d)-dimensional models of pinning of directed polymers on a one-dimensional random defect, (1 + 1)-dimensional models of wetting of disordered substrates, and the Poland-Scheraga model of DNA denaturation. By varying the average of the reward, the system undergoes a transition from a localized phase, where τ occupies a finite fraction of to a delocalized phase, where the density of τ vanishes. In absence of disorder (i.e., if the reward is independent of n), the transition is of first order for α > 1 and of higher order for α < 1. Moreover, for α ranging from 1 to 0, the transition ranges from first to infinite order. Presence of even an arbitrarily small (but extensive) amount of disorder is known to modify the order of transition as soon as α > 1/2 [11]. In physical terms, disorder is relevant in this situation, in agreement with the heuristic Harris criterion. On the other hand, for 0 < α < 1/2 it has been proven recently by K. Alexander [2] that, if disorder is sufficiently weak, critical exponents are not modified by randomness: disorder is irrelevant. In this work, generalizing techniques which in the framework of spin glasses are known as replica coupling and interpolation, we give a new, simpler proof of the main results of [2]. Moreover, we (partially) justify a small-disorder expansion worked out in [9] for α < 1/2, showing that it provides a free energy upper bound which improves the annealed one.     

Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R_G and bond length a , and an impenetrable spherical colloid particle of radius R . Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R _G and R/a . The correction vanishes for the continuous chain model (i.e. in the limit R/R _G → 0 and R/a → ∞ but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).     

Neutrino radiation by an electon in quantizing nuclear and strong magnetic fields

The probability and intensity of neutrino radiation of a hydrogen-like atom in the strong magnetic field B >> Z ²α² B ₀, α = e ² = 1/137, B ₀ = m ²/e = 4.41⋅10¹³ G are determined. The temperature dependence of the intensity of an atom ensemble is analyzed.     

Self-consistent equilibria in a cylindrical reversed-field pinch

Summary A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions:a) to the lowest order, the turbulent dynamo electric fieldE ^t is expressed as a homogeneous function of degree 1 of the magnetic fieldB, sayE ^t =α·B, with α being a 2nd-rank tensor, homogeneous of degree 0 inB, and generally depending on the plasma state;b)E ^t does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ₀/η for vanishing axial electric fieldE _z . This case has also been solved analytically, for whateverE _z , under circular, besides cylindrical, symmetry.     

Superconducting triplet spin valve

We study the critical temperature T _c of SFF trilayers (S is a singlet superconductor, F is a ferromagnetic metal), where the long-range triplet superconducting component is generated at noncollinear magnetizations of the F layers. We demonstrate that T _c can be a nonmonotonic function of the angle α between the magnetizations of the two F layers. The minimum is achieved at an intermediate α, lying between the parallel (P, α = 0) and antiparallel (AP, α = π) cases. This implies a possibility of a “triplet” spin-valve effect: at temperatures above the minimum T _c ^Tr but below T _c ^P and T _c ^AP, the system is superconducting only in the vicinity of the collinear orientations. At certain parameters, we predict a reentrant T _c (α) behavior. At the same time, considering only the P and AP orientations, we find that both the “standard” (T _c ^P < T _c ^AP) and “inverse” (T _c ^P > T _c ^AP) switching effects are possible depending on parameters of the system.