Peculiarities of the formation of high-defect states in mechanocomposites and powders of niobium and aluminum under severe deformation in planetary ball mills

The microstructural peculiarities of Nb powder and Nb + Al powder mixtures after mechanical activation in a high-energy planetary ball mill were investigated by transmission electron microscopy. The materials revealed two-level structural states: nanograins of size from 50 to 100 nm that contain subgrains of size ～20 nm and less with low-angle misorientation boundaries, elastic lattice curvature gC _ij ≈100°…200°μm^?1, curl or curvature gradient ?χ _ij /? _r > 100 μm^?2 and high (up to 10E μm^?1) local stress gradients (couples). An important factor in the formation of the above states is the capability of nano-objects to reach high elastic lattice curvature, high gradients of this curvature, and high local internal stress gradients at rather low absolute values of the internal stress.     

The formation of the superheavy hydrogen isotope <Superscript>6</Superscript>H in the absorption of stopped π<Superscript>−</Superscript>-mesons by nuclei

An experimental search for the superheavy hydrogen isotope ⁶H was conducted through studying the absorption of stopped π^?-mesons by ⁹Be and ¹¹B nuclei. A structure in the missing mass spectrum caused by the resonance states of ⁶H was observed in three reaction channels, namely, ⁹Be(π^?, pd)X, ¹¹B(π^?, d³He)X, and ¹¹B(π^?, p⁴He)X. The parameters of the lowest state E_r=6.6±0.7 MeV and Γ=5.5±2.0 MeV (E_r is the resonance energy with respect to the disintegration into the triton and three neutrons) are evidence that ⁶H is a more weakly bound system than ⁴H and ⁵H. Three excited states of ⁶H were observed. Their resonance levels (E_1r=10.7±0.7 MeV, Γ_1r=4±2 MeV, E_2r=15.3±0.7 MeV, Γ _2r=3±2 MeV, and E_3r=21.3±0.4 MeV, Γ_3r=3.5±1.0 MeV) are energetically capable of disintegrating into six free nucleons.     

Censored Glauber Dynamics for the Mean Field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss Model. It is well known that at high temperature (β<1) the mixing time is Θ(nlog?n), whereas at low temperature (β>1) it is exp?(Θ(n)). Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed β>1, the mixing-time of this model is Θ(nlog?n), analogous to the high-temperature regime of the original dynamics. Furthermore, they showed cutoff for the original dynamics for fixed β<1. The question whether the censored dynamics also exhibits cutoff remained unsettled.In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Curie-Weiss model. Namely, we found a scaling window of order \(1/\sqrt{n}\) around the critical temperature β _c =1, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging.In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if β=1+δ for some δ>0 with δ ² n→∞, then the mixing-time has order (n/δ)log?(δ ² n). The cutoff constant is (1/2+[2(ζ² β/δ?1)]^?1), where ζ is the unique positive root of g(x)=tanh?(β x)?x, and the cutoff window has order n/δ.     

Regularisierende Deltafunktionen

In the Laurent Schwartz theory of distributions the integral∫ δ(r)f(r)dτ _r is only defined for a certain class of test functions. Unfortunately, in physics, we obtain test functionsf(r) likee ^ikr /r, e ^?kr /r, ?(e ^ikr /r) and so on, which are not belonging to the Laurent Schwartz class (§1). Here, we want to extend the class of test functions so that it includes physically meaningful functions with poles of finte order inr=0. For this purpose we replaceLaurent Schwartz's axiomatic method defining theδ-distribution by a constructive one consideringδ(r) as a given set of sequences of functions (§2). First we prove that the redefinedδ-function satisfy the equations, axiomatically assumed byLaurent Schwartz (§3). Then we obtain well defined and finite results even in the case of test functions with poles atr=0 (§4). The Fourier components of the newδ-function are given (§5). Finally we show why theδ-function is Lorentz invariant (§6).     

Generalized Hölder Continuity and Oscillation Functions

We study a notion of generalized Hölder continuity for functions on ?^d. We show that for any bounded function f of bounded support and any r >?0, the r-oscillation of f defined as \(osc_{r} f (x):= \sup _{B_{r}(x)} f - \inf _{B_{r}(x)} f\) is automatically generalized Hölder continuous, and we give an estimate for the appropriate (semi)norm. This is motivated by applications in the theory of dynamical systems.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Slow dynamics in glycerol: collective de gennes narrowing and independent angstrom motion

The slow dynamics of microscopic density correlations in supercooled glycerol was studied by time-domain interferometry using ⁵⁷Fe-nuclear resonant scattering gamma rays of synchrotron radiation. The dependence of the relaxation time at 250 K on the momentum transfer q is maximum near the first peak of the static structure factor S(q) at q ～ 15 nm ^?1. The q-dependent behavior of the relaxation time known as de Gennes narrowing was confirmed in glycerol. Conversely, de Gennes narrowing around the second and third peaks of S(q) at q ～ 26 nm ^?1 and 54 nm ^?1 was not detected. The q dependence of the relaxation time was found to follow a power-law equation with power-law index of 1.9(2) in the q region well above the first peak of S(q) up to ～ 60 nm ^?1, which corresponds to angstrom scale, within experimental error. This suggests that in the angstrom-scale dynamics of supercooled glycerol, independent motions dominate over collective motion.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

An Analysis of Charged Anisotropic Star with de Sitter Spacetime

We propose a model for charged anisotropic star in de Sitter spacetime. We have taken Krori and Barua (J. Phys. A, Math. Gen. 8, 508, 1975) metric in de Sitter spacetime with non-zero cosmological constant. The model is free from singularity. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic charged star. To solve the Einstein-Maxwell field equations we assume the relation between the radial and transverse pressure as p _t ?p _r =g q(r)² r ² (where g is a non-zero positive constant). The physical conditions inside the stellar model are also discussed.     

Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².     

Full-Optical Two-Channel Adaptive System for Detecting Microcantilever Vibrations

We demonstrate a full-optical two-channel system for measuring mechanical vibrations of microoscillators, which is based on adaptive holographic interferometer using multiwave mixing in a photorefractive crystal. The orthogonal geometry of dynamic hologram recording makes possible independent operation of the measurement channels. The absolute detection limit of the system to cantilever vibrations in a channel amounted to 2.6·10 ^?6 nm·W^1/2 ·Hz ^?1/2. We tested the system in simultaneous detection of vibrations of two cantilevers with dimensions 215×40×15 μm.     

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent propertiesin two-electron atoms/ions which include the negatively charged Ps^? (e^?e⁺e^?)and H^? ions, Heatom and positively charged, helium-like ions from Li⁺ to Ni²⁶⁺. All these ions areconsidered in their ground 1¹S-state(s). The slowly convergent properties selected inthis study include the electron-nulceus (r^2k_eN) and electron-electron (r^2k_ee) expectation values for k = 2, 3, 4 and 5.     

Self-gravitating Brownian particles in two dimensions: the case of N = 2 particles

We study the motion of N = 2 overdamped Brownianparticles in gravitational interaction in a space of dimensiond = 2. This is equivalent to the simplified motion of twobiological entities interacting via chemotaxis when time delay anddegradation of the chemical are ignored. This problem also bearssimilarities with the stochastic motion of two point vorticesin viscous hydrodynamics [O. Agullo, A. Verga, Phys. Rev. E 63,056304 (2001)]. We analytically obtain the probability density offinding the particles at a distance r from each other at timet. We also determine the probability that the particles havecoalesced and formed a Dirac peak at time t(i.e. the probability that the reduced particle has reached r = 0at time t). Finally, we investigate the meansquare separation \(\langle\) r ² \(\rangle\) and discuss the proper formof the virial theorem for this system. The reduced particle has anormal diffusion behavior for small times with a gravity-modifieddiffusion coefficient \(\langle\) r ² \(\rangle\) = r ₀ ² + (4k _B /ξ μ)(T–\(T_{*}\))t, wherek _B \(T_{*}\) = Gm ₁ m ₂/2 is a critical temperature, and an anomalousdiffusion for large times \(\langle\) r ² \(\rangle\) \(\propto\) \(t^{1-T_*/T}\). As a by-product, our solution also describes thegrowth of the Dirac peak (condensate) that forms at large time inthe post collapse regime of the Smoluchowski-Poisson system (orKeller-Segel model in biology) for T < T _c = GMm/(4k _B ). We find thatthe saturation of the mass of the condensate to the total mass isalgebraic in an infinite domain and exponential in a boundeddomain. Finally, we provide the general form of the virial theoremfor Brownian particles with power law interactions.     

Zur Chronologie des alten Ägypten

The velocityv of the propagation of discharge along the anode of a self-quenchingG—M-counter is a function of total pressureP, pressure of the quenching gasP _D, radius of the cathoder _a and of the anoder _i andV _ü the difference between working- and starting-potential. For the mixtures argon-methylal, argon-alcohol and helium-alcohol isv=v ₀·exp[k·(V _ü/V _e)^1/2] withv ₀ the velocity at the starting potentialV _e v ₀=(a+b·P _D/P)·V _n ^1/2 ·exp [(c?d·P_D/P·V _n ^?1/2 ] andV _n=V _e·(lnr _a/r _i)^?1.k, a, b, c andd are characteristical constants of the filling gas.     

Finite-size scaling of correlation functions in finite systems

We propose the finite-size scaling of correlation functions in finite systems near their critical points.At a distance r in a ddimensional finite system of size L,the correlation function can be written as the product of|r|~(-(d-2+η))and a finite-size scaling function of the variables r/L and tL~(1/ν),where t=(T-T_c)/T_c,ηis the critical exponent of correlation function,andνis the critical exponent of correlation length.The correlation function only has a sigificant directional dependence when|r|is compariable to L.We then confirm this finite-size scaling by calculating the correlation functions of the two-dimensional Ising model and the bond percolation in two-dimensional lattices using Monte Carlo simulations.We can use the finite-size scaling of the correlation function to determine the critical point and the critical exponentη.     

Nonadiabatic theory of diamagnetic susceptibility of molecules

A nonadiabatic theory of diamagnetic susceptibility of molecules is presented in which the electrons and nuclei are considered to be a united system of charged particles whose motion is simultaneously per-turbed by a magnetic field. It is found that on separating out the translational motion of the molecule as a whole, there is certain freedom in choosing the phase of the wave function. Its optimum choice corresponds to the gauge of the vector potential with which two contributions opposite in sign to the magnetic susceptibility—the first order diamagnetism and the second order paramagnetism—have minimum magnitudes. Expressions for non-adiabatic calculations of the diamagnetic susceptibility of atoms and molecules are derived. The diamagnetic contributions to the energy of the hydrogen, helium, and lithium atoms, the hydrogen molecule, the π^?μ^?π⁺μ⁺ and p ^? K ^? p ⁺ K ⁺ mesomolecules, and the positronium molecule e ^? e ^? e ⁺ e ⁺ are calculated. The nonadiabatic contribution of the nuclear motion to the diamagnetic susceptibility amounts to 0.01–0.1% for ordinary atoms and molecules, is increased by several hundred times on passing to mesomolecules, and reaches 50% for the positronium molecule.     

Isomerieverschiebung im Eu151

The isomer shift of the 21.7 keVγ transition in Eu¹⁵¹ has been studied for various divalent and trivalent europium compounds using the Mössbauer technique. Theγ energy is lower by up to 1.1·10^?6 eV in divalent compounds than in trivalent compounds. Using data from atomic spectroscopy it is estimated that the electron density at the nucleus is larger by about 1.9·10²⁶cm^?3 for the configuration 4f ⁶ than for 4f ⁷ due to different shielding of thes ² shells. The difference of the mean square radii of the 21.7 keV state and the ground state is thenδ〈r²〉=+0.03 fm². The measured isomer shift between trivalent and metallic europium and the relatives-electron densities in the rare earth metals measured by the positron annihilation rates are used to establish a calibration scheme for isomer shifts in rare earth metals. This calibration scheme is used to deduce a changeδ〈r ²〉=+0.005₅ fm² between the 26 keV state and the ground state of Dy¹⁶¹.     

Vortex-antivortex oscillation and tunneling in Bose-Einstein condensates

We study interacting condensates in anisotropic traps. Employing a two-level mean-field theory, which is valid provided the interaction energy is much smaller than ?ω_x and ?ω_y and the number of particles N is much larger than unity, we see that even a small interaction can drastically modify the dynamics of the system as predicted by García-Ripoll et al. [Phys. Rev. Lett. 87, 140403 (2001)]. In the present work, we supplement the discussion of the previous work and point out the important role of coupling between population difference and phase difference between two p states in the x and y directions. We also explore the stability of the vortex state for small systems with N ～ O(1), for which the mean-field theory is inapplicable. We performed the full quantum mechanical calculations using up to six single-particle states and showed that, when N is comparable to unity, quantum tunneling between the vortex and antivortex states can occur even though the interaction coefficient is so large that the vortex-antivortex oscillation is prohibited within the mean-field theory.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.