Thermodynamics of photons on fractals

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.     

Mechanosynthesis of YIG and GdIG: A Structural and Mössbauer Study

We have investigated the mechanosynthesis of gadolinium and yttrium iron garnets by high-energy ball-milling of α-Fe₂O₃ and Gd₂O₃ or α-Fe₂O₃ and Y₂O₃, respectively, followed by short thermal annealings conducted at moderate temperatures. The samples were characterized by X-ray diffraction and Mössbauer spectroscopy, in order to determine the influence of the milling time and annealing conditions on the final products. For as-milled samples of each rare-earth system, the results revealed the formation of perovskite phases, in relative amounts that depend on the milling time. The formation of garnet phases was observed in as-annealed samples treated at 1000°C for 2 h or 1100°C for 3 h, i.e., at very modest annealing requirements when compared with ordinary solid-state-reaction processes performed without previous high-energy milling. Also, the occurrence was verified of a milling time for which the relative amount of garnet phases formed by annealing was maximized. This time depends on the rare-earth composing the garnet phase and on the annealing temperature.     

Rotational spectrum of trans-trans diethyl ether in the ground and three excited vibrational states

We report the results of a comprehensive reinvestigation of the rotational spectrum of diethyl ether based on broadband millimetre-wave spectra recently recorded at The Ohio State University and in Warsaw, covering the frequency region 108-366 GHz. The data set for the ground vibrational state of trans-trans diethyl ether has been extended to over 2000 lines and improved spectroscopic constants have been determined. Rotational spectra in the first excited vibrational states of the three lowest vibrational modes of trans-trans-diethyl ether, ν₂₀, ν₃₉, and ν₁₂ have been assigned. The v₂₀ = 1 and v₃₉ = 1 states are near 100 cm⁻¹ in vibrational term value and are coupled by a strong c-axis Coriolis interaction, which gives rise to many spectacular manifestations in the rotational spectrum. All of these effects have been successfully fitted for a dataset comprising over 3000 transitions, leading to precise determination of the energy difference between these states, (ΔE/hc)=10.400222(5) cm⁻¹. A newly developed software package for assignment and analysis of broadband spectra is described and made available.     

Residual stress determination in aluminium using electromagnetic acoustic transducers

The residual stresses in a shrink-fit specimen were measured ultrasonically, using shear-horizonal (SH) waves transmitted and received by noncontacting electromagnetic acoustic transducers. The presence of stress induces a small change in the velocity of the SH-waves. The difference in velocities of orthogonally polarized SH-waves (acoustic birefringence) was measured with a simple time-interval averaging system; this velocity difference can be related to the difference of principal stresses. The presence of material anisotropy (texture) in the specimen also causes relative velocity changes comparable to stress-induced changes. A simple method was used to remove the anisotropy-dependent component of the total relative velocity change, thereby allowing a determination of residual stress. This method consisted of measuring the birefringence in unstressed reference specimens and subtracting it from the birefringence measured at stressed locations. For the specimen used here, good agreement between theoretical and experimental values of stress was obtained.     

The second order optical potential for theπd system at the threshold

The second order optical potential for thed system is derived in the framework of the Watson formalism and applied to the calculation of the 1s-state energy shift of the atom and thed scattering lengtha _d . The results are in good agreement with those of the Faddeev type calculations.The authors wish to thank V. B. Belyaev, R. Mach, M. G. Sapozhnikov and R. A. Eramzhyan for stimulating discussions and helpful advice.     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

An elegant but “simple” form for the Dirac hydrogen atom

The operator structures for the constants of the motion of the relativistic hydrogen atom are examined. ThoughJ ³ andJ · J are constants of the motion,J is not. Its replacement, , is shown to emerge rather naturally in transforming the equation to spherical coordinates. The separation of variables is presented in hypercomplex number form. This leads to some interesting suggestions regarding the matter/antimatter operator for the Dirac equation.     

μ+ depolarization inAlGd alloys

The ⁺ depolarization rate in diluteAlGd alloys containing 50 and 450 atomic ppm Gd was measured in a transverse field of 80 Oe over the temperature range 6–300 K. For both alloys, A increased dramatically above 200 K, reaching values of 0.69 and 0.93 s^–1, respectively, near room temperature. The results are interpreted as providing evidence for a thermally-activated trapping mechanism.This work was supported by the U.S. Department of Energy.