Instability of incompressible cylinder rubber tubes under radial electric fields

The possibility of instability of cylindrical tubes of elastomers is analyzed taking into account Mooney-Rivlin (M. Mooney, J. Appl. Phys. 11, 582 (1940)) and Ogden (R.W. Ogden, Proc. R. Soc. London, Ser. A 326, 565 (1972)) models. In some aspects this paper is the elasto-electric counterpart of a previous paper by Bustamante, Dorfmann and Ogden (R. Bustamante, A. Dorfmann, R.W. Ogden, J. Engn. Math. 59, 139 (2007)). However in the present case the appearance of instability is checked. The results indicate that models more complex than the Mooney-Rivlin model are necessary to predict instability zones showing minimum critical points.     

Effect of an electric field on the deformation of incompressible rubbers: Bifurcation phenomena

Well above their glass transition temperatures, polymers behave like rubber materials. In the rubbery state, the elastic modulus is low enough to allow large deformations. Rubbery materials also deform under the application of an electric field. Rubbers can be referred as electromechanically active elastomers (EMAE) or lightweight materials that convert electrical into mechanical energy and vice versa [H. Xu, Z.-Y. Cheng, D. Olson, T. Mai, Q.M. Zang, G. Kavarnos, Ferroelectric and electromechanical properties of poly(vinylidene-fluoride-trifluoroethylene-chlrotrifluoroethylene) terpolymer, Appl. Phys. Lett. 78 (2001) 2360–2362]. Possible applications include biomedical prostheses, actuators, energy harvesters and robots [R.E. Pelrine, R.D. Kornbluh, J.P. Joseph, Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation, Sens. Actuators, A 64 (1998) 77–85; G. Kofod, W. Wirges, Energy minimization for self-organized structure formation and actuation, Appl. Phys. Lett., 90 (2007) 81916–81918; J.S. Plante, S. Dubowsky, Large-scale failure modes of dielectric elastomer actuators, Int. J. Solids Struct. 43 (2006) 7727–7751].However, although the engineering applications of EMAE are quite recent, the theoretical foundations of continua under simultaneous electrical and mechanical force fields date back the 1960s. In this paper we present the basis of the nonlinear electroelasticity according to the formulation by Dorfmann and Ogden [A. Dorfmann, R.W. Ogden, Nonlinear Electroelastic Deformations, J. Elasticity 82 (2006) 99–127; A. Dorfmann, R.W. Ogden, Nonlinear electroelasticity, Acta Mechanica 174 (2005) 167–183] and discuss the influence of an electrical field on the bifurcation phenomena appearing in some cases of electromechanical deformation in rubber materials.     

Effects of high-j intruder states in the fine structure of superdeformed bands

All known cases of ΔI=4 bifurcation in superdeformed bands are analyzed on the basis of the theory proposed by the author in a previous paper [I. M. Pavlichenkov, Phys. Rev. C 55, 1275 (1997)]. It is shown that the high-j intruder single-particle states play a critical role in the phenomenon. The bands in which fine structure can be observed are predicted. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 759–764 (25 December 1997)     

Efficient nonlinear-optical frequency conversion in periodic media in the presence of diffraction of the pump and harmonic fields

It has been predicted by Shelton and Shen [Phys. Rev. A 5, 1867 (1972)] and observed by Kajikawa et al. [Jpn. J. Appl. Phys. Lett. 31, L679 (1992)] and Yamada et al. [Appl. Phys. B 60, 485 (1995)] that the efficiency of nonlinear-optical frequency conversion increases significantly in a nonlinear periodic medium and, accordingly, the intensity of the generated harmonic increases as the fourth power of the sample thickness, as opposed to the square law observed in homogeneous media. In this paper it is shown that the same enhancement of the efficiency of nonlinear-optical frequency conversion in a nonlinear periodic medium can be achieved using an ordinary pump wave in the form of a plane wave when both the pump wave and the harmonics are diffracted by the periodic structure of the nonlinear medium. The phenomenon is analyzed quantitatively in the example of second-harmonic generation. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 793–799 (25 December 1999)     

Two-Particle Irreducible Effective Action in Gauge Theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) (G. Baym (1962). Physical Review 127, 1391; H. D. Dahmen and G. Jona Lasino (1962). Nuovo Cimento A 52, 807; C. de Dominicis and P. Martin (1964). Journal of Mathematical Physics 5, 14; J. Luttinger and J. Ward (1960). Physical Review 118, 1417; B. Vanderheyden and G. Baym (1998). Journal of Statistical Physics 98, 843; B. Vanderheyden and G. Baym (2000). In Progress in Nonequilibrium Green's Functions, World Scientific, Singapore). (or Cornwall–Jackiw–Tomboulis (CJT) (J. Cornwall, R. Jackiw, and E. Tomboulis (1974). Physical Review D 10, 2428; U. Kraemmer and A. Rebhan (2004). Reports on Progress in Physics 67, 351; R. Norton and J. Cornwall (1975). Annals of Physics 91, 106) effective action (EA) in a way appropiate to its application to nonequilibrium gauge theories. We hope this review article will stimulate new work into this field.     

Fermions at a half-quantum vortex

The spectrum of the fermion zero modes in the vicinity of a vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2-vortex in high-temperature superconductors made by [J.R. Kirtley, C.C. Tsuei, M. Rupp et al., Phys. Rev. Lett. 76, 1336 (1996)]. The fractional value of the winding number leads to a frac-tional value of the invariant which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the “half-crossing:” the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of fermion condensation is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 729–734 (10 May 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

The individual success of musicians, like that of physicists, follows a stretched exponential distribution by J.A. Davies

Comment on Eur. Phys. J. B 27, 445 (2002) We analyze the distribution of success of musicians, comparing a stretched exponential (found by J.A. Davies [Eur. Phys. J. B 27, 445 (2002)]) with a distribution of the family of the q-exponential (presenting an intermediate power-law regime with a crossover to an exponential tail). We find that both assumptions yield comparable results, within the available range of data, hence a definite conclusion cannot yet be taken. But this example joins many others that has been found to be fairly described by q-exponentials (or variations of it), which may be indicative that there is a (significantly large) class of systems described by nonextensive statistical mechanics, from where q-exponentials naturally appear. Received 17 October 2002 Published online 31 December 2002     

Expansion of matter heated by an ultrashort laser pulse

Recent experiments have utilizied high-power subpicosecond laser pulses to effect the ultrafast heating of a condensed material to temperatures far above the critical temperature. Using optical diagnostics it was established that a complicated density profile with sharp gradients, differing substantially from an ordinary rarefaction wave, forms in the expanding heated matter. The present letter is devoted to the analysis of the expansion of matter under the conditions of the experiments reported by D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Science 109/110, 1 (1996); K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri et al., Proc. Soc. Photo-Opt. Instum. Eng. 3343, 46 (1998); and, K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri et al., Phys. Rev. Lett. 81, 224 (1998). It is shown that if the unloading adiabat passes through the two-phase region, a thin liquid shell filled with low-density two-phase matter forms in the expanding material. The shell moves with a constant velocity. The velocity in the two-phase material is a linear function of the coordinate (flow with uniform deformation), and the density is independent of the coordinate and decreases with time as t ⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 4, 284–289 (25 February 1999)     

Are citations of scientific papers a case of nonextensivity?

The distribution N(x) of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner (Eur. Phys. J. B 4, 131 (1998)). To fit the data, a stretched exponential () has been used with only partial success. The success is not complete because the data exhibit, for large citation count x, a power law (roughly for the ISI data), which, clearly, the stretched exponential does not reproduce. This fact is then attributed to a possibly different nature of rarely cited and largely cited papers. We show here that, within a nonextensive thermostatistical formalism, the same data can be quite satisfactorily fitted with a single curve (namely, [0pt] for the available values of x. This is consistent with the connection recently established by Denisov (Phys. Lett. A 235, 447 (1997)) between this nonextensive formalism and the Zipf-Mandelbrot law. What the present analysis ultimately suggests is that, in contrast to Redner's conclusion, the phenomenon might essentially be one and the same along the entire range of the citation number x. Received 13 April 1999     

A study of Bi–Pb–Sn–Cd–Sb penta-alloys rapidly quenched from melt

Optical microscopy, X-ray diffractometry, the double bridge method, the Vickers microhardness testing and dynamic resonance techniques have been used to investigate structure, electrical resistivity, hardness, internal friction and elastic modulus of quenched Bi–Pb–Sn–Cd–Sb penta-alloys. The properties of these penta-alloys are greatly affected by rapid quenching. The intermetallic compound χ(Pb–Bi) or Bi₃Pb₇ is obtained after rapid quenching using the melt-spinning technique, and this is in agreement with reports by other authors [Marshall, T. J., Mott, G. T. and Grieverson, M. H. (1975). Br. J. Radiol., 48, 924; Kamal, M., El-Bediwi, A. B. and Karman, M. B. (1998). Structure, mechanical properties and electrical resistivity of rapidly solidified Pb–Sn–Cd and Pb–Bi–Sn–Cd alloys. J. Mater. Sci.: Mater. Electron., 9, 425; Borromêe-Gautier, C., Giessen, B. C. and Grrant, N. J. (1968). J. Chem. Phys., 48, 1905; Moon, K.-W., Boettinger, W. J., Kattner, U. R., Handwerker, C. A. and Lee, D.-J. (2001). The effect of Pb contamination on the solidification behavior of Sn–Bi solders. J. Electron. Mater., 30, 45.]. The quenched Bi_43.5Pb_44.5Cd₅Sn₂Sb₅ alloy has important properties for safety devices in fire detection and extinguishing systems.     

Line frequency and line intensity analyses of water vapour

Line position and line intensity analyses of new microwave and infrared data pertaining to water and involving the ground and (010) vibrational states are carried out using the same theoretical approach as in Coudert, L. H., 1997, J. molec. Spectrosc., 181, 246. The line position analysis involves the high J and K_a lines measured by Polyansky, O. L., Zobov, N. F., Viti, S., Tennyson, J., Bernath, P. F. and Wallace, L., 1997, J. molec. Spectrosc., 186, 422 and the ν₂ band transitions published by Toth, R. A., 1998, J. molec. Spectrosc., 190, 379. In contrast to the previous investigation, the maximum K_a value in the data set is 24 for the ground vibrational state and 21 for the (010) state. The data set considered in the line intensity analysis includes mainly the line intensities reported by Toth and is much more complete than that fitted in the present author's previous investigation as it contains many lines within the ground and (010) vibrational states. The theoretical approach accounts correctly for the observed data for both analyses. However, in the line position analysis, a few transitions had to be excluded from the fitting because they involved high lying perturbed rotational levels belonging to the (010) vibrational state.     

Logarithmic interaction under periodic boundary conditions: closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [J. Math. Phys., 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [J. Math. Phys., 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation.     

Spectroscopic Characterization of Eu(III) Complexes with New Monophosphorus Acid Derivatives of H<Subscript>4</Subscript>dota

The luminescence lifetimes of europium(III) complexes with new monophosphorus acid derivatives of H₄dota were measured by means of time-resolved laser-induced luminescence spectroscopy in H₂O and D₂O. The hydration numbers of these complexes were estimated using different empirical equations [Horrocks and Sudnick (1979) J. Am. Chem. Soc. 101 (1979) 334; Choppin and Barthelemy(1989) Inorg. Chem. 28, 3354–3357; Choppin and Bünzli Lanthanide probes in life, chemical and earth sciences. Theory and practice (1989); Kimura and Kato J. Alloys Comp. 275–277 (1998) 806; Parker (1999) J. Chem. Soc., Perkin Trans. 2, 493–503; Supkowski and Horroks (2002) Inorg. Chim. Acta. 340, 44–48]. It was shown that all the relationships gave similar results with a satisfactory precision. The hydration numbers of complexes of H₃do3a and H₄dota agreed with the literature values. One water molecule is coordinated in complexes of the new ligands. The results showed that the Choppin formula based on measurements only in H₂O can be satisfactorily used for estimation of the hydration numbers.     

Midpoints in gyrogroups

The obscured Thomas precessionof the special theory of relativity (STR) has been soared into prominence by exposing the mathematical structure, called a gyrogroup,to which it gives rise [A. A. Ungar, Amer. J. Phys.59,824 (1991)], and the role that it plays in the study of Lorentz groups [A. A. Ungar, Amer. J. Phys.60,815 (1992); A. A. Ungar, J. Math. Phys.35,1408 (1994); A. A. Ungar, J. Math. Phys.35,1881 (1994)]. Thomas gyrationresults from the abstraction of Thomas precession.As such, its study sheds light on relativistic velocity spaces and their symmetries which are concealed in Thomas precession. In order to uncover new properties of relativistic gyrogroups, we employ in this article the group theoretic concepts of divisible groupsand two-torsion free groupsto construct midpointsin gyrogroups. Systems of successive midpoints then describe straight gyrolinesand suggest a new, natural distance function that involves a Thomas gyration. These, in turn, reveal a new, interesting geometry that underlies relativistic velocity spaces. In this resulting gyrogeometrythe straight gyrolines form geodesics under a distance function which turns out to be the Poincaré hyperbolic distance function relaxed by a Thomas gyration. These geodesics do obey the parallel axiom of Euclidean geometry. Ironically, (i) attempts to understand the parallel postulate of Euclidean geometry gave rise to hyperbolic geometry in which the parallel postulate disappears;(ii) hyperbolic geometry gave rise to Einstein's STR; (iii) Einstein's STR established the bizarre and counterintuitive relativistic effect called Thomas precession, the abstraction of which is called Thomas gyration; and (iv) Thomas gyration now repairs in this article the Poincaré distance function of hyperbolic geometry to the point where the parallel postulate reappears.     

Surface tension of superfluid helium

Summary We present here the calculation of the expression for the surface tension depression by taking into consideration the finite size of the molecular superfluid helium. The agreement between the experimental results (J. R. Eckardt, D. O. Edwards, S. Y. Shen and F. M. Gasparini:Phys. Rev. B,16, 1944 (1977)) and the theoretical results is much better than previously published (K. R. Atkins:Can. J. Phys.,31, 1165 (1953)).     

On the gravitational effects of rotating masses: The Thirring-Lense papers

The purpose of this work is to provide a critical analysis of the classical papers of H. Thirring [Phys. Z.,19, 33 (1918);Phys. Z.,22, 29 (1921)] and J. Lense and H. Thirring [Phys. Z.,19, 156 (1918)] on rotating masses in the relativistic theory of gravitation and to render them accessible to a wider circle of scholars. An English translation of these papers is presented which follows the original German text as closely as possible. This is followed by a concise account of the significance of the results of these papers as well as the possibility of measuring the gravitational effects of rotating masses.     

A revised many-body potential energy function for the description of the H3O+(H2O)n clusters

A revised potential energy function that has been fitted to the latest set of Kebarle and coworkers [1982, J. Am. chem. Soc, 104, 1462] entropy and enthalpy measurements at T = 300 K is presented. The model assumes a rigid hydronium unit and accounts for all orders of many-body interactions explicitly. The difference with the older function that had been based on earlier measurements by Kebarle and co-workers [1972, J. Am. chem. Soc, 94, 7627; 1967, J. Am. chem. Soc, 89, 6393] is that more compact clusters are generated. We have studied the structural properties of water clusters in the size range 5–80 at T = 250 K within the framework of the (μPT) Grand Canonical ensemble. Clusters with sizes less than about 10 water molecules consist of a four-coordinated first shell, where the fourth water molecule is hydrogen bonded to the oxygen atom of the hydronium ion. The hydration number goes through a minimum value ～1.6, for a cluster size around 50, and it starts increasing again with further cluster growth, to ～2.5 for a cluster size of 250 water molecules, which is the largest cluster examined. On the other hand the water molecule coordination number shows a monotonic increase with cluster size. In small clusters, less than 10, water molecules prefer to be arranged in a chain-like fashion; at sizes around 50, tri-coordinated clathrate-like structures dominate whereas with further size increase the coordination number eventually levels off to the experimental bulk value, at 4.6.     

Casimir friction in terms of moving harmonic oscillators: equivalence between two different formulations

The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation ΔE for such a case [Europhys. Lett. 91, 60003 (2010); Eur. Phys. J. D 61, 335 (2011)]. A recent study of Barton [New J. Phys. 12, 113044 (2010)] seemingly leads to a different result for the dissipation. If such a discrepancy really were true, it would imply a delicate difficulty for the basic theory of Casimir friction. In the present note we show that the expressions for ΔE are in fact physically equivalent, at T = 0.     

The Green's Causal Functions of Bilocal Fields

On concrete examples it is demonstrated that in quantum field theory with three universal constants c, h, and k suggested in [1], the limiting value k ^–1 = 0 corresponding to local theory is a bifurcation point: the Green's causal function for finite k bifurcates into . The natural carrier of the latter is the Euclidean space-time R ₄, and its continuation from R ₄ to R _3,1 is regular. The former is singular at zero point and on the light cone and hence is rejected.