On the superfluidity of classical liquid in nanotubes,II. Case of odd number of neutrons

We show that the superfluidity effect in nanotubes arises in a classical liquid (regarded as the limit as h → 0 of the quantum liquid) and involves not only the Bogolyubov “running waves,” but also a “standing wave.” This is obtained from the variational equations in the context of ultrasecondary quantization. We consider cases of Bose and Fermi liquids.     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

The impact of collisions on platelet distribution in the blood flow

The impact of platelet collisions on their distribution in a viscous liquid flow has been analyzed. It has been shown that platelet distribution in the flow perpendicular to current lines resulting from their collisions can be described as “shear” diffusion. In the wide physiological range of shear velocities specific for blood, the coefficient of “shear” diffusion is much larger than the coefficient of “Brownian” diffusion. For a parabolic fluid velocity profile (Poiseuille flow) in cylindrical vessel “shear” diffusion causes uneven radial distribution of platelets over the vessel radius. “Shear” diffusion causes platelet concentration to grow from the wall toward the center (vessel axis). This effect appears to be a consequence of the specific distribution of platelet collision frequency reaching its maximum at the vessel wall.     

Geometry and Physics Today

“Geometry,” in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG). We explore potential physical implications of viewing things under the light of ADG, especially matters concerning the “gauge theories” of modern physics, when the latter are viewed (as they are actually regarded currently) as “physical theories of a geometrical character.” Thence, “physical geometry,” in connection with physical laws and the associated with them, within the background spacetime manifoldless context of ADG, “differential” equations, are also being discussed.     

Droplet suction on porous media

We study the forced aspiration of small ( mm) and large ( cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected “sponge-like”. Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a “locked” regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing () to finite receding () contact angle; 2) an “unlocked” regime, where the contour line recedes with a constant contact angle closed to . In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat “gravity pancake” for large ones. Received 19 January 2000     

Switching of banana liquid crystal mesophases under field

Taking advantage of the great number of bent-core or “banana" compounds synthesized and studied in the laboratory, we describe their behaviour under the application of an external electric field. If the field were a static one, we would work within the frame of an equilibrium phase diagram in a (field E, temperature T) space where some phases would be simple dielectrics and others ferroelectric ones with a macroscopic polarization, either spontaneous or induced by the field. In this paper, we deal with the basic responses of “banana” liquid crystals under the application of a low frequency (1 to 100 Hz) AC field. Firstly square-wave voltages allow us to locate the phase boundary between dielectric (at lower field) and ferroelectric phases (higher field) at a given temperature and field threshold. Then we apply slowly varying AC voltages with shapes like triangle or “triple-plateau” to check out the stability of the induced ferroelectric phase versus field removal. Three behaviours are encountered, the unstable one (short lifetime of the high-field ferroelectric phase) where the macroscopic polarization is destroyed and then rebuilt in the opposite direction during each half period and usually called “antiferroelectric”; the stable one (long lifetime) with a polarization that rotates at constant modulus which is labeled as “ferroelectric” and a new one where the macroscopic polarization is proportional to the applied fied, we named this behaviour as “superparaelectric”. Let us stress that these observations apply to the ferroelectric phases of the (E, T) phase diagram not to the zero field (0,T) phases observed in the usual phase characterization experiments except for an eventual spontaneous ferroelectric phase. Received 18 April 2002 and Received in final form 17 January 2003 Published online: 16 April 2003 RID="a" ID="a"e-mail: marcerou@crpp.u-bordeaux.fr RID="b" ID="b"URL: http://www.crpp-bordeaux.cnrs.fr     

Development of carbon-carbon nozzle extension for liquid fuel rocket motors

Successful experience of RSC “Energy” and SPA “Iskra” in the development of carbon-carbon extension for oxygen-kerosene liquid fuel rocket motor has been summarized. Methodological approach that served to completion of carbon-carbon extension development in full and at comparatively small expenses has been described. Results of practical application of carbon-carbon extension for liquid fuel rocket motor 11D58M have been presented within the framework of International Space Program “Sea Launch”.     

Quantitative analysis of lyotropic lamellar phases SANS patterns in powder oriented samples

We have developed a detailed numerical method based on the Caillé model to fit Small Angle Neutron Scattering profiles of powder-oriented lyotropic lamellar phases. We thus obtain quantitative values for the Caillé parameter and the smectic penetration length from which we can derive the smectic compression modulus and the membrane mean bending modulus. Our method, applied to a surfactant lamellar phase system decorated by amphiphilic copolymers, provides excellent fits for any intermembrane spacing or membrane concentration over the entire q-range of the SANS experiments. We compare our fits with those obtained from the model of Nallet et al. (J. Phys. II 3, 487 (1993)), which is reviewed. Good fits are obtained with both methods for samples exhibiting “hard” smectic order (sharp Bragg peak, moderate small angle scattering). Only our procedure, however, gives good fits in the case of “soft” smectic order (smooth Bragg peak, strong small angle scattering). A quantitative criterion to discriminate between these “soft” and “hard” samples is also proposed, based on a simple analogy with smectic-A liquid crystal in contact with an undulating solid surface. This allows us to anticipate the type of thermodynamic information that can be derived from the fits.     

Extended theories of gravity and their cosmological and astrophysical applications

Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large scale structure and cosmic dynamics. The emerging picture is a spatially flat, homogeneous Universe undergoing the today observed accelerated phase. Despite of the good quality of astrophysical surveys, commonly addressed as Precision Cosmology, the nature and the nurture of dark energy and dark matter, which should constitute the bulk of cosmological matter-energy, are still unknown. Furthermore, up to now, no experimental evidence has been found, at fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of General Relativity in its simplest formulation (a linear theory in the Ricci scalar R, minimally coupled to the standard perfect fluid matter) and claiming for the “correct” theory of gravity as that derived by matching the largest number of observational data, without imposing any theory a priori. As a working hypothesis, accelerating behavior of cosmic fluid, large scale structure, potential of galaxy clusters, rotation curves of spiral galaxies could be reproduced by means of extending the standard theory of General Relativity. In other words, gravity could acts in different ways at different scales and the above “shortcomings” could be due to incorrect extrapolations of the Einstein gravity, actually tested at short scales and low energy regimes. After a survey of what is intended for Extended Theories of Gravity in the so called “metric” and “Palatini” approaches, we discuss some cosmological and astrophysical applications where the issues related to the dark components are addressed by enlarging the Einstein theory to more general f (R) Lagrangians, where f (R) is a generic function of Ricci scalar R, not assumed simply linear. Obviously, this is not the final answer to the problem of “dark-components” but it can be considered as an operative scheme whose aim is to avoid the addition of unknown exotic ingredients to the cosmic pie.     

The interplay between “low” and “high” energy CP-violation in leptogenesis

We analyse, within the “flavoured” leptogenesis scenario of baryon asymmetry generation, the interplay of “low energy” CP-violation, originating from the PMNS neutrino mixing matrix U, and “high energy” CP-violation, which can be present in the matrix of neutrino Yukawa couplings, λ, and can manifest itself only in “high” energy scale processes. The type I see-saw model with three heavy right-handed Majorana neutrinos having a hierarchical spectrum is considered. The “orthogonal” parameterisation of the matrix of neutrino Yukawa couplings, which involves a complex orthogonal matrix R, is employed. In this approach the matrix R is the source of “high energy” CP-violation. Results for normal hierarchical (NH) and inverted hierarchical (IH) light neutrino mass spectrum are derived in the case of decoupling of the heaviest right-handed Majorana neutrino. It is shown that taking into account the contribution to Y _B due to the CP-violating phases in the neutrino mixing matrix U can change drastically the predictions for Y _B , obtained assuming that only “high energy” CP-violation from the R-matrix is operative in leptogenesis. In the case of the IH spectrum, in particular, there exist significant regions in the corresponding parameter space where the purely “high energy” contribution in Y _B plays a subdominant role in the production of baryon asymmetry compatible with the observations. Also at Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.     

BRST analysis of topologically massive gauge theory: novel observations

A dynamical non-Abelian 2-form gauge theory (with B∧F term) is endowed with the “scalar” and “vector” gauge symmetry transformations. In our present endeavor, we exploit the latter gauge symmetry transformations and perform the Becchi–Rouet–Stora–Tyutin (BRST) analysis of the four (3+1)-dimensional (4D) topologically massive non-Abelian 2-form gauge theory. We demonstrate the existence of some novel features that have, hitherto, not been observed in the context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form and 3-form gauge theories. We comment on the differences between the novel features that emerge in the BRST analysis of the “scalar” and “vector” gauge symmetries.     

Experimental study of boiling-up kinetics and superheat limit for n-hexane on solid powder-like structures

The experimental setup is described and results are presented for measuring average boiling-up lag time for superheated n-hexane mixed with solid structures (activated coal, cellulose, silica gel) as function of temperature under atmospheric pressure. The “aging” of the cell with the filler was carried out before measurements: this was about 600–1000 boiling events. We developed a new method for analysing of “aging” procedure: comparison of average flux (frequency) of boiling-up events (processing of experimental data) and the frequency of nucleation obtained from exponential model. By the end of aging of the cell with silica gel the average empirical flux reduces by factor of four relative to the “exponential” value. But for activated coal and cellulose the difference in these fluxes is about 20 %. In all experiments, the event flux was nonstationary. For n-hexane in tested systems, the margin of superheating was T _n/T _cr ≅ 0.873–0.875, although it was T _n/T _cr ≅ ≅ 0.883 for n-pentane in systems filled by nickel powder (sintered porous nickel with grains of 1.5 or 5.0 micron size) and in the presence of a smooth copper plate. The average time of boiling-up lag in n-hexane at low normalized temperatures was also smaller than for n-pentane. For all systems, the lag time is almost the same for the temperature range T _n/T _cr ≅ 0.860–0.874 (plateau). Thus, a smaller amount of superheated liquid or its division into smaller liquid elements does not result in longer liquid lifetime for superheat liquid and the maximal superheat temperature, as one could expect from the classical theory of homogeneous nucleation. Research was supported by the RF Presidential Foundation (NS-905.2003.2) and Russian Foundation for Basic Research (Grant No. 04-02-16285).     

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been identified in any form before. We present their Lax pair formulations and describe their bihamiltonian structures. We prove local wellposedness of the corresponding Cauchy problem and include results on blow-up as well as global existence of solutions. Moreover, we construct “peakon” and “multi-peakon” solutions for all λ ≠ 0, 1, and “shock-peakons” for λ = 3. We argue that there is a natural geometric framework for these equations that includes other well-known integrable equations and which is based on V. Arnold’s approach to Euler equations on Lie groups.     

Half-life estimation under indefinite “mother-daughter” relation

An algorithm has been proposed to build an estimate of the half-life of a “daughter” nucleus in case, when it is unknown, which nucleus is its “mother” (“indefinite start time”). For a decay of the “mother” at an instant t we can determine P—a probability of such a decay, if we assume that each “mother”, which has been decayed before t has equal chances to be “mother” of this “daughter”:

A global version of the quantum duality principle

The “quantum duality principle” states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a formal Poisson group yields a quantisation of the dual Lie bialgebra as well. We extend this to a much more general result: namely, for any principal ideal domainR and for each primepεR we establish an “inner” Galois’ correspondence on the categoryHA of torsionless Hopf algebras overR, using two functors (fromHA to itself) such that the image of the first and the second is the full subcategory of those Hopf algebras which are commutative and cocommutative, modulop, respectively (i.e., they are“quantum function algebras” (=QFA) and“quantum universal enveloping algebras” (=QUEA), atp, respectively). In particular we provide a machine to get two quantum groups — a QFA and a QUEA — out of any Hopf algebraH over a fieldk: apply the functors tok[ν] ⊗k H forp=ν. A relevant example occurring in quantum electro-dynamics is studied in some detail. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001     

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

Generating conjecture and some einstein-maxwell fields of high symmetry

For stationary cylindrically symmetric solutions of the Einstein-Maxwell equation we have shown that the “charged” solutions of McCrea, Chitre et al. (CGN), Van den Bergh and Wils (VW) can be obtained from the seed metrics using generating conjecture. The McCrea “charged” solution has as a seed vacuum metric the Van Stockum solution with a Killing vector (0, 0, 1, 0). The CGN “charged” solution and the VW “charged” solution have the static seed metrics connected by the complex substitutiont → iz, z → it and the Killing vector which is a simple linear combination of∂ _ϕ and∂ _t Killing vectors (VW), respectively∂ _ϕ and∂ _z Killing vectors (CGN).     

Hysteresis Phenomenon in Deterministic Traffic Flows

We study phase transitions of a system of particles on the one-dimensional integer lattice moving with constant acceleration, with a collision law respecting slower particles. This simple deterministic “particle-hopping” traffic flow model being a straightforward generalization to the well known Nagel–Schreckenberg model covers also a more recent slow-to-start model as a special case. The model has two distinct ergodic (unmixed) phases with two critical values. When traffic density is below the lowest critical value, the steady state of the model corresponds to the “free-flowing” (or “gaseous”) phase. When the density exceeds the second critical value the model produces large, persistent, well-defined traffic jams, which correspond to the “jammed” (or “liquid”) phase. Between the two critical values each of these phases may take place, which can be interpreted as an “overcooled gas” phase when a small perturbation can change drastically gas into liquid. Mathematical analysis is accomplished in part by the exact derivation of the life-time of individual traffic jams for a given configuration of particles. This research has been partially supported by Russian Foundation for Fundamental Research and French Ministry of Education grants.     

Medium effects in the production and π0γ decay of ω-mesons in pA collisions in the GeV region

The ω resonance production and its π⁰γ decay in pA reactions close to threshold is considered within the Intranuclear Cascade (INC) model. The π⁰γ invariant-mass distribution shows two components which correspond to the ω decay “inside” and “outside” the nucleus, respectively. The “inside” component is distorted by medium effects, which introduce a mass shift as well as collisional broadening for the ω-meson and its decaying pion. The relative contribution of the “inside” component is analyzed in detail for different kinematical conditions and nuclear targets. It is demonstrated that a measurement of the correlation in azimuthal angle between the π⁰ and γ momenta allows to separate events related to the “inside”ω decay from different sources of background when uncorrelated π⁰'s and γ's are produced. Received: 2 April 2001 / Accepted: 5 June 2001