Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(ε³), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy. Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp     

Stability of fluid flow past a membrane

The stability of the flow of a fluid past a solid membrane of infinitesimal thickness is investigated using a linear stability analysis. The system consists of two fluids of thicknesses R and H R and bounded by rigid walls moving with velocities and , and separated by a membrane of infinitesimal thickness which is flat in the unperturbed state. The fluids are described by the Navier-Stokes equations, while the constitutive equation for the membrane incorporates the surface tension, and the effect of curvature elasticity is also examined for a membrane with no surface tension. The stability of the system depends on the dimensionless strain rates and in the two fluids, which are defined as and for a membrane with surface tension , and and for a membrane with zero surface tension and curvature elasticity K. In the absence of fluid inertia, the perturbations are always stable. In the limit , the decay rate of the perturbations is O(k ³ ) smaller than the frequency of the fluctuations. The effect of fluid inertia in this limit is incorporated using a small wave number asymptotic analysis, and it is found that there is a correction of smaller than the leading order frequency due to inertial effects. This correction causes long wave fluctuations to be unstable for certain values of the ratio of strain rates and ratio of thicknesses H. The stability of the system at finite Reynolds number was calculated using numerical techniques for the case where the strain rate in one of the fluids is zero. The stability depends on the Reynolds number for the fluid with the non-zero strain rate, and the parameter , where is the surface tension of the membrane. It is found that the Reynolds number for the transition from stable to unstable modes, , first increases with , undergoes a turning point and a further increase in the results in a decrease in . This indicates that there are unstable perturbations only in a finite domain in the plane, and perturbations are always stable outside this domain. Received: 29 May 1997 / Revised: 9 October 1997 / Accepted: 26 November 1997     

Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe

We study the semiclassical limit of the (generalized) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In particular, we show that in the semiclassical limit the solution of the KdV equation: i) converges in H ^s to the solution of the Hopf equation, provided the initial data belongs to H ^s , ii) admits an asymptotic expansion in powers of the semiclassical parameter, if the initial data belongs to the Schwartz class. The result is also generalized to KdV equations with higher order linearities.     

A simple model for nuclear structure functions at small x in the dipole picture

A simple model for nuclear structure functions in the region of small x and small and moderate Q² is presented. It is a parameter-free extension, in the Glauber-Gribov approach to nuclear collisions, of a saturation model for the nucleon. A reasonable agreement with experimental data on the ratios of nuclear structure functions is obtained. Nuclear effects in the longitudinal-to-transverse cross section ratios are found to be small. Predictions of the model for values of x smaller than those available to present experiments are given. The unintegrated gluon distribution and the behaviour of the saturation scale which result from this model are shown and discussed. Received: 5 June 2002 / Revised version: 27 June 2002 / Published online: 16 October 2002     

Stability Theorems for Chiral Bag Boundary Conditions

We study asymptotic expansions of the smeared L ²-traces Fe^{−t P^2} and FPe^{−tP^2}, where P is an operator of Dirac type and F is an auxiliary smooth endomorphism. We impose chiral bag boundary conditions depending on an angle θ. Studying the θ-dependence of the above trace invariants, θ-independent pieces are identified. The associated stability theorems allow one to show the regularity of the eta function for the problem and to determine the most important heat kernel coefficient on a four dimensional manifold. Mathematics Subject Classification (2000). 58J50     

Search for the Standard Model Higgs boson with the OPAL detector at LEP

This paper summarises the search for the Standard Model Higgs boson in e ⁺ e ^- collisions at centre-of-mass energies up to 209 GeV performed by the OPAL Collaboration at LEP. The consistency of the data with the background hypothesis and various Higgs boson mass hypotheses is examined. No indication of a signal is found in the data and a lower bound of 112.7 Gev/c² is obtained on the mass of the Standard Model Higgs boson at the 95% CL. Received: 13 March 2002 / Revised version: 9 October 2002 / Published online: 13 December 2002     

<Emphasis Type="Italic">EPJdirect</Emphasis>

Quark mass effects are analyzed at high Q² in the current fragmentation region of DIS. It is found that the linear combination F ₂ -2.75F ^c ₂ scales at large Q² and small x. We obtained a lower bound for the ratio F ^c ₂/F ₂ which lies very close to the data from HERA. Received: 14 January 2002 / Revised version: 9 October 2002 Published online: 9 December 2002 RID="a" ID="a" e-mail: ryutin@th1.ihep.su     

Invariance quantum group of the fermionic oscillator

The fermionic oscillator defined by the algebraic relations cc ^* +c ^* c = 1 and c ² = 0 admits the homogeneous group O(2) as its invariance group. We show that the structure of the inhomogeneus invariance group of this oscillator is a quantum group. Received: 15 July 2002 / Revised version: 14 October 2002 / Published online: 19 February 2003     

The neutron and proton two-particle nucleus 134Sb: New low-spin states observed in the decay of 134Sn and an estimate of the energy of the 7- isomer

Excited states in the ¹³⁴Sb nucleus, populated in the β^--decay of ¹³⁴Sn, have been studied at the mass separator OSIRIS. The ¹³⁴Sn activity was produced via fast neutron-induced fission of ²³⁸U target. A main result was the discovery of a very low-lying first-excited state of ¹³⁴Sb, at 13keV, which has led to a strong revision of the level scheme. The new results are compared with different theoretical calculations and with the known data for the analogous neutron and proton two-particle nucleus in the ²⁰⁸Pb region. On the basis of this comparison, the energy of the ( πg _7/2νf _7/2)_7- isomer is estimated to be about 250keV, some 100keV lower than previously reported. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: anovak@fuw.edu.pl     

Probing shell structure in neutron-rich nuclei with in-beam γ-spectroscopy

The structure of neutron-rich light nuclei around N = 20 and 28 has been investigated at GANIL by means of in-beam gamma-spectroscopy using fragmentation reactions of ³⁶S and ⁴⁸Ca beams on a Be target. Gamma-decay of relatively high-lying excited states have been measured for the first time in nuclei around ³²Mg and ⁴⁴S. Level schemes are proposed and discussed for a large number of these neutron-rich nuclei around N = 20 and N = 28. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: azaiez@ipno.in2p3.fr     

Asymptotic Stability of the Stationary Solution to the Compressible Navier–Stokes Equations in the Half Space

We investigate the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for the compressible Navier–Stokes equation in a half space. The main concern is to analyze the phenomena that happens when the fluid blows out through the boundary. Thus, it is natural to consider the problem in the Eulerian coordinate. We have obtained the two results for this problem. The first result is concerning the existence of the stationary solution. We present the necessary and sufficient condition which ensures the existence of the stationary solution. Then it is shown that the stationary solution is time asymptotically stable if an initial perturbation is small in the suitable Sobolev space. The second result is proved by using an L²-energy method with the aid of the Poincaré type inequality.The second author's work was supported in part by Grant-in-Aid for Scientific Research (C)(2) 14540200 of the Ministry of Education, Culture, Sports, Science and Technology and the third author's work was supported by JSPS postdoctoral fellowship under P99217.     

Parton symmetries and the NuTeV anomaly

Recently the NuTeV Collaboration (Phys. Rev. Lett. 88, 091802 (2002)) announced a new measurement of which was approximately three standard deviations above the currently accepted standard model value. The NuTeV analysis depends on the assumption that various quark-parton model symmetries are not broken. In particular the analysis takes and d _V ⁿ (x) = u _V ^p (x). However models which break these symmetries are known. We examine the predictions of these models and their effect on the NuTeV result. In most instances the effect is to decrease the discrepancy between the NuTeV result and the accepted value.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.15. + g Neutrino interactions - 11.30.Hv Flavor symmetries     

The measurement of the electronic g-factor in hydrogen-like ions --A promising tool for determining fundamental and nuclear constants

We describe a double-Penning-trap experiment suitable for testing QED in strong fields by determining the electronic g-factor of a single hydrogen-like ion in its ground state. Our measurements on ¹²C^{5 +} reach a relative accuracy of 2×10^-9, where the largest uncertainty results from the mass of the electron. Together with equally precise theoretical predictions therefore, it is possible to evaluate a new value for the electron's mass. The possibilities to obtain other fundamental constants and nuclear parameters are lined out. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: t.beier@gsi.de     

Physics with heavy neutron-rich RIBs at the HRIBF

The Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory has recently produced the world's first post-accelerated beams of heavy neutron-rich nuclei. The first experiments with these beam are described, and the results discussed. B(E2;0⁺ → 2⁺) values for neutron-rich ^126,128Sn and ^132,134,136Te isotopes have been measured by Coulomb excitation in inverse kinematics. The results for ¹³²Te and ¹³⁴Te (N = 80, 82) show excellent agreement with systematics of lighter Te isotopes, but the B(E2) value for ¹³⁶Te (N = 84) is unexpectedly small. Single-neutron transfer reactions with a ¹³⁴Te beam on ^natBe and ¹³C targets at energies just above the Coulomb barrier have also been studied. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: radford@mail.phy.ornl.gov     

Integrable Nonlinear Evolution Equations on the Half-Line

 A rigorous methodology for the analysis of initial-boundary value problems on the half-line, is applied to the nonlinear §(NLS), to the sine-Gordon (sG) in laboratory coordinates, and to the Korteweg-deVries (KdV) with dominant surface tension. Decaying initial conditions as well as a smooth subset of the boundary values are given, where n=2 for the NLS and the sG and n=3 for the KdV. For the NLS and the KdV equations, the initial condition q(x,0) = q ₀ (x) as well as one and two boundary conditions are given respectively; for the sG equation the initial conditions q(x,0) = q ₀ (x), q _t (x,0) = q ₁ (x), as well as one boundary condition are given. The construction of the solution q(x,t) of any of these problems involves two separate steps: (a) Given decaying initial conditions define the spectral (scattering) functions {a(k),b(k)}. Associated with the smooth functions , define the spectral functions {A(k),B(k)}. Define the function q(x,t) in terms of the solution of a matrix Riemann-Hilbert problem formulated in the complex k-plane and uniquely defined in terms of the spectral functions {a(k),b(k),A(k),B(k)}. Under the assumption that there exist functions such that the spectral functions satisfy a certain global algebraic relation, prove that the function q(x,t) is defined for all , it satisfies the given nonlinear PDE, and furthermore that . (b) Given a subset of the functions as boundary conditions, prove that the above algebraic relation characterizes the unknown part of this set. In general this involves the solution of a nonlinear Volterra integral equation which is shown to have a global solution. For a particular class of boundary conditions, called linearizable, this nonlinear equation can be bypassed and {A(k),B(k)} can be constructed using only the algebraic manipulation of the global relation. For the NLS, the sG, and the KdV, the following particular linearizable cases are solved: , respectively, where χ is a real constant. Received: 22 October 2001 / Accepted: 22 March 2002 Published online: 22 August 2002     

The contribution of off-shell gluons to the structure functions F 2 and F_{\mathrm {L}}^c and the unintegrated gluon distributions

We calculate the perturbative parts of the structure functions F ₂ ^c and for a gluon target having non-zero transverse momentum squared at order . The results of the double convolution (with respect to the Bjorken variable and the transverse momentum) of the perturbative part and the unintegrated gluon densities are compared with the HERA experimental data for F ₂ ^c . The contribution from the structure function ranges in 10-30% of that of F ₂ ^c at the kinematical range of the HERA experiments. Received: 18 April 2002 / Revised version: 24 July 2002 / Published online: 7 October 2002 RID="a" ID="a" e-mail: kotikov@sunse.jinr.ru RID="b" ID="b" e-mail: gonzalo@fpaxp1.usc.es     

Symmetry in exotic nuclei

Symmetries have played an important role in the elucidation of the structure of nuclei and will continue to do so for exotic nuclei. As an example, an application of pseudo-SU(4) symmetry is discussed. It can be used as a starting point for a boson model that includes T = 0 as well as T = 1 bosons (IBM-4); applications are presented for N = Z nuclei from ⁵⁸Cu to ⁷⁰Br. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: isacker@ganil.fr     

Shape coexistence and the N = 20 shell closure far from stability by inelastic scattering

Following mass measurements in the region N = 20 and N = 28, we have studied inelastic nuclear scattering for the nuclei ³⁴Si, ³³Al and ³²Mg. No evidence for a low-lying shape isomeric 0⁺ state was found in ³⁴Si, and an upper limit for the population cross-section could be established, rendering its existence very unlikely. A new transition was found in ³³Al, that is a good candidate for a 2p-2h state and therefore a determination of the 2p-2h gap at N = 20. Inelastic nuclear scattering strongly excites 3^- states, as seen in ³⁴Si. A strong transition was found in ³²Mg that should correspond to the first 3^- in this nucleus, lying very low as compared to theory and systematics in this region. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: mittig@ganil.fr     

Application of wavelet analysis to the spectrum of \omega' states and ratio R e+e-

We demonstrate the advantages of the wavelet analysis (WA) for resolving the structures in experimental data on e ⁺ e ^- annihilation into hadron states with quantum numbers of meson. The WA yields a useful set of starting conditions for analysis of states with multiresonance unitary Breit-Wigner method. We also apply the WA for the ratio R _e+e- . Received: 4 February 2002 / Revised version: 28 August 2002 / Published online: 18 October 2002 RID="a" ID="a" e-mail: vhenner@python.physics.louisville.edu and henner@psu.ru     

Stability and Instability of the KDV Solitary Wave Under the KP-I Flow

We consider the KP-I and gKP-I equations in \mathbbR × (\mathbbR/2p\mathbbZ){{\mathbb{R}}\,\times\,({\mathbb{R}}/2\pi{\mathbb{Z}})}. We prove that the KdV soliton with subcritical speed 0 < c < c* is orbitally stable under the global KP-I flow constructed by Ionescu and Kenig (Ann Math Stud 163:181–211, 2007). For supercritical speeds c > c*, in the spirit of the work by Duyckaerts and Merle (GAFA 18:1787–1840, 2009), we sharpen our previous instability result and construct a global solution which is different from the solitary wave and its translates and which converges to the solitary wave as time goes to infinity. This last result also holds for the gKP-I equation.