Semiclassical evaluation of average nuclear one- and two-body matrix elements

Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results, and it is demonstrated that the semiclassical matrix elements, as function of energy, well pass through the average of the scattered quantum values. For the one-body matrix elements it is shown how the Thomas-Fermi approach can be projected on good parity and also on good angular momentum. For the two-body case, the pairing matrix elements are considered explicitly.

Density matrix functional theory that includes pairing correlations

The extension of density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the application of existing DFT plus pairing approaches to atoms, molecules, ultracooled and magnetically trapped atomic Fermi gases, and atomic nuclei where the number of particles is conserved exactly. The connection with Hartree-Fock-Bogoliubov (HFB) theory is discussed, and the method of quasilocal reduction of the nonlocal theory is also described. This quasilocal reduction allows equations of motion to be obtained which are much simpler for numerical solution than the equations corresponding to the nonlocal case. Our theory is applied to the study of some even Sn isotopes, and the results are compared with those obtained in the standard HFB theory and with the experimental ones.

Initial state of ultrarelativistic heavy ion collision

A model for energy, pressure, and flow velocity distributions at the beginning of ultrarelativistic heavy ion collisions is presented, which can be used as an initial condition for hydrodynamic calculations. Our model takes into account baryon recoil for both target and projectile, arising from the acceleration of partons in an effective field F mu nu produced in the collision. The typical field strength (string tension) for RHIC energies is about 512 GeV/fm, which allows us to talk about string ropes. The results show that a quark-gluon plasma forms a tilted disk, such that the direction of the largest pressure gradient stays in the reaction plane, but deviates from both the beam and the usual transverse flow directions. Such initial conditions may lead to the creation of antiflow or third flow component [L. P. Csernai and D. Rhrich, Phys. Rev. Lett. B 458, 454 (1999)].

Fission stability diagram of 240Pu

We have used an axially symmetric deformed Thomas-Fermi model to evaluate the fission barrier of 240Pu as a function of the quadrupole moment Q2 for different values of the angular momentum L and temperature T. The fission stability diagram of this nucleus is investigated.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Comment on "Influence of bulk properties on the surface structure of finite nuclei"

We comment on a recent paper by Uma Maheswari et al. in which it is claimed that quantal calculations of the half-infinite nuclear matter, in contrast to semiclassical approximations, exhibit an unusually strong dependence of the 90%10% surface thickness of the density profile on the Fermi momentum kF at saturation. This conclusion was carried over to the surface incompressibility. On the contrary we find essential agreement between semiclassical and quantal results and very weak dependence on kF of the quantities in question.

A new accelerometric method to assess the daily walking practice.

OBJECTIVE: To describe a method to obtain a profile of the duration and intensity (speed) of walking periods over 24 hours in women under free-living conditions. DESIGN: A new method based on accelerometry was designed for analyzing walking activity. In order to take into account inter-individual variability of acceleration, an individual calibration process was used. Different experiments were performed to highlight the variability of acceleration vs walking speed relationship, to analyze the speed prediction accuracy of the method, and to test the assessment of walking distance and duration over 24-h. SUBJECTS: Twenty-eight women were studied (mean+/-s.d.) age: 39.3+/-8.9 y; body mass: 79.7+/-11.1 kg; body height: 162.9+/-5.4 cm; and body mass index (BMI) 30.0+/-3.8 kg/m(2). RESULTS: Accelerometer output was significantly correlated with speed during treadmill walking (r=0.95, P<0.01), and short unconstrained walks (r=0.86, P<0.01), although with a large inter-individual variation of the regression parameters. By using individual calibration, it was possible to predict walking speed on a standard urban circuit (predicted vs measured r=0.93, P<0.01, s.e.e.=0.51 km/h). In the free-living experiment, women spent on average 79.9+/-36.0 (range: 31.7-168.2) min/day in displacement activities, from which discontinuous short walking activities represented about 2/3 and continuous ones 1/3. Total walking distance averaged 2.1+/-1.2 (range: 0.4-4.7) km/day. It was performed at an average speed of 5.0+/-0.5 (range: 4.1-6.0) km/h. CONCLUSION: An accelerometer measuring the anteroposterior acceleration of the body can estimate walking speed together with the pattern, intensity and duration of daily walking activity.

Repeated sprinting on natural grass impairs vertical stiffness but does not alter plantar loading in soccer players.

This study aimed to determine changes in spring-mass model (SMM) characteristics, plantar pressures, and muscle activity induced by the repetition of sprints in soccer-specific conditions; i.e., on natural grass with soccer shoes. Thirteen soccer players performed 6 × 20 m sprints interspersed with 20 s of passive recovery. Plantar pressure distribution was recorded via an insole pressure recorder device divided into nine areas for analysis. Stride temporal parameters allowed to estimate SMM characteristics. Surface electromyographic activity was monitored for vastus lateralis, rectus femoris, and biceps femoris muscles. Sprint time, contact time, and total stride duration lengthened from the first to the last repetition (+6.7, +12.9, and +9.3%; all P < 0.05), while flight time, swing time, and stride length remained constant. Stride frequency decrease across repetitions approached significance (-6.8%; P = 0.07). No main effect of the sprint number or any significant interaction between sprint number and foot region was found for maximal force, mean force, peak pressure and mean pressure (all P > 0.05). Center of mass vertical displacement increased (P < 0.01) with time, together with unchanged (both P > 0.05) peak vertical force and leg compression. Vertical stiffness decreased (-15.9%; P < 0.05) across trials, whereas leg stiffness changes were not significant (-5.9%; P > 0.05). Changes in root mean square activity of the three tested muscles over sprint repetitions were not significant. Although repeated sprinting on natural grass with players wearing soccer boots impairs their leg-spring behavior (vertical stiffness), there is no substantial concomitant alterations in muscle activation levels or plantar pressure patterns.

Anomalous roughening of Hele-Shaw flows with quenched disorder

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents is introduced.

High-Momentum Response of Liquid 3He

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid 3He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitly through a new additive term which depends on the semidiagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for good agreement with available deep-inelastic neutron scattering data.

Off-axis vortices in trapped Bose-condensed gases: Angular momentum and frequency splitting

We consider noncentered vortices and their arrays in a cylindrically trapped Bose-Einstein condensate at zero temperature. We study the kinetic energy and the angular momentum per particle in the Thomas-Fermi regime and their dependence on the distance of the vortices from the center of the trap. Using a perturbative approach with respect to the velocity field of the vortices, we calculate, to first order, the frequency shift of the collective low-lying excitations due to the presence of an off-center vortex or a vortex array, and compare these results with predictions that would be obtained by the application of a simple sum-rule approach, previously found to be very successful for centered vortices. It turns out that the simple sum-rule approach fails for off-centered vortices.

Interaction of a discrete breather with a lattice junction

We study the scattering of a moving discrete breather (DB) on a junction in a Fermi-Pasta-Ulam chain consisting of two segments with different masses of the particles. We consider four distinct cases: (i) a light-heavy (abrupt) junction in which the DB impinges on the junction from the segment with lighter mass, (ii) a heavy-light junction, (iii) an up mass ramp in which the mass in the heavier segment increases continuously as one moves away from the junction point, and (iv) a down mass ramp. Depending on the mass difference and DB characteristics (frequency and velocity), the DB can either reflect from, or transmit through, or get trapped at the junction or on the ramp. For the heavy-light junction, the DB can even split at the junction into a reflected and a transmitted DB. The latter is found to subsequently split into two or more DBs. For the down mass ramp the DB gets accelerated in several stages, with accompanying radiation (phonons). These results are rationalized by calculating the Peierls-Nabarro barrier for the various cases. We also point out implications of our results in realistic situations such as electron-phonon coupled chains.

Prescription footwear for severe injuries of foot and ankle: effect on regularity and symmetry of the gait assessed by trunk accelerometry.

After foot and/or ankle fracture, the restoration of optimal gait symmetry is one of the criteria of recovery. Orthotic insoles and orthopaedic shoes improve gait symmetry and regularity by controlling joint motion and improving alignment. The aim of the present study was to assess the effect of prescription footwear on gait quality by using accelerometers attached to the lower back. Sixteen adult patients with persistent disability after ankle and/or foot fractures performed two 30-s walking trials with and without prescription footwear (insoles and stabilizing shoes). Sixteen control subjects were also tested for comparison. The autocorrelation function was computed from the acceleration signal and the first two dominant periods were assessed (d1 and d2). Two parameters were used: (1) Stride Regularity (SR) which expresses the similarity between strides over time (d2), and (2) Stride Symmetry (SS) a ratio (d1/d2) which expresses the left/right similarity of gait independently of repeatability in the successive movements of each limb. In control subjects, SR and SS were 0.86+/-0.05 (correlation coefficient) and 81+/-10%, respectively. In the patient group, the effect of footwear was significant (SR: 0.88+/-0.06 vs. 0.90+/-0.05, SS: 38+/-23% vs. 46+/-27%). Pain was also significantly reduced (-34%). By using a rapid and low-cost method, we objectively quantified gait quality improvement after footwear intervention, concomitant to pain reduction. Substantial inter-patient variability in the footwear outcome was observed. In conclusion, we believe that trunk accelerometry can be a useful tool in the field of gait rehabilitation.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

High-precision satellite positioning system as a new tool to study the biomechanics of human locomotion.

New Global Positioning System (GPS) receivers allow now to measure a location on earth at high frequency (5Hz) with a centimetric precision using phase differential positioning method. We studied whether such technique was accurate enough to retrieve basic parameters of human locomotion. Eight subjects walked on an athletics track at four different imposed step frequencies (70-130steps/min) plus a run at free pace. Differential carrier phase localization between a fixed base station and the mobile antenna mounted on the walking person was calculated. In parallel, a triaxial accelerometer, attached to the low back, recorded body accelerations. The different parameters were averaged for 150 consecutive steps of each run for each subject (total of 6000 steps analyzed). We observed a perfect correlation between average step duration measured by accelerometer and by GPS (r=0.9998, N=40). Two important parameters for the calculation of the external work of walking were also analyzed, namely the vertical lift of the trunk and the velocity variation per step. For an average walking speed of 4.0km/h, average vertical lift and velocity variation were, respectively, 4.8cm and 0.60km/h. The average intra-individual step-to-step variability at a constant speed, which includes GPS errors and the biological gait style variation, were found to be 24. 5% (coefficient of variation) for vertical lift and 44.5% for velocity variation. It is concluded that GPS technique can provide useful biomechanical parameters for the analysis of an unlimited number of strides in an unconstrained free-living environment.