Limit Analysis of Strain Softening Frames Allowing for Geometric Nonlinearity

This paper extends classical limit analysis to account for strain softening and 2nd-order geometric nonlinearity simultaneously. The formulation is an instance of the challenging class of socalled (nonconvex) mathematical programs with equilibrium constraints (MPECs). A penalty algorithm is proposed to solve the MPEC. A practical frame example is provided to illustrate the approach

Quantum Criticality of 1D Attractive Fermi Gas

We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gas for all parameter regime in current experiments. From the equation of state we derive universal scaling functions that control whole thermodynamical properties in quantum critical regimes and illustrate physical origin of quantum criticality. It turns out that the critical properties of the system are described by these of free fermions and those of mixtures of fermions with mass $m$ and $2m$. We also show how these critical properties of bulk systems can be revealed from the density profile of trapped Fermi gas at finite temperatures and can be used to determine the T=0 phase boundaries without any arbitrariness.Comment: extended version, 9 pages, 7 eps figures, corrections of few typo

The DSC monitoring of oil melting to follow the oil curing

The drying of an oil paint is due to the polyunsaturations of the oil in the binder. Polyunsaturated oils dry trough an autoxidation process in which the double bonds of linolenic and linoleic acids naturally react with the oxygen present in the atmosphere. The gradual conversion of the liquid oil through a soft gel to a rubbery solid occurs as a result of a multistep free radical chain reaction. During the propagation step, hydroperoxides are formed. A method frequently used to follow the oil curing is the DSC monitoring of the peroxide decomposition peak during time. Since the oil polymerization affects its crystallinity, we propose here an altemative method to asses the oil curing. The melting peak of linseed oil samples is measured at different times of curing and compared with the pro\ufb01le of the peroxide decomposition peak over time. The comparison shows that the two phenomena are strongly correlated and that, when the maximum of the peroxide content is reached, the melting peak disappears. The study of the DSC melting peak is therefore proposed as a valid alternative tool to monitor the curing of an oil paint

Development of a stochastic computational fluid dynamics approach for offshore wind farms

In this paper, a method for stochastic analysis of an offshore wind farm using computational fluid dynamics (CFD) is proposed. An existing offshore wind farm is modelled using a steady-state CFD solver at several deterministic input ranges and an approximation model is trained on the CFD results. The approximation model is then used in a Monte-Carlo analysis to build joint probability distributions for values of interest within the wind farm. The results are compared with real measurements obtained from the existing wind farm to quantify the accuracy of the predictions. It is shown that this method works well for the relatively simple problem considered in this study and has potential to be used in more complex situations where an existing analytical method is either insufficient or unable to make a good prediction

Iterative limit analysis of structures within a scaled boundary finite element framework

This paper presents an iterative elastic analysis approach to determine the collapse load limit of structures. The proposed scheme is based on the use of a modified elastic compensation method, where the structure is modeled within a scaled boundary finite element framework. The formulation takes the general form of polygon scaled boundary finite elements, which overcomes the challenges associated with stress singularities and complex geometries. The approach provides coarse mesh accuracy and numerical stability under incompressibility conditions, and is suitable for large scale problems that often require a large number of iterations to converge to the collapse load solution. A number of successfully solved examples, one of which has been given herein, illustrate the robustness and efficiency of the proposed method to compute the collapse load of structures

Structure of vortices in two-component Bose-Einstein condensates

We develop a three-dimensional analysis of the phase separation of two-species Bose-Einstein condensates in the presence of vorticity within the Thomas-Fermi approximation. We find different segregation features according to whether the more repulsive component is in a vortex or in a vortex-free state. An application of this study is aimed at describing systems formed by two almost immiscible species of rubidium-87 that are commonly used in Bose-Einstein condensation experiments. In particular, in this work we calculate the density profiles of condensates for the same conditions as the states prepared in the experiments performed at JILA [Matthews et al., Phys. Rev. Lett. 83, 2498 (1999)]Comment: 4 pages, 3 figure

Implications of SU(2) symmetry on the dynamics of population difference in the two-component atomic vapor

We present an exact many body solution for the dynamics of the population difference $N_2-N_1$ induced by an rf-field in the two-component atomic cloud characterized by equal scattering lengths. This situation is very close to the actual JILA experiments with the two-component $^{87}$Rb vapor. We show that no intrinsic decoherence exists for $N_2-N_1$, provided the exact SU(2) symmetry holds. This contrasts with finite dissipation of the normal modes even in the presence of the SU(2) symmetry. The intrinsic decoherence for \$N_2-N_1$ may occur as long as deviations from the exact SU(2) symmetry are taken into account. Such decoherence, however, should be characterized by very long times governed by the smallness of the deviations from the symmetry. We suggest testing the evolution of $N_2-N_1$ by conducting echo-type experiments.Comment: 5 RevTex pages, no figures, typos correcte

Frequencies and Damping rates of a 2D Deformed Trapped Bose gas above the Critical Temperature

We derive the equation of motion for the velocity fluctuations of a 2D deformed trapped Bose gas above the critical temperature in the hydrodynamical regime. From this equation, we calculate the eigenfrequencies for a few low-lying excitation modes. Using the method of averages, we derive a dispersion relation in a deformed trap that interpolates between the collisionless and hydrodynamic regimes. We make use of this dispersion relation to calculate the frequencies and the damping rates for monopole and quadrupole mode in both the regimes. We also discuss the time evolution of the wave packet width of a Bose gas in a time dependent as well as time independent trap.Comment: 13 pages, latex fil