A new primal-dual path-following interior-point algorithm for semidefinite optimization

AbstractIn this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, O(nlognϵ), which is as good as the linear analogue

Interior-point methods for P∗(κ)-linear complementarity problem based on generalized trigonometric barrier function

Recently, M.~Bouafoa, et al. investigated a new kernel function which differs from the self-regular kernel functions. The kernel function has a trigonometric Barrier Term. In this paper we generalize the analysis presented in the above paper for $P_{*}(\kappa)$ Linear Complementarity Problems (LCPs). It is shown that the iteration bound for primal-dual large-update and small-update interior-point methods based on this function is as good as the currently best known iteration bounds for these type methods. The analysis for LCPs deviates significantly from the analysis for linear optimization. Several new tools and techniques are derived in this paper.publishedVersio

Multi-scale input-output analysis of consumption-based water resources: Method and application

This work develops a method of multi-scale input-output analysis for the embodied water accounting of an economy. This method can distinguish between the different virtual water contents of imported and local products and is therefore capable of accurately estimating the virtual water that is embodied in trade. As a simplified model rather than a multi-regional input-output analysis, this method substantially minimizes the data requirements. With the support of averaged Eora global embodied water intensity databases for the world and Chinese economies, a three-scale embodied water input-output analysis of the Beijing economy in 2007 has been conducted. Dozens of virtual water flows that relate to the Beijing economy have been identified and analyzed. Only 15% of the total water resources embodied in Beijing's local final demand were from local water withdrawal; 85% were from domestically and internationally imported products. The virtual water import is revealed to play a more important role than physical water transfer in easing Beijing's water shortage. Since the average water use efficiency of the Beijing economy is much higher than that of the Chinese economy but somewhat lower that of the rest of the world, Beijing is suggested to shifting its imports to foreign countries to optimize global water use. The method developed can be useful for water saving strategies for multiple responsible entities holding different opinions, and it can be easily applied to the embodied water accounting of a sub-national or even smaller economic community

Antiflow of kaons in relativistic heavy ion collisions

We compare relativistic transport model calculations to recent data on the sideward flow of neutral strange K^0_s mesons for Au+Au collisions at 6 AGeV. A soft nuclear equation of state is found to describe very well the positive proton flow data measured in the same experiment. In the absence of kaon potential, the K^0 flow pattern is similar to that of protons. The kaon flow becomes negative if a repulsive kaon potential determined from the impulse approximation is introduced. However, this potential underestimates the data which exhibits larger antiflow. An excellent agreement with the data is obtained when a relativistic scalar-vector kaon potential, that has stronger density dependence, is used. We further find that the transverse momentum dependence of directed and elliptic flow is quite sensitive to the kaon potential in dense matter.Comment: 5 pages, Revtex, 4 figure

Blow up criterion for compressible nematic liquid crystal flows in dimension three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.Comment: 22 page

Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations

We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty-Beals paper. We prove the nonlinear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove local in time stability of W^{1, \infty}(\RR^3) solutions where the perturbations are entropy-weak solutions of the EP equations. Finally, we give a uniform (in time) a-priori estimate for entropy-weak solutions of the EP equations

Preparation of new composite membranes for water desalination using electrodialysis

The use of polyethersulfone (PES), an excellent but highly hydrophobic thermoplastic, as a matrix material for ion-exchange membranes was investigated. To make PES ion-exchangeable, sulfonate groups were introduced to the polymer chains by sulfonation reaction with chlorosulfonic acid. The degree of sulfonation of sPES was estimated to be 21%. Preliminary experiments investigated the effect of polyethylene glycol (PEG) and Pluronic F127 as fillers to improve the hydrophilicity of the membranes. Moreover, a lab scale electrodialysis cell has been designed and set up to evaluate the performance of these novel membranes compared to the benchmark of commercial membranes. The results show promising properties of ion-exchange capacity, water uptake, conductivity and hydophilicity from blended membranes, comparable to commercial membranes, though the performance of the prepared membranes did not exceed the commercial one. Further characterization of the transport properties of ion-exchange membranes need to be investigated to be able to understand the effects of the fillers on the performance of the membranes in ED application

K^+ versus \Lambda flow in relativistic heavy-ion collisions

We study $K^+$ and $\Lambda$ flow in heavy-ion collisions at beam energies of about 2A GeV. We present our results in both the `traditional' (i.e., in terms of the average transverse momentum in the reaction plane) as well as `modern' (i.e., in terms of coefficients of the Fourier analysis of azimuthal distributions) methods of flow analysis. We find significant differences between the $K^+$ and the $\Lambda$ flow: while the $\Lambda$ flow is basically similar to that of nucleons, the $K^+$ flow almost disappears. This difference is attributed chiefly to their different mean field potentials in dense matter. The comparisons with the experimental data, as well as theoretical results from independent calculations, indicate clearly the pivotal roles of both $K^+$ and $\Lambda$ medium effects. We emphasize that similar experimental data from independent collaborations are essential for the eventual verification of these medium effects.Comment: RevTeX, 11 pages, including 18 postscript figures, to be published in Nuclear Physics

Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with the supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbation of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler-Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role

Isospin influences on particle emission and critical phenomenon in nuclear dissociation

Features of particle emission and critical point behavior are investigated as functions of the isospin of disassembling sources and temperature at a moderate freeze-out density for medium-size Xe isotopes in the framework of isospin dependent lattice gas model. Multiplicities of emitted light particles, isotopic and isobaric ratios of light particles show the strong dependence on the isospin of the dissociation source, but double ratios of light isotope pairs and the critical temperature determined by the extreme values of some critical observables are insensitive to the isospin of the systems. Values of the power law parameter of cluster mass distribution, mean multiplicity of intermediate mass fragments ($IMF$), information entropy ($H$) and Campi's second moment ($S_2$) also show a minor dependence on the isospin of Xe isotopes at the critical point. In addition, the slopes of the average multiplicites of the neutrons ($N_n$), protons ($N_p$), charged particles ($N_{CP}$), and IMFs ($N_{imf}$), slopes of the largest fragment mass number ($A_{max}$), and the excitation energy per nucleon of the disassembling source ($E^*/A$) to temperature are investigated as well as variances of the distributions of $N_n$, $N_p$, $N_{CP}$, $N_{IMF}$, $A_{max}$ and $E^*/A$. It is found that they can be taken as additional judgements to the critical phenomena.Comment: 9 Pages, 8 figure