7,211 research outputs found

    Stability of Attached Transonic Shocks in Steady Potential Flow past Three-Dimensional Wedges

    Full text link
    We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the perturbation is away from the wedge edge in the previous results is removed. One of the key ingredients is to identify a "good" direction of the boundary operator of a boundary condition of the shock along the wedge edge, based on the non-obliqueness of the boundary condition for the weak shock on the edge. With the identification of this direction, an additional boundary condition on the wedge edge can be assigned to make sure that the shock is attached on the edge and linearly stable under small perturbation. Based on the linear stability, we introduce an iteration scheme and prove that there exists a unique fixed point of the iteration scheme, which leads to the global existence and nonlinear structural stability of the attached weak transonic shock. This approach is based on neither the hodograph transformation nor the spectrum analysis, and should be useful for other problems with similar difficulties.Comment: 28 Pages; 2 figure

    Scaling in the distribution of intertrade durations of Chinese stocks

    Full text link
    The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis qq-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the qq-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the qq-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.Comment: 16 elsart pages including 3 eps figure

    Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws

    Full text link
    We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the L1L^1-estimate between the entropy solution and the geometric optics expansion function is bounded by O(ε2)O(\varepsilon^2), {\it independent of} the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation.Comment: 30 pages, 2 figure

    Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations

    Full text link
    We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in C1,1C^{1,1} and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent from the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, have been clarified.Comment: 32 pages, 1 figure. arXiv admin note: text overlap with arXiv:0907.3276 by other author

    Bandlimited wavelets

    Get PDF
    Master'sMASTER OF SCIENC

    Dynamics of Order Parameter in Photoexcited Peierls Chain

    Get PDF
    The photoexcited dynamics of order parameter in Peierls chain is investigated by using a microscopic quantum theory in the limit where the hot electrons may establish themselves into a quasi-equilibrium state described by an effective temperature. The optical phonon mode responsible for the Peierls instability is coupled to the electron subsystem, and its dynamic equation is derived in terms of the density matrix technique. Recovery dynamics of the order parameter is obtained, which reveals a number of interesting features including the change of oscillation frequency and amplitude at phase transition temperature and the photo-induced switching of order parameter.Comment: 5 pages, 3 figure

    Possible pi-phase shift at interface of two pnictides with antiphase s-wave pairing

    Get PDF
    We examine the nature of Josephson junction between two identical Fe-pnictides with anti-phase s-wave pairing. pi-phase shift is found if the junction barrier is thick and the two Fe-pnictides are oriented in certain directions relative to the interface. Our theory provides a possible explanation for the observed half integer flux quantum transitions in a niobium/polycrystal NdFeAsO loop, and attributes the pi-phase shift to intergrain junctions of Fe-pnictides.Comment: 4 pages, 2 figure
    corecore