5,569 research outputs found
Seismic Response of a Linear, 2-D Model of the Marina District
The recorded response of the Marina District of the City of San Francisco to an aftershock of the 1989 Loma Prieta earthquake is simulated using a two-dimensional model of the sedimentary deposits. Even though the response of the Marina is truly three-dimensional, the two-dimensional model successfully captures some important aspects of the response and consequently may be useful for predicting strong ground motion in the Marina District for engineering applications
Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
We present an efficient method for preparing the initial state required by
the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method
can be applied when solving continuous Hermitian eigenproblems, e.g., the
Schroedinger equation, on a discrete grid. We start with a classically obtained
eigenvector for a problem discretized on a coarse grid, and we efficiently
construct, quantum mechanically, an approximation of the same eigenvector on a
fine grid. We use this approximation as the initial state for the eigenvalue
estimation algorithm, and show the relationship between its success probability
and the size of the coarse grid.Comment: 4 page
On a Dirichlet problem with -Laplacian and parametric concave-convex nonlinearity
A homogeneous Dirichlet problem with -Laplace differential operator
and reaction given by a parametric -convex term plus a -concave one is
investigated. A bifurcation-type result, describing changes in the set of
positive solutions as the parameter varies, is proven. Since for
every admissible the problem has a smallest positive solution , both monotonicity and continuity of the map are studied.Comment: 12 pages, comments are welcom
Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation
We analyze the effect of pure additive noise on the long-time dynamics of the
noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability
onset. We show that when the noise is highly degenerate, in the sense that it
acts only on the first stable mode, the solution of the KS equation undergoes
several transitions between different states, including a critical on-off
intermittent state that is eventually stabilized as the noise strength is
increased. Such noise-induced transitions can be completely characterized
through critical exponents, obtaining that both the KS and the noisy Burgers
equation belong to the same universality class. The results of our numerical
investigations are explained rigorously using multiscale techniques.Comment: 4 pages, 4 figure
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