Combining All Pairs Shortest Paths and All Pairs Bottleneck Paths Problems

We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call this new problem the All Pairs Shortest Paths for All Flows (APSP-AF) problem. We firstly solve the APSP-AF problem on directed graphs with unit edge costs and real edge capacities in $\tilde{O}(\sqrt{t}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}n^{2.843})$ time, where $n$ is the number of vertices, $t$ is the number of distinct edge capacities (flow amounts) and $O(n^{\omega}) < O(n^{2.373})$ is the time taken to multiply two $n$-by-$n$ matrices over a ring. Secondly we extend the problem to graphs with positive integer edge costs and present an algorithm with $\tilde{O}(\sqrt{t}c^{(\omega+5)/4}n^{(\omega+9)/4}) = \tilde{O}(\sqrt{t}c^{1.843}n^{2.843})$ worst case time complexity, where $c$ is the upper bound on edge costs

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction

Characteristics of liquid cluster ion beam for surface treatment

A liquid cluster ion source, which is an ion source for the cluster beams produced with liquid materials, has been developed for the surface treatment of solid materials. The electrodes were designed for increasing the cluster beam intensity by a computer simulation of beam trajectories. The peaks of the cluster size distributions of the water and ethanol cluster ion beams of 3 atm vapor pressure were approximately at 2.4×103 and 1.6×103 molecules, respectively. The cluster size distributions of ethanol clusters were not sensitive to the variations of the acceleration voltages (Ve) and currents (Ie) of the electrons for ionization when the Ve and Ie were larger than approximately 200 V and 200 mA, respectively

Probability density function of turbulent velocity fluctuation

The probability density function (PDF) of velocity fluctuations is studied experimentally for grid turbulence in a systematical manner. At small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At intermediate distances, where the turbulence is fully developed, the PDF is Gaussian. At large distances, where the turbulence has decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity fluctuations always have Gaussian PDFs. At intermediate distances from the grid, the Fourier transforms are statistically independent of each other. This is the necessary and sufficient condition for Gaussianity of the velocity fluctuations. At small and large distances, the Fourier transforms are dependent.Comment: 7 pages, 8 figures in a PS file, to appear in Physical Review

Observation of the screening signature in the lateral photovoltage of electrons in the Quantum Hall regime

The lateral photovoltage generated in the plane of a two-dimensional electron system (2DES) by a focused light spot, exhibits a fine-structure in the quantum oscillations in a magnetic field near the Quantum Hall conductivity minima. A double peak structure occurs near the minima of the longitudinal conductivity oscillations. This is the characteristic signature of the interplay between screening and Landau quantization.Comment: 4 pages, 4 figures, to be published in Phys. Rev.

Enhancement of piezoelectricity in a mixed ferroelectric

We use first-principles density-functional total energy and polarization calculations to calculate the piezoelectric tensor at zero temperature for both cubic and simple tetragonal ordered supercells of Pb_3GeTe_4. The largest piezoelectric coefficient for the tetragonal configuration is enhanced by a factor of about three with respect to that of the cubic configuration. This can be attributed to both the larger strain-induced motion of cations relative to anions and higher Born effective charges in the tetragonal case. A normal mode decomposition shows that both cation ordering and local relaxation weaken the ferroelectric instability, enhancing piezoelectricity.Comment: 5 pages, revtex, 2 eps figure

A New Class of Resonances at the Edge of the Two Dimensional Electron Gas

We measure the frequency dependent capacitance of a gate covering the edge and part of a two-dimensional electron gas in the quantum Hall regime. In applying a positive gate bias, we create a metallic puddle under the gate surrounded by an insulating region. Charging of the puddle occurs via electron tunneling from a metallic edge channel. Analysis of the data allows direct extraction of this tunneling conductance. Novel conductance resonances appear as a function of gate bias. Samples with gates ranging from 1-170~$\mu$m along the edge display strikingly similar resonance spectra. The data suggest the existence of unexpected structure, homogeneous over long length scales, at the sample edge.Comment: 13 pages (revtex) including 4 figure

The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

Thermodynamics of C incorporation on Si(100) from ab initio calculations

We study the thermodynamics of C incorporation on Si(100), a system where strain and chemical effects are both important. Our analysis is based on first-principles atomistic calculations to obtain the important lowest energy structures, and a classical effective Hamiltonian which is employed to represent the long-range strain effects and incorporate the thermodynamic aspects. We determine the equilibrium phase diagram in temperature and C chemical potential, which allows us to predict the mesoscopic structure of the system that should be observed under experimentally relevant conditions.Comment: 5 pages, 3 figure

Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at http://www.mis.mpg.de/preprints/index.html