We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D b...

A computational method of reduced complexity is developed for simulating vascular hemodynamics by combination of one-dimensional (1D) wave propagation models for the blood vessels with zero-dimensional (0D) lumped models for the microcirculation. Despite the reduced dimension, current algorithms used to solve the model equations and simulate pressure and flow are rather complex, thereby limitin...

We model long-range correlations of nucleotides in the human DNA sequence using the long-range one-dimensional (1D) Ising model. We show that, for distances between 10(3) and 10(6) bp, the correlations show a universal behavior and may be described by the non-mean-field limit of the long-range 1D Ising model. This allows us to make some testable hypothesis on the nature of the interaction betwe...

We provide an exposition of the hypergraph models for parallel sparse matrix-vector multiplies based on one-dimensional (1D) matrix partitioning. Our aim is to emphasize the expressive power of the hypergraph models. We first set forth an elementary hypergraph model in which vertices represent the data elements of a matrix-vector multiply operation and nets encode data dependencies. We then app...

We study a simple model of a quantum Hall system with the electrons confined to a linear, narrow channel. The system is mapped to a 1D system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. In a previous paper (Part I) we studied this mapping at the microscopic level, and discussed the r...

Some aspects of physics on interacting fermions in 1D are discussed in a tutoriallike manner. We begin by showing that the non-analytic corrections to the Fermiliquid forms of thermodynamic quantities result from essentially 1D collisions embedded into a higher-dimensional phase space. The role of these collisions increases progressively as dimensionality is reduced until, finally, they lead to...

We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the random discrete nonlinear Schrödinger equation, appearing with a finite probability for a given initial condition with sufficiently small norm. Numerical support ...

We investigate the scaling properties of the excitation energies and transition amplitudes of the one-dimensional spin-1 2 antiferromagnetic Heisenberg model exposed to an external perturbation. Two types of perturbations are discussed in detail: a staggered field and a dimerized field.

Aims. The knowledge of how the specific intensity is distributed over the stellar disk is crucial for interpreting the light curves of extrasolar transiting planets, double-lined eclipsing binaries, and other astrophysical phenomena. To provide theoretical inputs for light curve modelling codes, we present new calculations of limb-darkening coefficients for the spherically symmetric phoenixmode...

In areas that are occasionally inundated by floods, it is essential to know the quantity and density of vegetation that can be allowed while avoiding flooding beyond the intended floodplains. An unsteady flow model was developed for a channel with vegetated floodplains, to take into account the retention effects of the vegetated areas on flood wave conveyance. A one-dimensional (1D) unsteady fl...