%me-dependent solutions of the two-dimensional Chem-Simons gauged nonlinear SchrSdinger equation are investigakd in terms of an initial-value problem. We prove that this Cauchy problem is locally well posed in H2@*), and that global solutions exist in HI(@) provided that the initial data are small enough in L2(R2). On the other hand, under certain conditions ensuring, for example a negative Hamiltonian, solutions blow up in a finite time which only depends on the initial data. The diverging shape of collapsing Structures is finally discussed throughout a self-similar analysis.
A reservoir carbonate core plug has been imaged in 3D across a range of length scales using high resolution X-ray microtomography (µ-CT). Data from the original 40-mm diameter plug was obtained at the vug scale (42 µm resolution) and allows the size, shape and spatial distribution of the disconnected vuggy porosity, φ vug = 3.5% to be measured. Within the imaged volume over 32,000 separate vugs are identified and a broad vug size distribution is measured. Higher resolution images, down to 1.1 µm resolution, on subsets of the plug exhibit interconnected porosity and allow one to measure characteristic, intergranular pore size. Pore scale structure and petrophysical properties (permeability, drainage capillary pressure, formation factor, and NMR response) are derived directly on the highest resolution tomographic dataset. We show that data over a range of porosity can be computed from a single plug fragment. Data for the carbonate core is compared to results derived from 3D images of clastic cores and strong differences noted. Computations of permeability are compared to conventional laboratory measurements on the same core material with good agreement. This demonstrates the feasibility of combining digitized images with numerical calculations to predict properties and derive cross-correlations for carbonate lithologies.
We analyze the shape and stability of localized states in nonlinear cubic media with space-dependent potentials modeling an inhomogeneity. By means of a static variational approach, we describe the ground states and vortexlike stationary solutions, either in dilute atom gases or in optical cavities, with an emphasis on parabolic-type potentials. First, we determine the existence conditions for soliton and vortex structures for both focusing and defocusing nonlinearity. It is shown that, even for a defocusing medium, soliton modes can exist with a confining potential. Second, step potentials and boundedness effects in hollow capillaries are investigated, which both proceed from a similar analysis. Finally, we discuss applications of this procedure to charged vortices in dilute quantum gases and to Bose-Einstein condensates trapped in the presence of a light-induced Gaussian barrier.
A novel modification of the resistive pulse technique (Coulter principle) has been used to investigate how the measured resistance pulse amplitude depends on the off-axis particle position in long pores. By pressure drive, a particle enters a current-carrying pore and an increase in resistance proportional to the particle volume is detected. When the particle exits the pore, the pressure is reversed such that the particle re-enters the pore and the same particle can thus be studied for a long time. In Poiseuille flow, solid spheres migrate to an off-axis equilibrium position and this non-linear hydrodynamic effect has been utilised to study how the measured pulse amplitude from a single particle flowing back and forth through a pore increases when the particle migrates closer to the pore wall. The increase in pulse amplitude corresponding to a radial particle displacement from the pore axis to the wall is found to be less than 10% for all particle and pore sizes studied. This is considerably less than predicted by the off-axis upper-limit theory of Smythe.
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