The spectral shift function and Levinson's theorem for quantum star graphs

We consider the Schr\"odinger operator on a star shaped graph with $n$ edges joined at a single vertex. We derive an expression for the trace of the difference of the perturbed and unperturbed resolvent in terms of a Wronskian. This leads to representations for the perturbation determinant and the spectral shift function, and to an analog of Levinson's formula

Use of Phosphoric Acid and Furfuryl Alcohol for Soil Stabilization

This paper presents results of an investigation of the effects of phosphoric acid and furfuryl alcohol on the resistance and strengths of a clayey soil and of a sandy soil. Results indicate that greater water resistance and higher strengths can be obtained with both soils by using the admixtures. For the sandy soil, a certain optimum amount of phosphoric acid gives the maximum strengths for all furfuryl alcohol contents. The stabilization mechanism for the clayey soil is thought to be a combination of the formation of phosphoric gels and of a resin product of a furfuryl alcohol polymerization reaction. The mechanism for the sandy soil is the formation of the polymerization resin product

Use of Phosphates in Soil Stabilization

The use of phosphates for stabilizing soil to be used for road building is a new development. Lyons (1) apparently was one of the first to have appreciated the possibility. He reports that compacted plastic clay soils containing about 2 per cent phosphoric acid have greatly improved resistance to water and weathering, but he gives no explanation of the mechanism of soil-phosphoric acid stabilization. In agriculture it has been known for some time that phosphates are fixed in soil (2). It is also known that sodium phosphates may be used to disperse soils in water for particle size analysis (3). This paper presents a tentative explanation, based on limited experimental evidence, of the mechanism of soil stabilization with phosphates

The role of the nature of the noise in the thermal conductance of mechanical systems

Focussing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the thermal conductance. For white noises, we prove that the L\'evy-It\^o composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a non-equilibrium linearly coupled chain, which signals the independence between mechanical and thermodynamical properties. On the other hand, for the non-linearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.Comment: 9 pages, 2 figures. To be published in Physical Review

Asymptotic behaviour of dam break flow for small times

Two dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained

Hybrid analytical and numerical approach for modeling fluid flow in simplified three-dimensional fracture networks

<jats:p>Modeling fluid flow in three-dimensional fracture networks is required in a wide variety of applications related to fractured rocks. Numerical approaches developed for this purpose rely on either simplified representations of the physics of the considered problem using mesh-free methods at the fracture scale or complex meshing of the studied systems resulting in considerable computational costs. Here, we derive an alternative approach that does not rely on a full meshing of the fracture network yet maintains an accurate representation of the modeled physical processes. This is done by considering simplified fracture networks in which the fractures are represented as rectangles that are divided into rectangular subfractures such that the fracture intersections are defined on the borders of these subfractures. Two-dimensional analytical solutions for the Darcy-scale flow problem are utilized at the subfracture scale and coupled at the fracture-network scale through discretization nodes located on the subfracture borders. We investigate the impact of parameters related to the location and number of the discretization nodes on the results obtained, and we compare our results with those calculated using reference solutions, which are an analytical solution for simple configurations and a standard finite-element modeling approach for complex configurations. This work represents a first step towards the development of 3D hybrid analytical and numerical approaches where the impact of the surrounding matrix will be eventually considered.</jats:p&gt

Metalorganic chemical vapor deposition growth and thermal stability of the AllNN/GaN high electron mobility transistor structure

Cataloged from PDF version of article.The AlxIn1-xN barrier high electron mobility transistor (HEMT) structure has been optimized with varied barrier composition and thickness grown by metalorganic chemical vapor deposition. After optimization, a transistor structure comprising a 7 nm thick nearly lattice-matched Al0.83In0.17 N barrier exhibits a sheet electron density of 2.0 x 10(13) cm(-2) with a high electron mobility of 1540 cm(2) V-1 s(-1). AnAl(0.83)In(0.17)N barrier HEMT device with 1 mu m gate length provides a current density of 1.0 A mm(-1) at V-GS = 0 V and an extrinsic transconductance of 242 mS mm(-1), which are remarkably improved compared to that of a conventional Al0.3Ga0.7N barrier HEMT. To investigate the thermal stability of the HEMT epi-structures, post-growth annealing experiments up to 800 degrees C have been applied to Al0.83In0.17N and Al0.3Ga0.7N barrier heterostructures. As expected, the electrical properties of an Al0.83In0.17N barrier HEMT structure showed less stability than that of an Al0.3Ga0.7N barrier HEMT to the thermal annealing. The structural properties of Al0.83In0.17N/GaN also showed more evidence for decomposition than that of the Al0.3Ga0.7N/GaN structure after 800 degrees C post-annealing

An analysis of integrative outcomes in the Dayton peace negotiations

The nature of the negotiated outcomes of the eight issues of the Dayton Peace Agreement was studied in terms of their integrative and distributive aspects. in cases where integrative elements were Sound, further analysis was conducted by concentrating on Pruitt's five types of integrative solutions: expanding the pie, cost cutting, non-specific compensation, logrolling, and bridging. The results showed that real world international negotiations can arrive at integrative agreements even when they involve redistribution of resources tin this case the redistribution of former Yugoslavia). Another conclusion was that an agreement can consist of several distributive outcomes and several integrative outcomes produced by different kinds of mechanisms. Similarly, in single issues more than one mechanism can be used simultaneously. Some distributive bargaining was needed in order to determine how much compensation was required. Finally, each integrative formula had some distributive aspects as well

Surface Roughness and Effective Stick-Slip Motion

The effect of random surface roughness on hydrodynamics of viscous incompressible liquid is discussed. Roughness-driven contributions to hydrodynamic flows, energy dissipation, and friction force are calculated in a wide range of parameters. When the hydrodynamic decay length (the viscous wave penetration depth) is larger than the size of random surface inhomogeneities, it is possible to replace a random rough surface by effective stick-slip boundary conditions on a flat surface with two constants: the stick-slip length and the renormalization of viscosity near the boundary. The stick-slip length and the renormalization coefficient are expressed explicitly via the correlation function of random surface inhomogeneities. The effective stick-slip length is always negative signifying the effective slow-down of the hydrodynamic flows by the rough surface (stick rather than slip motion). A simple hydrodynamic model is presented as an illustration of these general hydrodynamic results. The effective boundary parameters are analyzed numerically for Gaussian, power-law and exponentially decaying correlators with various indices. The maximum on the frequency dependence of the dissipation allows one to extract the correlation radius (characteristic size) of the surface inhomogeneities directly from, for example, experiments with torsional quartz oscillators.Comment: RevTeX4, 14 pages, 3 figure