Interaction of point sources and vortices for incompressible planar fluids

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.Comment: 9 page

Data on Apollo 11 and 12 samples. Speculations on petrologic differentiation Final report

Petrologic and mineralogic studies of Apollo 11 and 12 lunar rock

Service user leadership: training and development for service users to take the lead

Purpose – This paper outlines the concept of service user leadership and both describes and reflects on an accredited training programme that enables mental health service users to take a leadership role. Design/methodology/approach – The authors argue for a service user leadership approach and the training programme is reviewed by previous participants Findings – Service users can take on a leadership role if they are given suitable and relevant training and development opportunities. Service user led training can be transformational. Practical implications – Commissioners of mental health services should consider how to support service user leadership programmes, which can reach places and achieve outcomes that traditional mental health services are unable to attain. Originality/value – The concept of service user leadership is relatively new and the training programme described in this paper is both original and highly valued by participants with many significant outcomes. Keywords Service user leadership, Peer support, Empowerment, Service user involvement, Confidence, Wellbeing, Leadership, Trainin

Effect of surface roughness on the microwave emission from soils

The effect of surface roughness on the brightness temperature of a moist terrain was studied through the modification of Fresnel reflection coefficient and using the radiative transfer equation. The modification involves introduction of a single parameter to characterize the roughness. It is shown that this parameter depends on both the surface height variance and the horizontal scale of the roughness. Model calculations are in good quantitative agreement with the observed dependence of the brightness temperature on the moisture content in the surface layer. Data from truck mounted and airborne radiometers are presented for comparison. The results indicate that the roughness effects are greatest for wet soils where the difference between smooth and rough surfaces can be as great as 50K

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Microwave soil moisture measurements and analysis

An effort to develop a model that simulates the distribution of water content and of temperature in bare soil is documented. The field experimental set up designed to acquire the data to test this model is described. The microwave signature acquisition system (MSAS) field measurements acquired in Colby, Kansas during the summer of 1978 are pesented

Completeness of the Coulomb scattering wave functions

Completeness of the eigenfunctions of a self-adjoint Hamiltonian, which is the basic ingredient of quantum mechanics, plays an important role in nuclear reaction and nuclear structure theory. However, until now, there was no a formal proof of the completeness of the eigenfunctions of the two-body Hamiltonian with the Coulomb interaction. Here we present the first formal proof of the completeness of the two-body Coulomb scattering wave functions for repulsive unscreened Coulomb potential. To prove the completeness we use the Newton's method [R. Newton, J. Math Phys., 1, 319 (1960)]. The proof allows us to claim that the eigenfunctions of the two-body Hamiltonian with the potential given by the sum of the repulsive Coulomb plus short-range (nuclear) potentials also form a complete set. It also allows one to extend the Berggren's approach of modification of the complete set of the eigenfunctions by including the resonances for charged particles. We also demonstrate that the resonant Gamow functions with the Coulomb tail can be regularized using Zel'dovich's regularization method.Comment: 12 pages and 1 figur

Influence of branch points in the complex plane on the transmission through double quantum dots

We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S-matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.Comment: 30 pages, 14 figure