A clarification of the Goodwin model of the growth cycle

We show that there is a difficulty in the original Goodwin model which isalso found in some more recent applications. In it both the labour share and theproportion employed can exceed unity, properties which are untenable. However, weshow that the underlying dynamic structure of the model can be reformulated toensure that these variables cannot exceed unity. An illustrative example extends theoriginal model, and we argue it is both plausible and satisfies the necessary unit boxrestrictions. We show that there is a difficulty in the original Goodwin model which isalso found in some more recent applications. In it both the labour share and theproportion employed can exceed unity, properties which are untenable. However, weshow that the underlying dynamic structure of the model can be reformulated toensure that these variables cannot exceed unity. An illustrative example extends theoriginal model, and we argue it is both plausible and satisfies the necessary unit boxrestrictions

Microscale application of column theory for high resolution force and displacement sensing

We present the design, fabrication and experimental validation of a novel device that exploits the amplification of displacement and attenuation of structural stiffness in the post-buckling deformation of slender columns to obtain pico-Newton force and nanometer displacement resolution even under an optical microscope. The extremely small size, purely mechanical sensing scheme and vacuum compatibility of the instrument makes it compatible with existing visualization tools of nanotechnology. The instrument has a wide variety of potential applications ranging from electro-mechanical characterization of one dimensional solids to single biological cells

Solar Gamma Rays Powered by Secluded Dark Matter

Secluded dark matter models, in which WIMPs annihilate first into metastable mediators, can present novel indirect detection signatures in the form of gamma rays and fluxes of charged particles arriving from directions correlated with the centers of large astrophysical bodies within the solar system, such as the Sun and larger planets. This naturally occurs if the mean free path of the mediator is in excess of the solar (or planetary) radius. We show that existing constraints from water Cerenkov detectors already provide a novel probe of the parameter space of these models, complementary to other sources, with significant scope for future improvement from high angular resolution gamma-ray telescopes such as Fermi-LAT. Fluxes of charged particles produced in mediator decays are also capable of contributing a significant solar system component to the spectrum of energetic electrons and positrons, a possibility which can be tested with the directional and timing information of PAMELA and Fermi.Comment: 22 pages, 3 figure

Homotopy Analysis Approach of Boussinesq Equation for Infiltration Phenomenon in Unsaturated Porous Medium.

oai:ojs.pkp.sfu.ca:article/11Boussinesq’s equation is one-dimensional nonlinear partial differential equation which represents the infiltration phenomenon. This equation is frequently used to study the infiltration phenomenon in unsaturated porous medium. Infiltration is the process in which the groundwater of the water reservoir has entered in the unsaturated soil through vertical permeable wall. An approximate analytical solution of nonlinear partial differential equation is presented by homotopy analysis method. The convergence of homotopy analysis solution is discussed by choosing proper value of convergence control parameter. The solution represents the height of free surface of infiltrated water