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

The Character and Determinants of Corporate Capital Gains

This paper analyzes how corporate capital gains taxes affect the capital gain realization decisions of firms. The paper outlines the tax treatment of corporate capital gains, the consequent incentives for firms with gains and losses, the efficiency consequences of these taxes in the context of other taxes and capital market distortions, and the response of firms to these incentives. Despite receiving limited attention, corporate capital gain realizations have averaged 30 percent of individual capital gain realizations over the last fifty years and have increased dramatically in importance over the last decade. By 1999, the ratio of net long-term capital gains to income subject to tax was 21 percent and was distributed across a variety of industries suggesting the importance of realization behavior to corporate financing decisions. Time-series analysis of aggregate realization behavior demonstrates that corporate capital gains taxes impact realization behavior significantly. Similarly, an analysis of firm-level investment and property, plant, and equipment (PPE) disposal decisions and gain recognition behavior similarly suggests an important role for these taxes in determining when firms raise money by disposing of assets and realizing gains.Capital gains; capital gains taxation; corporate taxation;

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

Clonal Interference, Multiple Mutations, and Adaptation in Large Asexual Populations

Two important problems affect the ability of asexual populations to accumulate beneficial mutations, and hence to adapt. First, clonal interference causes some beneficial mutations to be outcompeted by more-fit mutations which occur in the same genetic background. Second, multiple mutations occur in some individuals, so even mutations of large effect can be outcompeted unless they occur in a good genetic background which contains other beneficial mutations. In this paper, we use a Monte Carlo simulation to study how these two factors influence the adaptation of asexual populations. We find that the results depend qualitatively on the shape of the distribution of the effects of possible beneficial mutations. When this distribution falls off slower than exponentially, clonal interference alone reasonably describes which mutations dominate the adaptation, although it gives a misleading picture of the evolutionary dynamics. When the distribution falls off faster than exponentially, an analysis based on multiple mutations is more appropriate. Using our simulations, we are able to explore the limits of validity of both of these approaches, and we explore the complex dynamics in the regimes where neither are fully applicable.Comment: 24 pages, 5 figure

Ultracold neutron depolarization in magnetic bottles

We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magneto-gravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an extension of the semi-classical Majorana approach as well as an approximate quantum mechanical analysis, both pioneered by Walstrom et al. [Nucl. Instr. Meth. Phys. Res. A 599, 82 (2009)]. In contrast with this previous work we do not restrict the analysis to purely vertical modes of neutron motion. The lateral motion is shown to cause the predominant depolarization loss in a magnetic storage trap. The system studied also allowed us to estimate the depolarization loss suffered by ultracold neutrons totally reflected on a non-magnetic mirror immersed in a magnetic field. This problem is of preeminent importance in polarized neutron decay studies such as the measurement of the asymmetry parameter A using ultracold neutrons, and it may limit the efficiency of ultracold neutron polarizers based on passage through a high magnetic field.Comment: 18 pages, 6 figure

Spin flip loss in magnetic storage of ultracold neutrons

We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magneto-gravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an approximate quantum mechanical analysis such as pioneered by Walstrom \emph{et al} [Nucl. Instrum. Methods Phys. Res. A 599, 82 (2009)]. Our analysis is not restricted to purely vertical modes of neutron motion. The lateral motion is shown to cause the predominant depolarization loss in a magnetic storage trap.Comment: 12 pages, 3 figures, for Proceedings of Neutron Lifetime Worksho

Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\"odinger equation

Pendlebury $\textit{et al.}$ [Phys. Rev. A $\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.Comment: 11 pages, 4 figure