Dynamical instability criterion for circular (vorton) string loops

Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium (i.e. vorton) state of a closed string loop it is shown that the fundamental axisymmetric ($n=0$) and lowest order ($n=1$) nonaxisymmetric perturbation modes can never be unstable. However, stability for modes of higher order ($n\geq 2$) is found to be non-trivially dependent on the values of the characteristic propagation velocity, $c$ say, of longitudinal perturbations and of the corresponding extrinsic perturbation velocity, $v$ say. For each mode number the criterion for instability is the existence of nonreal roots for a certain cubic eigenvalue equation for the corresponding mode frequency. A very simple sufficient but not necessary condition for reality of the roots and therefore absence of instability is that the characteristic velocity ratio, $c/v$ be greater than or equal to unity. Closer examination of the low velocity (experimentally accessible) nonrelativistic regime shows that in that limit the criterion for instability is just that the dimensionless characteristic ratio $c/v$ be less than a critical value $\chi_c$ whose numerical value is approximately $1\over 2$. In the relativistic regime that is relevant to superconducting cosmic strings the situation is rather delicate, calling for more detailed investigation that is postponed for future work.Comment: 20 page TeX file (with typo corrections and added reference) of manuscript published (with shorter title) in Annals of Physic

15 Years of New Growth Economics: What Have We Learnt?

Paul Romer’s paper Increasing Returns and Long Run Growth, now 15 years old, led to resurgence in the research on economic growth. Since then, growth literature has expanded dramatically and has shifted the research focus of many generations of macroeconomists. The new line of work has emphasized the role of human capital, social and political variables, as well as the importance of institutions as driving forces of long-run economic growth. This paper presents an insight into the theoretical and empirical literature of the past fifteen years, highlighting the most significant contributions for our understanding of economics.

15 years of new growth economics: What have we learnt?

This paper evaluates the empirical and theoretical contributions of the Economic Growth Literature since the publication of Paul Romer’s seminal paper in 1986.Economic gowth, technological progress, empirics of growth

I just ran four million regressions

In this paper I try to move away from the Extreme Bounds method of identifying ``robust'' empirical relations in the economic growth literature. Instead of analyzing the extreme bounds of the estimates of the coefficient of a particular variable, I analyze the entire distribution. My claim in this paper is that, if we do this, the picture emerging from the empirical growth literature is not the pessimistic ``Nothing is Robust'' that we get with the extreme bound analysis. Instead, we find that a substantial number of variables can be found to be strongly related to growth.Economic growth, growth regressions, empirical determinants of economic growth

Dynamics of Cosmic Necklaces

We perform numerical simulations of cosmic necklaces (systems of monopoles connected to two strings each) and investigate the conditions under which monopoles annihilate. When the total monopole energy is large compared to the string energy, we find that the string motion is no longer periodic, and thus the strings will be chopped up by self intersection. When the total monopole energy is much smaller than the string energy, the string motion is periodic, but that of the monopoles is not, and thus the monopoles travel along the string and annihilate with each other