HARVESTING PROCEDURES WITH MANAGEMENT POLICY IN ITERATIVE DENSITY-DEPENDENT POPULATION MODELS

This paper analyzes harvesting in simple one species iterative density-dependent population models. Several harvest management policies are considered, including a constant effort policy, an on-off constant harvest policy, and several policies that include protective strategies. Results for quadratic, Ricker, and Beverton-Holt growth functions are contrasted. It is found that even for the Beverton-Holt case, there are parameter regions where periodic or chaotic behavior can occur under certain harvest policies. In fact, regions of stability and irregularity can alternate.     

Novel motifs for magnetic exchange interactions as exemplified in one dimensional magnets based on the FeCl3-α-di-imine system: Nuclear gamma resonance evidence of slow paramagnetic relaxation and 3D-ordering

The extremes of single ion slow paramagnetic relaxation and cooperative 3D-antiferromagnetic order are exemplified in a series of structurally characterized complexes based on the anhydrous FeCl₃-α-di-imine system. “Soft” Cl−Cl contacts, C−C (π-π) and hydrogen bonding interactions are found to lead to surprisingly strong magnetic exchange among five and six coordinate high-spin iron III monomers. The latter form the building blocks of novel “double chain” polymer magnets held together via the preceding “weak” interactions.     

Crumpling a thin sheet

Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled material decreases logarithmically in time for periods up to three weeks. We also find hysteretic behavior when measuring the compression as a function of applied force. By using a pretreating protocol, we control this hysteresis and find reproducible scaling behavior for the size of the crumpled material as a function of the applied force.     

Instability of the Kaluza-Klein vacuum

It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum.     

Chiral symmetry,the 1/N expansion and the SU(N) thirring model

In the two-dimensional SU(N) Thirring model, the 1/N expansion seems to predict spontaneous breaking of the continuous chiral symmetry. This is impossible in two-dimensions. Reasoning along the lines of Berezinski, Kosterlitz and Thouless for the two-dimensional XY model, we argue that, in fact, rather than showing long-range order, $\text{〈}\text{ψ}\text{ψ(x)}\text{ψ}\text{ψ(0)〉}$ vanishes in this model as |x|^?1/N at large |x|. The 1/N expansion is, in fact, a rather good guide to the properties of this model.     

Elliptic genera and quantum field theory

It is shown that in elliptic cohomology — as recently formulated in the mathematical literature — the supercharge of the supersymmetric nonlinear signa model plays a role similar to the role of the Dirac operator inK-theory. This leads to several insights concerning both elliptic cohomology and string theory. Some of the relevant calculations have been done previously by Schellekens and Warner in a different context.Supported in part by NSF grants PHY 80-19754 and PHY 86-16129     

Gauge theories, vertex models, and quantum groups

It is known that the Jones polynomial of knot theory, and its generalizations, are closely related to the integrable “vertex models” of two-dimensional statistical mechanics, and to quantum groups. In this paper, an attempt is made to show on a priori grounds, starting only from general covariance of three-dimensional Chern-Simons gauge theory and two-dimensional “duality”, why this must be so.     

Eigenvalue inequalities for fermions in gauge theories

We show that QCD with a sufficient number of fermions of zero bare mass has physical massless particles. That result also follows from triangle anomalies, so only our method is novel. Our method involves proving special cases of recently conjectured paramagnetic inequalities for fermions. The proofs are simple applications of the Atiyah-Patodi-Singer theorem on spectral flow.Supported in part by the National Science Foundation Grant No. PHY80-19754Supported in part by DOE Grant No. DE-AC02-76ER02220