The Specific Heat of a Ferromagnetic Film.

We analyze the specific heat for the $O(N)$ vector model on a $d$-dimensional film geometry of thickness $L$ using ``environmentally friendly'' renormalization. We consider periodic, Dirichlet and antiperiodic boundary conditions, deriving expressions for the specific heat and an effective specific heat exponent, \alpha\ef. In the case of $d=3$, for $N=1$, by matching to the exact exponent of the two dimensional Ising model we capture the crossover for \xi_L\ra\infty between power law behaviour in the limit {L\over\xi_L}\ra\infty and logarithmic behaviour in the limit {L\over\xi_L}\ra0 for fixed $L$, where $\xi_L$ is the correlation length in the transverse dimensions.Comment: 21 pages of Plain TeX. Postscript figures available upon request from [email protected]

Erwin Schrödinger and quantum wave mechanics

The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.Publisher PDFPeer reviewe

Mavora : development of a planning process for reconciliation of interests in wilderness

Published by Centre for Resource Management for Tussock Grasslands and Mountain Lands Institute Lincoln College, New Zealand, September 1982.The Mavora Lakes area has been a subject of regional interest and some controversy for a number of years. Geographically, the Mavora is intermediate between an acknowledged zone of preservation and a zone of land development. Historically it represents a zone of interaction between different agency interests, notably those of the New Zealand Forest Service and those of both the nature conservation and pastoral administration and development arms of the Department of Lands and Survey. Extensive pastoralism as private enterprise has yielded ground in the district to pastoral development and farm settlement. The limits to this process have tended to be set by progressive experience on the land available for farm settlement. A working plan had been drafted for the adjacent Snowdon Forest. More active management planning for lands administered separately by these two major central government agencies served to bring into sharper contrast any differences between such development proposals if they remained ineffectively co-ordinated. Meanwhile the long-valued fishery resource of the Mavora Lakes and the Mararoa River has itself commanded greater attention because of increased use by anglers and the improved road access to the area which has itself increased boating and other shoreline recreation. While discharge from the lakes in the Mararoa River is being directed down-stream into Manapouri for power production, some thought has been given to using it in part to augment the summer low flows of the Oreti to Invercargill. Different communities of interest show varying degrees of support and aversion for the different kinds of resource use outlined above. Decisions are needed to determine the optimal use of resources before any further development which may irreversibly change the resources and their character

Field Theory Entropy, the HH-theorem and the Renormalization Group

We consider entropy and relative entropy in Field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized $H$ theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions.Comment: 25 pages, plain TeX (macros included), 6 ps figures. Addition in title. Entropy of cutoff Gaussian model modified in section 4 to avoid a divergence. Therefore, last figure modified. Other minor changes to improve readability. Version to appear in Phys. Rev.

Candidates for giant lobes projecting from the LBV stars P Cygni and R 143

Deep, wide-field, continuum-subtracted, images in the light of the Halpha+[NII] 6548 & 6584 A and [O III] 5007 A nebular emission lines have been obtained of the environment of the Luminous Blue Variable (LBV) star P Cygni. A previously discovered, receding, nebulous filament along PA 50 deg has now been shown to extend up to 12' from this star. Furthermore, in the light of [O III] 5007 A, a southern counterpart is discovered as well as irregular filaments on the opposite side of P Cygni. Line profiles from this nebulous complex indicate that this extended nebulosity is similar to that associated with middle-aged supernova remnants. However, there are several indications that it has originated in P Cygni and is not just a chance superposition along the same sight-line. This possibility is explored here and comparison is made with a new image of the LBV star R 143 in the LMC from which similar filaments appear to project. The dynamical age of the P Cygni giant lobe of ~5x10^{4} yr is consistent with both the predicted and observed durations of the LBV phases of 50M stars after they have left the main sequence. Its irregular shape may have been determined by the cavity formed in the ambient gas by the energetic wind of the star, and shaped by a dense torus, when on the main sequence. The proper motion and radial velocity of P Cygni, with respect to its local environment, could explain the observed angular and kinematical shifts of the star compared with the giant lobe.Comment: 7 pages, 3 figures, accepted for publication in A&

Topological Phase Transitions and Holonomies in the Dimer Model

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general bond activities we find that the phase transition in this model is a topological one, where the torus degenerates and its modular parameter becomes real at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion.Comment: 7 pages, 4 figures. Minor corrections with additional figure

An ab initio Calculation of the Universal Equation of State for the O(N) Model

Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity properties in the limits $x\to 0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on a phenomenological scaling ansatz the scaling function is derived solely from the underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$ which exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the strong coupling fixed point associated with the Goldstone modes on the coexistence curve. We give explicit results for N=2, 3 and 4 to one-loop order and compare with known results.Comment: 12 pages, to appear in Journal of Physics

Dimensional Crossover in the Large N Limit

We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover scaling forms for the free energy and the equation of state. We compare the results obtained using ``environmentally friendly'' renormalization with those found using a direct, non-renormalization group approach. A set of effective critical exponents are calculated and scaling laws for these exponents are shown to hold exactly, thereby yielding non-trivial relations between the various thermodynamic scaling functions.Comment: 25 pages of PlainTe

Virtual Design of a Four-Bed Molecular Sieve for Exploration

Aboard the International Space Station, CO2 is removed from the cabin atmosphere by a four-bed molecular sieve (4BMS) process called the Carbon Dioxide Removal Assembly (CDRA).1 This 4BMS process operates by passing the CO2-laden air through a desiccant bed to remove any humidity and then passing the dried air through a sorbent bed to remove the CO2. While one pair of beds is in use, the other pair is thermally regenerated to allow for continuous CO2 removal