Size structure and inequality in a commercial stand of the seaweed gelidium-sesquipedale

The temporal dynamics of the frequency distributions of 2 measures of Gelidium sesquipedale frond size, length and weight, was investigated in a subtidal stand under commercial exploitation. Frond weight/length allometry was highly variable, both seasonally and between years, showing that in this species weight and length cannot be used interchangeably as a measure of frond size. Physical disturbances played a fundamental role in allometric variability. The loss of branches due to commercial harvest and storms reduced the slope of the log weight/log length relationship. During spring the slope increased, indicating the production and growth of lateral branches. Size differences among individuals in the population (inequality) were quantified by 3 statistics: the skewness coefficient (g(1)), the coefficient of variation (CV), and the Gini coefficient (G). Highly significant changes in frond length inequality, but not weight, were shown. These correspond to periods when G. sesquipedale length structure varied due to the combined effects of the demographic parameters that regulate the population (frond recruitment, survival, breakage and growth). Graphical analysis of significantly different length structures revealed that a recruitment peak of vegetatively developed fronds occurred during winter, following periods of high frond mortality and breakage caused by both human (summer harvesting) and natural (late fall storms) disturbances. During late spring and summer, the density of smaller fronds decreased due to mortality and growth into higher size classes. To assess density-dependent regulation processes, such as suppressed growth of smaller fronds and self-thinning, the time variation of both relationships, inequality/mean frond weight and biomass/density, was analysed. Inequality/mean frond weight and biomass/density values decreased from summer to winter and increased to the following summer. The increase of inequality while mean frond weight is increasing is consistent with the asymmetric competition theory on the development of crowded plant stands, and supports the hypothesis that the slower growth of smaller fronds during this period (Santos 1994; Mar. Ecol. Prog. Ser. 107: 295-305) is due to intraspecific competition. The time trajectory of the biomass/density relationship is perpendicular to and lies above the theoretical self-thinning line. Evidence for self-thinning was thus not detected. A conceptual model for the functioning of this population is proposed. Thinning and frond breakage caused by disturbances might be keeping intraspecific competition in these G. sesquipedale crowded stands (up to 18 000 fronds m(-2)) at low levels.info:eu-repo/semantics/publishedVersio

Higher order self-dual models for spin-3 particles in D=2+1D=2+1

In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$ particles carrying both helicities $\pm s$ (parity doublets), such Lagrangians can also be used in $D=3+1$ to describe massive spin-$s$ particles. From this point of view the parity singlets (self-dual models) in $D=2+1$ are the building blocks of real massive elementary particles in $D=3+1$. In the three cases $s=1,\, 3/2,\, 2$ there are $2s$ self-dual models of order $1,2, \cdots, 2s$ in derivatives. In the spin-3 case the 5th order model is missing in the literature. Here we deduce a 5th order spin-3 self-dual model and fill up this gap. It is shown to be ghost free by means of a master action which relates it with the top model of 6th order. We believe that our approach can be generalized to arbitrary integer spin-$s$ in order to obtain the models of order $2s$ and $2s-1$. We also comment on the difficulties in relating the 5th order model with their lower order duals

Experimental Signatures of Fermiophobic Higgs bosons

The most general Two Higgs Doublet Model potential without explicit CP violation depends on 10 real independent parameters. Excluding spontaneous CP violation results in two 7 parameter models. Although both models give rise to 5 scalar particles and 2 mixing angles, the resulting phenomenology of the scalar sectors is different. If flavour changing neutral currents at tree level are to be avoided, one has, in both cases, four alternative ways of introducing the fermion couplings. In one of these models the mixing angle of the CP even sector can be chosen in such a way that the fermion couplings to the lightest scalar Higgs boson vanishes. At the same time it is possible to suppress the fermion couplings to the charged and pseudo-scalar Higgs bosons by appropriately choosing the mixing angle of the CP odd sector. We investigate the phenomenology of both models in the fermiophobic limit and present the different branching ratios for the decays of the scalar particles. We use the present experimental results from the LEP collider to constrain the models.Comment: 23 pages, 18 figures included, newer experimental data include

On the elementary symmetric functions of a sum of matrices

Often in mathematics it is useful to summarize a multivariate phenomenon with a single number and in fact, the determinant -- which is represented by det -- is one of the simplest cases. In fact, this number it is defined only for square matrices and a lot of its properties are very well-known. For instance, the determinant is a multiplicative function, i.e. det(AB)=detA detB, but it is not, in general, an additive function. Another interesting function in the matrix analysis is the characteristic polynomial -- in fact, given a matrix A, this function is defined by $p_A(t)=det(tI-A)$ where I is the identity matrix -- which elements are, up a sign, the elementary symmetric functions associated to the eigenvalues of the matrix A. In the present paper new expressions related with the determinant of sum of matrices and the elementary symmetric functions are given. Moreover, the connection with the Mobius function and the partial ordered sets (poset) is presented. Finally, a problem related with the determinant of sum of matrices is solved

Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduce finite-size effects in some ground state properties; calculations in the grand canonical ensemble together with a local-density approximation (LDA) allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A `phase diagram' in terms of an effective density and the on-site repulsion is proposed, as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative) display detectable signatures of the core-ring transition. Some spin correlation functions are also calculated, and predict the existence N\'eel ordering within Mott cores and rings.Comment: 5 pages, 6 figure

Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late