Lithology and palynology of cave floor sediment cores from Wakulla Spring, Wakulla County, Florida

Five short bottom sediment cores taken in Wakulla Spring Wakulla County, Florida, were described lithologically and sampled for palynological study. Four of the cores were recoveredfrom sediments at the spring cave entrance (130 feet water depth). One core was taken in a fossil vertebrate bone bed, 280 feet distance into the main spring cave at a water depth of 240 feet. Sediments in the cores are composed of alternating intervals of quartz sand and calcilitite, containing freshwater diatoms, freshwater mollusk shells and plant remains. The predominant pollen present in all cores consists of a periporate variety typical of the herb families Chenopodiaceae and Amaranthaceae. Arboreal flora, typical of the area surrounding the spring today, represent a very low percentage of thle pollen assemblage in the cores. Clustered Chenopod-Amaranth type pollen observed in one core suggest minimal transport prior to deposition, and indicate that the bottom sediments in the cave may be essentially In situ. An absence of exotic flora suggests a Quaternary age for the sediments. (PDF contains 11 pages.

Possible Lattice Distortions in the Hubbard Model for Graphene

The Hubbard model on the honeycomb lattice is a well known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most six atoms per unit cell as compared to two atoms for the undistorted lattice.Comment: 5 pages, 3 figure

Geology and geomorphology of Florida's coastal marshes

(PDF contains 16 pages.

Selected Cenozoic Benthic Foraminifera from Florida : poster

(1 poster - no publication date on poster, but since early in series likely to be early 1990's)

Energy Cost to Make a Hole in the Fermi Sea

The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.Comment: 4 pages, final version published in Phys. Rev. Let

Earth Systems: the foundation of Florida’s Ecosystems

(1 poster

Common Cenozoic Echinoids from Florida

(1 poster

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Eigenvalue bounds for Schr\"odinger operators with a homogeneous magnetic field

We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.Comment: 12 page

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.Comment: 19 page