Surface water dynamics of shallow lakes following wildfire in boreal Alaska

Thesis (M.S.) University of Alaska Fairbanks, 2013Wildfire is ubiquitous to interior Alaska and is the primary large-scale disturbance regime affecting thawing permafrost and ecosystem processes in boreal forests. Since surface and near surface hydrology is strongly affected by permafrost occurrence, and wildfire can consume insulating organic layers that partially control the thickness of the active layer overlying permafrost, changes in the active layer thickness following fire may mark a distinct change in surface hydrology. In this study, we examined surface area dynamics of lakes following wildfire in four regions of Interior Alaska during a 25-year period from 1984 - 2009. We compared the surface water dynamics of lakes in burned areas relative to lakes in adjacent unburned (control) areas. Lake area changes in the short-term (0-5 years), mid-term (5-10 years), and long-term (>10 years) were analyzed. Burn severity, as a function of radiant surface temperature change, was also explored. Surface water changes were greatest during the short-term (0-5 years) period following fire, where burn lakes increased 10% and control lakes decreased -8% (P=0.061). Over the 5-10 year post-fire period, there was no significant difference in lake dynamics within burned areas relative to control unburned areas. On average, there was an 18 percent decrease in surface water within burned areas over the >10 year post fire time period, while unburned control lakes averaged a 1 percent decline in surface water. The long term declining trend within burned areas may have been due to talik expansion and/or increased evapotranspiration with revegetation of broadleaf plants. Fire had the greatest effect on radiant surface temperature within two years of a fire, where radiant temperatures increased 3-7°C in the most severely impacted areas. Temperature differences between burn and control areas remained less than 1°C as vegetation reestablished. There was no correlation between radiant temperature change and decreasing lake area change. Conversely, there was a trend between lake area differences increasing in size and increases in temperature. While fire displayed the greatest effect on lake area in the short-term, a combination of fire, climate, and site-specific conditions dominate long-term lake area dynamics in Alaska boreal forest

Langevin Thermostat for Rigid Body Dynamics

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the NVT distribution in a simulation of rigid molecules. We propose simple, quasi-symplectic second-order numerical integrators and test their performance on the TIP4P model of water. We also investigate the optimal choice of thermostat parameters.Comment: 15 pages, 13 figures, 1 tabl

Electron-vibration coupling constants in positively charged fullerene

Recent experiments have shown that C60 can be positively field-doped. In that state, fullerene exhibits a higher resistivity and a higher superconducting temperature than the corresponding negatively doped state. A strong intramolecular hole-phonon coupling, connected with the Jahn-Teller effect of the isolated positive ion, is expected to be important for both properties, but the actual coupling strengths are so far unknown. Based on density functional calculations, we determine the linear couplings of the two a_g, six g_g, and eight h_g vibrational modes to the H_u HOMO level of the C60 molecule. The couplings predict a D_5 distortion, and an H_u vibronic ground state for C60^+. They are also used to generate the dimensionless coupling constant which controls the superconductivity and the phonon contribution to the electrical resistivity in the crystalline phase. We find that is 1.4 times larger in positively-charged C60 than in the negatively-doped case. These results are discussed in the context of the available transport data and superconducting temperatures. The role of higher orbital degeneracy in superconductivity is also addressed.Comment: 22 pages - 3 figures. This revision includes few punctuation corrections from proofreadin

The s=1/2s=1/2 Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters

The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using the permutational and spin inversion symmetries of the Hamiltonian the low energy spectrum is calculated for all the irreducible representations of the symmetry group of each cluster. Frustration and connectivity result in non-trivial low energy properties, with the lowest excited states being singlets except for $n=28$. Same hexagon and same pentagon correlations are the most effective in the minimization of the energy, with the $n=32-D_{3h}$ symmetry cluster having an unusually strong singlet intra-pentagon correlation. The magnetization in a field shows no discontinuities unlike the icosahedral $I_h$ fullerene clusters, but only plateaux with the most pronounced for $n=28$. The spatial symmetry as well as the connectivity of the clusters appear to be important for the determination of their magnetic properties.Comment: Extended to include low energy spectra, correlation functions and magnetization data of clusters up to 32 site

Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schr\"odinger Equation with a Kronig-Penney Potential

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schr\"odinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for experimental phenomena.Comment: Version 2. Fixed typos, added referenc

Nonequilibrium electron spin polarization in a double quantum dot. Lande mechanism

In moderately strong magnetic fields, the difference in Lande g-factors in each of the dots of a coupled double quantum dot device may induce oscillations between singlet and triplet states of the entangled electron pair and lead to a nonequilibrium electron spin polarization. We will show that this polarization may partially survive the rapid inhomogeneous decoherence due to random nuclear magnetic fields.Comment: New version contains figures. New title better reflects the content of the pape

Irreducible Representations of Diperiodic Groups

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a generalized translational group and an axial point group. The results are presented in the form of the tables, containing the matrices of the irreducible representations of the generators of the groups. General properties and some physical applications (degeneracy and topology of the energy bands, selection rules, etc.) are discussed.Comment: 30 pages, 5 figures, 28 tables, 18 refs, LaTex2.0

New Langevin and Gradient Thermostats for Rigid Body Dynamics

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.Comment: 16 pages, 4 figure

Group projector generalization of dirac-heisenberg model

The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found. With help of the modified group projector technique, this result is applied to the system of identical particles with spin independent interaction, to derive the Dirac-Heisenberg hamiltonian and its effective space for arbitrary orbital occupation numbers and arbitrary spin. This gives transparent insight into the physical contents of this hamiltonian, showing that formal generalizations with spin greater than 1/2 involve nontrivial additional physical assumptions.Comment: 10 page