Upscaling Tree Demography to Heterogenous Landscapes Using Models and Remote Sensing

Tree demography is foundational to ecology and conservation, from mass tree die-offs to forest recovery. Plot-level studies of tree demography, including field measurements of tagged individuals, have been fundamental for developing ecological theory and forest management strategies. However, the limited spatial extent of field plots impedes generalizing plot-level models for spatial predictions across heterogeneous landscapes. Novel high-spatial resolution remote sensing imagery has opened the possibility for measuring tree demographic rates with continuous spatial coverage at landscape to regional extents. Remote sensing derived measurements could address pressing research questions, including disentangling causes of high variation in natural regeneration across secondary forest landscapes. Despite the promise of high-spatial resolution imagery for ecology, applying these data to ecological questions will require novel modeling approaches that can account for large amounts of spatial data that often include hierarchical structure. In this thesis, I apply high-resolution remote sensing to upscale tree demography at landscape scales, and provide guidelines for ecologists seeking to parametrize spatially explicit models for neighbor interactions by combining field data, high-resolution remote sensing, and Bayesian quantitative methods. Chapter 1 demonstrates how high-spatial resolution remote sensing can help improve predictions of tree recruitment at the landscape scale. This chapter is the first step towards new support tools that inform restoration projects about where and which species will regenerate naturally in agricultural landscapes. Chapter 2 addresses how to optimize neighbor interaction models using the Hamiltonian Monte Carlo algorithm. I demonstrate how ragged matrices could solve data storage inefficiencies associated with the neighbor interaction models' pairwise structure. I also provide code for a model parametrization that solves a sampling pathology associated with high correlation in hierarchical structures and an overview of metrics to assess when this hierarchical structure pathology is present. Chapter 3 explores the influence of biophysical and anthropogenic drivers on tree mortality in agricultural landscapes using high-resolution remote sensing data. The results suggest that accessibility and land management are core factors that could be managed to prevent the mortality of agricultural trees. Educational initiatives and new policies that address anthropogenic factors could be the answer to reduce agricultural tree loss. Overall, this thesis brings together Bayesian statistical methods with novel high-resolution remote sensing to overcome the spatial limitation of field measurements and produce spatial predictions and inference on drivers of tree demography across heterogeneous landscapes.

Roton-like acoustical dispersion relations in 3D metamaterials

Roton dispersion relations have been restricted to correlated quantum systems at low temperatures, such as liquid Helium-4, thin films of Helium-3, and Bose–Einstein condensates. This unusual kind of dispersion relation provides broadband acoustical backward waves, connected to energy flow vortices due to a “return flow”, in the words of Feynman, and three different coexisting acoustical modes with the same polarization at one frequency. By building mechanisms into the unit cells of artificial materials, metamaterials allow for molding the flow of waves. So far, researchers have exploited mechanisms based on various types of local resonances, Bragg resonances, spatial and temporal symmetry breaking, topology, and nonlinearities. Here, we introduce beyond-nearest-neighbor interactions as a mechanism in elastic and airborne acoustical metamaterials. For a third-nearest-neighbor interaction that is sufficiently strong compared to the nearest-neighbor interaction, this mechanism allows us to engineer roton-like acoustical dispersion relations under ambient conditions.

Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) [Formula: see text]. The ferromagnetic long-range interactions considered in this paper decay as [Formula: see text] with the distance [Formula: see text] between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of [Formula: see text] and [Formula: see text]. At finite temperatures and in the region [Formula: see text] in which [Formula: see text] is dependent of [Formula: see text], the ferromagnetic-paramagnetic phase transition survives for [Formula: see text] and no phase transition exists for [Formula: see text]. At [Formula: see text], the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for [Formula: see text]. The ground state of the system keeps ferromagnetic when [Formula: see text]. But for [Formula: see text], the system becomes antiferromagnetic at all temperatures.

Exact solution of a cluster model with next-nearest-neighbor interaction

A 1D cluster model with next-nearest-neighbor interactions and two additional composite interactions is solved; the free energy is obtained and a correlation function is derived exactly. The model is diagonalized by a transformation obtained automatically from its interactions, which is an algebraic generalization of the Jordan–Wigner transformation. The gapless condition is expressed as a condition on the roots of a cubic equation, and the phase diagram is obtained exactly. We find that the distribution of roots for this algebraic equation determines the existence of long-range order, and we again obtain the ground-state phase diagram. We also derive the central charges of the corresponding conformal field theory. Finally, we note that our results are universally valid for an infinite number of solvable spin chains whose interactions obey the same algebraic relations.

Ripples in Graphene: A Variational Approach

Suspended graphene samples are observed to be gently rippled rather than being flat. In Friedrich et al. (Z Angew Math Phys 69:70, 2018), we have checked that this nonplanarity can be rigorously described within the classical molecular-mechanical frame of configurational-energy minimization. There, we have identified all ground-state configurations with graphene topology with respect to classes of next-to-nearest neighbor interaction energies and classified their fine nonflat geometries. In this second paper on graphene nonflatness, we refine the analysis further and prove the emergence of wave patterning. Moving within the frame of Friedrich et al. (2018), rippling formation in graphene is reduced to a two-dimensional problem for one-dimensional chains. Specifically, we show that almost minimizers of the configurational energy develop waves with specific wavelength, independently of the size of the sample. This corresponds remarkably to experiments and simulations.

Ground states for infinite lattices with nearest neighbor interaction

Sun and Ma (J. Differ. Equ. 255:2534–2563, 2013) proved the existence of a nonzero T-periodic solution for a class of one-dimensional lattice dynamical systems, $$\begin{aligned} \ddot{q_{i}}=\varPhi _{i-1}'(q_{i-1}-q_{i})- \varPhi _{i}'(q_{i}-q_{i+1}),\quad i\in \mathbb{Z}, \end{aligned}$$ q i ¨ = Φ i − 1 ′ ( q i − 1 − q i ) − Φ i ′ ( q i − q i + 1 ) , i ∈ Z , where $q_{i}$ q i denotes the co-ordinate of the ith particle and $\varPhi _{i}$ Φ i denotes the potential of the interaction between the ith and the $(i+1)$ ( i + 1 ) th particle. We extend their results to the case of the least energy of nonzero T-periodic solution under general conditions. Of particular interest is a new and quite general approach. To the best of our knowledge, there is no result for the ground states for one-dimensional lattice dynamical systems.