Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions

Size-dependent patterns of reproductive investment in the North American invasive plant species Triadica sebifera (L.) Small (Euphorbiaceae)

Knowledge of sex allocation trade-offs with tree growth in insect-pollinated woody plants is limited, particularly in invasive plants. This study examined patterns of growth and reproductive investment in a North American invasive plant species, Triadica sebifera, I hypothesized that the energy limitations of smaller trees may result in the production of more male reproductive structures that are energetically less costly. Diameter at breast height was a significant predictor of seed and catkin mass and regression can describe these relationships across sites. Seed and catkin mass were positively correlated across sites. The relationship between the seed mass:catkin mass ratio and DBH was not significant, nor was seed mass:catkin mass and total investment. Results showed a significant positive relationship between total reproductive investment and tree size across sites. Seed mass:catkin mass ratio and reproduction investment showed substantial variation among individual trees of similar size within sites

Chromosome Number Evolution, Phylogeography, and the Effects of Climate Change on Species Distributions in Polyploid Plant Systems

Polyploidy, a term used to describe organisms with cells having more than two paired sets of chromosomes, is a significant driver of diversification among land plants. Over a century of research has advanced our understanding of polyploidization in some taxa, but polyploid organisms remain understudied. In this dissertation, I investigate chromosome number evolution, phylogeographic structure, genetic differentiation, and the effects of climate change on ploidy level distribution using polyploid plant systems. In the first chapter, I inferred a molecular phylogeny of Allium, an economically important genus that includes cultivated crops and ornamentals, to investigate evolutionary transitions in chromosome number using likelihood-based methods. The best-fit model of chromosome evolution showed that chromosome transitions within Allium occurred through the constant gains and losses of single chromosomes as well as demi-polyploidization events, with the rate of chromosome gain events being approximately 2.5 to 4.5 times more likely to occur than demi-polyploidization and loss events, respectively. In the second chapter, I used nuclear and chloroplast DNA sequences generated from eight populations in the North American Coastal Plain (NACP) biodiversity hotspot and one nearby population in Kansas to examine genetic diversity and population structure of A. canadense var. canadense, a polyploid species that exhibits vegetative reproduction which may lead to low genetic diversity within extant populations. A total of 12 ITS ribosomal and 10 chloroplast DNA haplotypes were identified, and significant genetic subdivision among populations was detected across all populations by analysis of molecular variance. In the third chapter, I used ecological niche modeling to evaluate the differences in niche identity among diploid and polyploid plants endemic to the NACP at the generic level using current bioclimatic variables, then niche overlap and habitat suitability using future climate change scenarios were assessed. I found that congeneric ploidy level pairs differed significantly in niche identity, and niche overlap varied across genera. I also identified 11 genera that showed greater than 100% increases in habitat suitability and six genera that showed almost no remaining suitable habitat in at least one future climate scenario. Based on these results, I provide future directions for continued studies in the NACP

Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

Linear superposition in nonlinear wave dynamics

We study nonlinear dispersive wave systems described by hyperbolic PDE's in R^{d} and difference equations on the lattice Z^{d}. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi-Pasta-Ulam model and many other not completely integrable systems, satisfy a superposition principle. The principle essentially states that if a nonlinear evolution of a wave starts initially as a sum of generic wavepackets (defined as almost monochromatic waves), then this wave with a high accuracy remains a sum of separate wavepacket waves undergoing independent nonlinear evolution. The time intervals for which the evolution is considered are long enough to observe fully developed nonlinear phenomena for involved wavepackets. In particular, our approach provides a simple justification for numerically observed effect of almost non-interaction of solitons passing through each other without any recourse to the complete integrability. Our analysis does not rely on any ansatz or common asymptotic expansions with respect to the two small parameters but it uses rather explicit and constructive representation for solutions as functions of the initial data in the form of functional analytic series.Comment: New introduction written, style changed, references added and typos correcte

Has Affirmative Action Been Negated? A Closer Look at Public Employment

First, this Article argues that affirmative action is right and necessary in certain circumstances. Second, it examines whether affirmative action has survived under current case law. Part II.A reviews the Supreme Court decisions that define the test of strict scrutiny in the public employment context. Part II.B discusses the current focus of the Court\u27s debate on affirmative action. Part III looks at how strict scrutiny analysis and the Supreme Court\u27s precedents are being applied by the lower federal courts. Part IV concludes that more guidance is needed from the Supreme Court on the first prong of the strict scrutiny analysis as to when a compelling government interest exists. Last, this Article suggests that the Supreme Court firmly establish an inferential standard for proving past discrimination by a public employer sufficient to warrant current affirmative action

Thermally driven ballistic rectifer

The response of electric devices to an applied thermal gradient has, so far, been studied almost exclusively in two-terminal devices. Here we present measurements of the response to a thermal bias of a four-terminal, quasi-ballistic junction with a central scattering site. We find a novel transverse thermovoltage measured across isothermal contacts. Using a multi-terminal scattering model extended to the weakly non-linear voltage regime, we show that the device's response to a thermal bias can be predicted from its nonlinear response to an electric bias. Our approach forms a foundation for the discovery and understanding of advanced, nonlocal, thermoelectric phenomena that in the future may lead to novel thermoelectric device concepts.Comment: 4 pages, 4 figures; minor to moderate clarifications and simplifications in v

The decay of turbulence in rotating flows

We present a parametric space study of the decay of turbulence in rotating flows combining direct numerical simulations, large eddy simulations, and phenomenological theory. Several cases are considered: (1) the effect of varying the characteristic scale of the initial conditions when compared with the size of the box, to mimic "bounded" and "unbounded" flows; (2) the effect of helicity (correlation between the velocity and vorticity); (3) the effect of Rossby and Reynolds numbers; and (4) the effect of anisotropy in the initial conditions. Initial conditions include the Taylor-Green vortex, the Arn'old-Beltrami-Childress flow, and random flows with large-scale energy spectrum proportional to $k^4$. The decay laws obtained in the simulations for the energy, helicity, and enstrophy in each case can be explained with phenomenological arguments that separate the decay of two-dimensional from three-dimensional modes, and that take into account the role of helicity and rotation in slowing down the energy decay. The time evolution of the energy spectrum and development of anisotropies in the simulations are also discussed. Finally, the effect of rotation and helicity in the skewness and kurtosis of the flow is considered.Comment: Sections reordered to address comments by referee

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale $L_f$, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the \textit{inverse cascade} range at a small but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several {numerical simulations with} helical and non-helical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with {reasonably} large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$} scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$} spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to 2D modes. {The spectrum that} emerges {depends on} the anisotropy of the forcing function{,} the former solution prevailing for forcings in which more energy is injected into 2D modes while the latter prevails for isotropic forcing. {In the case of anisotropic forcing, whence the energy} goes from the 2D to the 3D modes at low wavenumbers, large-scale shear is created resulting in another time scale $\tau_{sh}$, associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the {total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$} scaling