Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques

The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison, and study the effects of varying the disk radius. Adopting a marginally stable disk profile (Q_init=1), we validate the numerical robustness of our model for different spatial extensions, from compact to larger, extended disks (R_disk = 10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combining our findings from the resolution and parameter studies we find a lower limit of the resolution to be able to resolve GI induced fragmentation features and distinct, turbulence inducing clumps. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells, which holds as a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures.Comment: 12 pages, 12 figures; accepted for publication in A&A; for associated movie files, see http://timlichtenberg.net/publications/gi1

On the local nature and scaling of chaos in weakly nonlinear disordered chains

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the presentwork it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found

Quantum resonance, Anderson localisation and selective manipulations in molecular mixtures by ultrashort laser pulses

We demonstrate that the current laser technology used for field-free molecular alignment via a cascade of Raman rotational transitions allows for observing long-discussed non-linear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localisation in the angular momentum. Based on these findings, we suggest a novel approach to tunable selective rotational excitation and alignment in a molecular mixture, using trains of short laser pulses. We demonstrate the efficiency of this approach by applying it to a mixture of two nitrogen isotopologues (14N2 and 15N2), and show that strong selectivity is possible even at room temperature

Corporate Investment Decisions and Security Values

The study of the impact of the announcement of various investment decisions of firms on their security values has occupied a central role in research in the area of finance. One has merely to skim the title pages of finance journals to confirm this preeminent position. The studies, to date, have generally used the Capital Asset Pricing Model to analyze the impact of these announcements. The development of the literature in the area of contingent claim pricing provides a new methodology in tackling the above issues. This thesis uses the option pricing framework to study the effects of two specific firm investment decisions--mergers, and stock repurchases. The first essay examines the pure financial effects of conglomerate mergers. Using the technique for valuing compound options, equations are derived for post-merger values of equity, short-term debt, and long-term debt. With the help of these valuation equations it is shown that the merger can result in wealth transfers from equity to both debts, from equity and one debt to the other debt, and from long-term debt to equity and short-term debt. The existence of these wealth transfers provide a rationale for the protective covenants against mergers that are commonly seen in debt contracts. In addition, it is shown that these protective covenants imply that the post-merger capital structure of the firm would be different from a simple pooling of the pre-merger capital structure of the individual firms. The second essay examines the effects of an announcement by a firm to repurchase a fraction of its outstanding equity . Given the existence of protective covenants in debt contracts against repurchases, and the voting rights of shareholders, it is theoretically shown that a repurchase must convey some information about the firm\u27s future prospects for it to be approved by all securityholders. In addition, it is shown that the signal must be firm value increasing, and firm risk decreasing. The theoretical signaling effects of repurchases are also shown to be consistent with empirical results obtained in recent studies

Ray model and ray-wave correspondence in coupled optical microdisks

We introduce a ray model for coupled optical microdisks, in which we select coupling-efficient rays among the splitting rays. We investigate the resulting phase-space structure and report island structures arising from the ray-coupling between the two microdisks. We find the microdisks's refractive index to influence the phase-space structure and calculate the stability and decay rates of the islands. Turning to ray-wave correspondence, we find many resonances to be directly related to the presence of these islands. We study the relation between the (ray-picture originating) island structures and the (wave-picture originating) spectral properties of resonances, especially the leakiness of the resonances which is represented as the imaginary part of the complex wave vector.Comment: 9 pages, 8 figure

Classical diffusion in double-delta-kicked particles

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2\delta$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $\epsilon \ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta$-KP including all important correlations which were used to analyze the experimental data. We find a new asymptotic ($t \to \infty$) regime of `hindered' diffusion: while for the Standard Map the diffusion rate, for $K \gg 1$, $D \sim K^2/2[1- J_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we find analytically, that the $2\delta$-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical `accelerator modes' of the Standard Map. We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, where quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte

Pion-proton scattering and isospin breaking in the Δ0−Δ++\Delta^0-\Delta^{++} system

We determine the mass and width of the $\Delta^{++}\ (\Delta^0)$ resonance from data on $\pi^+ p\ (\pi^- p)$ scattering both, in the pole of the $S$-matrix and conventional Breit-Wigner approaches to the scattering amplitude. We provide a simple formula that relates the two definitions for the parameters of the $\Delta$. Isospin symmetry breaking in the \d0-\dm system depends on the definition of the resonant properties: we find $M_0-M_{++} = 0.40 \pm 0.57\ {\rm MeV},\ \Gamma_0 -\Gamma_{++} = 6.89 \pm 0.95\ {\rm MeV}$ in the pole approach while $\wt{M}_0-\wt{M}_{++} = 2.25 \pm 0.68\ {\rm MeV},\ \wt{\Gamma}_0 - \wt{\Gamma}_{++} = 8.45 \pm 1.11\ {\rm MeV}$ in the conventional approach.Comment: Latex, 23 pages, two figures upon reques

Web-assisted tunneling in the kicked harmonic oscillator

We show that heating of harmonically trapped ions by periodic delta kicks is dramatically enhanced at isolated values of the Lamb-Dicke parameter. At these values, quasienergy eigenstates localized on island structures undergo avoided crossings with extended web-states.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. Let

Coherent acceleration of material wavepackets in modulated optical fields

We study the quantum dynamics of a material wavepacket bouncing off a modulated atomic mirror in the presence of a gravitational field. We find the occurrence of coherent accelerated dynamics for atoms beyond the familiar regime of dynamical localization. The acceleration takes place for certain initial phase space data and within specific windows of modulation strengths. The realization of the proposed acceleration scheme is within the range of present day experimental possibilities