Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit \simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.Comment: 14 Pages, 13 Figures. Submitted to MNRA

Elastic and plastic effects on heterogeneous nucleation and nanowire formation

We investigate theoretically the effects of elastic and plastic deformations on heterogeneous nucleation and nanowire formation. In the first case, the influence of the confinement of the critical nucleus between two parallel misfitting substrates is investigated using scaling arguments. We present phase diagrams giving the nature of the nucleation regime as a function of the driving force and the degree of confinement. We complement this analytical study by amplitude equations simulations. In the second case, the influence of a screw dislocation inside a nanowire on the development of the morphological surface stability of the wire, related to the Rayleigh-Plateau instability, is examined. Here the screw dislocation provokes a torsion of the wire known as Eshelby twist. Numerical calculations using the finite element method and the amplitude equations are performed to support analytical investigations. It is shown that the screw dislocation promotes the Rayleigh-Plateau instability.Comment: 16 page

Image processing applied to gravity and topography data covering the continental United States

The applicability of fairly standard image processing techniques to processing and analyzing large geologic data sets in addressed. Image filtering techniques were used to interpolate between gravity station locations to produce a regularly spaced data array that preserves detail in areas with good coverage, and that produces a continuous tone image rather than a contour map. Standard image processing techniques were used to digitally register and overlay topographic and gravity data, and the data were displayed in ways that emphasize subtle but pervasive structural features. The potential of the methods is illustrated through a discussion of linear structures that appear in the processed data between the midcontinent gravity high and the Appalachians

Concentration fields near air-water interfaces during interfacial mass transport: oxygen transport and random square wave analysis

Mass transfer across a gas-liquid interface was studied theoretically and experimentally, using transfer of oxygen into water as the gas-liquid system. The experimental results support the conclusions of a theoretical description of the concentration field that uses random square waves approximations. The effect of diffusion over the concentration records was quantified. It is shown that the peak of the normalized rms concentration fluctuation profiles must be lower than 0.5, and that the position of the peak of the rms value is an adequate measure of the thickness of the diffusive layer. The position of the peak is the boundary between the regions more subject to molecular diffusion or to turbulent transport of dissolved mass

Coreness of Cooperative Games with Truncated Submodular Profit Functions

Coreness represents solution concepts related to core in cooperative games, which captures the stability of players. Motivated by the scale effect in social networks, economics and other scenario, we study the coreness of cooperative game with truncated submodular profit functions. Specifically, the profit function $f(\cdot)$ is defined by a truncation of a submodular function $\sigma(\cdot)$: $f(\cdot)=\sigma(\cdot)$ if $\sigma(\cdot)\geq\eta$ and $f(\cdot)=0$ otherwise, where $\eta$ is a given threshold. In this paper, we study the core and three core-related concepts of truncated submodular profit cooperative game. We first prove that whether core is empty can be decided in polynomial time and an allocation in core also can be found in polynomial time when core is not empty. When core is empty, we show hardness results and approximation algorithms for computing other core-related concepts including relative least-core value, absolute least-core value and least average dissatisfaction value

CasTuner: a degron and CRISPR/Cas-based toolkit for analog tuning of endogenous gene expression

Certain cellular processes are dose-dependent, requiring a specific quantity of gene products or a defined stoichiometry between them. This is exemplified by haploinsufficiency or by the need for dosage compensation for X-linked genes between the sexes in many species. Understanding dosage-sensitive processes requires the ability to perturb endogenous gene products in a quantitative manner. Here we present CasTuner, a CRISPR-based toolkit that allows analog tuning of endogenous gene expression. In the CasTuner system, activity of Cas-derived repressors is controlled through a FKBP12F36V degron domain and can thereby be quantitatively tuned by titrating the small molecule degrader dTAG-13. The toolkit can be applied at the transcriptional level, using the histone deacetylase hHDAC4 fused to dCas9, or at the post-transcriptional level, using the RNA-targeting CasRx. To optimise efficiency, inducibility and homogeneity of repression we target a fluorescently tagged endogenous gene, Esrrb, in mouse embryonic stem cells. Through flow cytometry, we show that CasTuner allows analog tuning of the target gene in a homogeneous manner across cells, as opposed to the widely used KRAB repressor domain, which exhibits a digital mode of action. We quantify repression and derepression dynamics for CasTuner and use it to measure dose-response curves between the pluripotency factor NANOG and several of its target genes, providing evidence for target-specific dose dependencies. CasTuner thus provides an easy-to-implement tool to perturb gene expression in an inducible, tunable and reversible manner and will be useful to study dose-responsive processes within their physiological contex

Surveys of Galaxy Clusters with the Sunyaev Zel'dovich Effect

We have created mock Sunyaev-Zel'dovich effect (SZE) surveys of galaxy clusters using high resolution N-body simulations. To the pure surveys we add `noise' contributions appropriate to instrument and primary CMB anisotropies. Applying various cluster finding strategies to these mock surveys we generate catalogues which can be compared to the known positions and masses of the clusters in the simulations. We thus show that the completeness and efficiency that can be achieved depend strongly on the frequency coverage, noise and beam characteristics of the instruments, as well as on the candidate threshold. We study the effects of matched filtering techniques on completeness, and bias. We suggest a gentler filtering method than matched filtering in single frequency analyses. We summarize the complications that arise when analyzing the SZE signal at a single frequency, and assess the limitations of such an analysis. Our results suggest that some sophistication is required when searching for `clusters' within an SZE map.Comment: 8 pages, 7 figure