391 research outputs found

### Mathematical Modelling of Tyndall Star Initiation

The superheating that usually occurs when a solid is melted by volumetric
heating can produce irregular solid-liquid interfaces. Such interfaces can be
visualised in ice, where they are sometimes known as Tyndall stars. This paper
describes some of the experimental observations of Tyndall stars and a
mathematical model for the early stages of their evolution. The modelling is
complicated by the strong crystalline anisotropy, which results in an
anisotropic kinetic undercooling at the interface; it leads to an interesting
class of free boundary problems that treat the melt region as infinitesimally
thin

### Wellposedness of an elliptic-dispersive coupled system for MEMS

In this work, we study the local wellposedness of the solution to a nonlinear
elliptic-dispersive coupled system which serves as a model for a
Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated
MEMS capacitor device consists of two parallel plates separated by a gas-filled
thin gap. The nonlinear elliptic-dispersive coupled system modelling the device
combines a linear elliptic equation for the gas pressure with a semilinear
dispersive equation for the gap width. We show the local-in-time existence of
strict solutions for the system, by combining elliptic regularity results for
the elliptic equation, Lipschitz continuous dependence of its solution on that
of the dispersive equation, and then local-in-time existence for a resulting
abstract dispersive problem. Semigroup approaches are key to solve the abstract
dispersive problem.Comment: 27 page

### Predictions of the causal entropic principle for environmental conditions of the universe

The causal entropic principle has been proposed as a superior alternative to
the anthropic principle for understanding the magnitude of the cosmological
constant. In this approach, the probability to create observers is assumed to
be proportional to the entropy production \Delta S in a maximal causally
connected region -- the causal diamond. We improve on the original treatment by
better quantifying the entropy production due to stars, using an analytic model
for the star formation history which accurately accounts for changes in
cosmological parameters. We calculate the dependence of \Delta S on the density
contrast Q=\delta\rho/\rho, and find that our universe is much closer to the
most probable value of Q than in the usual anthropic approach and that
probabilities are relatively weakly dependent on this amplitude. In addition,
we make first estimates of the dependence of \Delta S on the baryon fraction
and overall matter abundance. Finally, we also explore the possibility that
decays of dark matter, suggested by various observed gamma ray excesses, might
produce a comparable amount of entropy to stars.Comment: RevTeX4, 13pp, 10 figures; v2. clarified introduction, added ref

### On the quenching behaviour of a semilinear wave equation modelling MEMS technology

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems - Series A following peer review. The definitive publisher-authenticated version 2015, 35(3), pp. 1009-1037 is available online at: http://dx.doi.org/10.3934/dcds.2015.35.100

### The Clustering of Massive Halos

The clustering properties of dark matter halos are a firm prediction of
modern theories of structure formation. We use two large volume,
high-resolution N-body simulations to study how the correlation function of
massive dark matter halos depends upon their mass and formation history. We
find that halos with the lowest concentrations are presently more clustered
than those of higher concentration, the size of the effect increasing with halo
mass; this agrees with trends found in studies of lower mass halos. The
clustering dependence on other characterizations of the full mass accretion
history appears weaker than the effect with concentration. Using the integrated
correlation function, marked correlation functions, and a power-law fit to the
correlation function, we find evidence that halos which have recently undergone
a major merger or a large mass gain have slightly enhanced clustering relative
to a randomly chosen population with the same mass distribution.Comment: 10 pages, 8 figures; text improved, references and one figure added;
accepted for publication in Ap

### The Robustness of Dark Matter Density Profiles in Dissipationless Mergers

We present a comprehensive series of dissipationless N-body simulations to
investigate the evolution of density distribution in equal-mass mergers between
dark matter (DM) halos and multicomponent galaxies. The DM halo models are
constructed with various asymptotic power-law indices ranging from steep cusps
to core-like profiles and the structural properties of the galaxy models are
motivated by the LCDM paradigm of structure formation. The adopted force
resolution allows robust density profile estimates in the inner ~1% of the
virial radii of the simulated systems. We demonstrate that the central slopes
and overall shapes of the remnant density profiles are virtually identical to
those of the initial systems suggesting that the remnants retain a remarkable
memory of the density structure of their progenitors, despite the relaxation
that accompanies merger activity. We also find that halo concentrations remain
approximately constant through hierarchical merging involving identical systems
and show that remnants contain significant fractions of their bound mass well
beyond their formal virial radii. These conclusions hold for a wide variety of
initial asymptotic density slopes, orbital energies, and encounter
configurations, including sequences of consecutive merger events, simultaneous
mergers of severals ystems, and mergers of halos with embedded cold baryonic
components in the form of disks, spheroids, or both. As an immediate
consequence, the net effect of gas cooling, which contracts and steepens the
inner density profiles of DM halos, should be preserved through a period of
dissipationless major merging. Our results imply that the characteristic
universal shape of DM density profiles may be set early in the evolution of
halos.Comment: Accepted for publication in ApJ, 20 pages, 10 figures, LaTeX (uses
emulateapj.cls

### Close Pairs as Proxies for Galaxy Cluster Mergers

Galaxy cluster merger statistics are an important component in understanding
the formation of large-scale structure. Unfortunately, it is difficult to study
merger properties and evolution directly because the identification of cluster
mergers in observations is problematic. We use large N-body simulations to
study the statistical properties of massive halo mergers, specifically
investigating the utility of close halo pairs as proxies for mergers. We
examine the relationship between pairs and mergers for a wide range of merger
timescales, halo masses, and redshifts (0<z<1). We also quantify the utility of
pairs in measuring merger bias. While pairs at very small separations will
reliably merge, these constitute a small fraction of the total merger
population. Thus, pairs do not provide a reliable direct proxy to the total
merger population. We do find an intriguing universality in the relation
between close pairs and mergers, which in principle could allow for an estimate
of the statistical merger rate from the pair fraction within a scaled
separation, but including the effects of redshift space distortions strongly
degrades this relation. We find similar behavior for galaxy-mass halos, making
our results applicable to field galaxy mergers at high redshift. We investigate
how the halo merger rate can be statistically described by the halo mass
function via the merger kernel (coagulation), finding an interesting
environmental dependence of merging: halos within the mass resolution of our
simulations merge less efficiently in overdense environments. Specifically,
halo pairs with separations less than a few Mpc/h are more likely to merge in
underdense environments; at larger separations, pairs are more likely to merge
in overdense environments.Comment: 12 pages, 9 figures; Accepted for publication in ApJ. Significant
additions to text and two figures changed. Added new findings on the
universality of pair mergers and added analysis of the effect of FoF linking
length on halo merger

### Cellular-level versus receptor-level response threshold hierarchies in T-Cell activation

Peptide-MHC (pMHC) ligand engagement by T-cell receptors (TCRs) elicits a variety of cellular responses, some of which require substantially more TCR-mediated stimulation than others. This threshold hierarchy could reside at the receptor level, where different response pathways branch off at different stages of the TCR/CD3 triggering cascade, or at the cellular level, where the cumulative TCR signal registered by the T-cell is compared to different threshold values. Alternatively, dual-level thresholds could exist. In this study, we show that the cellular hypothesis provides the most parsimonious explanation consistent with data obtained from an in-depth analysis of distinct functional responses elicited in a clonal T-cell system by a spectrum of biophysically defined altered peptide ligands across a range of concentrations. Further, we derive a mathematical model that describes how ligand density, affinity, and off-rate all affect signaling in distinct ways. However, under the kinetic regime prevailing in the experiments reported here, the TCR/pMHC class I (pMHCI) dissociation rate was found to be the main governing factor. The CD8 coreceptor modulated the TCR/pMHCI interaction and altered peptide ligand potency. Collectively, these findings elucidate the relationship between TCR/pMHCI kinetics and cellular function, thereby providing an integrated mechanistic understanding of T-cell response profiles

### Halo Substructure and the Power Spectrum

In this proceeding, we present the results of a semi-analytic study of CDM
substructure as a function of the primordial power spectrum. We apply our
method to several tilted models in the LCDM framework with n=0.85-1.1,
sigma_8=0.65-1.2 when COBE normalized. We also study a more extreme, warm dark
matter-like spectrum that is sharply truncated below a scale of 10^10 h^-1
Msun. We show that the mass fraction of halo substructure is not a strong
function of spectral slope, so it likely will be difficult to constrain tilt
using flux ratios of gravitationally lensed quasars. On the positive side, all
of our CDM-type models yield projected mass fractions in good agreement with
strong lensing estimates: f \sim 1.5% at M \sim 10^8 Msun. The truncated model
produces a significantly smaller fraction, f \lsim 0.3%, suggesting that warm
dark matter-like spectra may be distinguished from CDM spectra using lensing.
We also discuss the issue of dwarf satellite abundances, with emphasis on the
cosmological dependence of the map between the observed central velocity
dispersion of Milky Way satellites and the maximum circular velocities of their
host halos. In agreement with earlier work, we find that standard LCDM
over-predicts the estimated count of Milky Way satellites at fixed Vmax by an
order of magnitude, but tilted models do better because subhalos are less
concentrated. Interestingly, under the assumption that dwarfs have isotropic
velocity dispersion tensors, models with significantly tilted spectra (n \lsim
0.85, sigma_8 \lsim 0.7) may under-predict the number of large Milky Way
satellites with Vmax \gsim 40 km/s.Comment: 5 pages, 2 figures. Poster contribution to the 13th Annual
Astrophysics Conference in Maryland, The Emergence of Cosmic Structur

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