Computational bounds on polynomial differential equations

In this paper we study from a computational perspective some prop-erties of the solutions of polynomial ordinary di erential equations. We consider elementary (in the sense of Analysis) discrete-time dynam-ical systems satisfying certain criteria of robustness. We show that those systems can be simulated with elementary and robust continuous-time dynamical systems which can be expanded into fully polynomial ordinary diferential equations with coe cients in Q[ ]. This sets a computational lower bound on polynomial ODEs since the former class is large enough to include the dynamics of arbitrary Turing machines. We also apply the previous methods to show that the problem of de-termining whether the maximal interval of defnition of an initial-value problem defned with polynomial ODEs is bounded or not is in general undecidable, even if the parameters of the system are computable and comparable and if the degree of the corresponding polynomial is at most 56. Combined with earlier results on the computability of solutions of poly-nomial ODEs, one can conclude that there is from a computational point of view a close connection between these systems and Turing machines

Computability with polynomial differential equations

In this paper, we show that there are Initial Value Problems de ned with polynomial ordinary di erential equations that can simulate univer- sal Turing machines in the presence of bounded noise. The polynomial ODE de ning the IVP is explicitly obtained and the simulation is per- formed in real time

The Role of Electron Captures in Chandrasekhar Mass Models for Type Ia Supernovae

The Chandrasekhar mass model for Type Ia Supernovae (SNe Ia) has received increasing support from recent comparisons of observations with light curve predictions and modeling of synthetic spectra. It explains SN Ia events via thermonuclear explosions of accreting white dwarfs in binary stellar systems, being caused by central carbon ignition when the white dwarf approaches the Chandrasekhar mass. As the electron gas in white dwarfs is degenerate, characterized by high Fermi energies for the high density regions in the center, electron capture on intermediate mass and Fe-group nuclei plays an important role in explosive burning. Electron capture affects the central electron fraction Y_e, which determines the composition of the ejecta from such explosions. Up to the present, astrophysical tabulations based on shell model matrix elements were only available for light nuclei in the sd-shell. Recently new Shell Model Monte Carlo (SMMC) and large-scale shell model diagonalization calculations have also been performed for pf-shell nuclei. These lead in general to a reduction of electron capture rates in comparison with previous, more phenomenological, approaches. Making use of these new shell model based rates, we present the first results for the composition of Fe-group nuclei produced in the central regions of SNe Ia and possible changes in the constraints on model parameters like ignition densities and burning front speeds.Comment: 26 pages, 8 figures, submitted to Ap

On representation of the t-J model via spin-charge variables

We show that the t-J Hamiltonian is not in general reduced to H(S,f), where S and f stand for independent ([S,f]=0) SU(2) (spin) generators and spinless fermionic (hole) field, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su(2|1) superalgebra in the degenerate fundamental representation and ensuing SU(2|1) path integral representation of the partition function.Comment: 15 pages, latex, no figure

Functional roles of the factor VIII B domain

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74800/1/j.1365-2516.2009.02026.x.pd

Deep-water Tectono-Stratigraphy at a Plate Boundary Constrained by Large N-Detrital Zircon and Micropaleontological Approaches: Peninsular Ranges Forearc, Baja California, Mexico

The distribution of sedimentary systems on Earth’s surface is intimately linked to tectonics, therefore, at plate boundaries the stratigraphic archive can unlock the timing and style of tectonism and relative plate motions. Using large-n detrital zircon and micropaleontological analyses, tied to field mapping and data collection, we unravel the timing of strike-slip motion and its influence on the development of a Cretaceous submarine canyon on a long-lived oblique-convergent margin. Structural analysis demonstrates that the canyon bedrock, composed of fluvial rocks (La Bocana Roja Fm., of maximum depositional age (MDA): 93.6±1.1 Ma), underwent both syn- and post-depositional contractional and extensional deformation during the Cenomanian-Turonian in response to dextral strike-slip movement. Relative sea-level rise associated with basin subsidence and hinterland uplift was coincident with incision and fill of a submarine canyon system (Punta Baja Fm., MDA 87.1±1.5 Ma to 84.9±2.0 Ma), which exploited structural lineaments in the bedrock. The canyon was filled by sediment derived from an uplifted magmatic arc during the Coniacian to Santonian, most likely shed from erosional topography associated with plutonic intrusions to the NE. Structural data suggest that oblique dextral strike-slip motion on the Pacific margin controlled the development and location of submarine erosion, and had ended by the earliest Santonian, significantly earlier than previously estimated. Basinward tilting led to uplift, followed by transgression and wave ravinement of the canyon fill, which was then overlain by a shallow-marine to fluvial system. Thus, the canyon was cut, filled, buried, uplifted and rotated basinward, planed off through wave ravinement, and onlapped by shallow-marine to fluvial sediments within an 8 Myr period. Our findings, in part, reconcile contrasting basin evolution models for the Late Mesozoic Pacific margin

Enhanced rock-slope failure following ice-sheet deglaciation : timing and causes

This research was supported by NERC Cosmogenic Isotope Analysis Facility [Grant Number: 9046.0308]The temporal pattern of rock-slope failures (RSFs) following Late Pleistocene deglaciation on tectonically stable terrains is controversial: previous studies variously suggest (1) a rapid response due to removal of supporting ice (‘debuttressing’), (2) a progressive decline in RSF frequency, and (3) a millennial-scale delay before peak RSF activity. We test these competing models through beryllium-10 (10Be) exposure dating of five closely-spaced quartzite RSFs on the Isle of Jura, Scotland, to establish the relationship between timing of failure and those of deglaciation, episodes of rapid warming and periods of rapid glacio-isostatic uplift. All five dated RSFs occurred at least 720–2240 years after deglaciation, with the probability of failure peaking ~2 ka after deglaciation, consistent with millennial-scale delay model (3). This excludes debuttressing as an immediate cause of failure, though it is likely that time-dependent stress release due to deglacial unloading resulted in progressive development of failure planes within the rock. Thaw of permafrost ice in joints is unlikely to have been a prime trigger of failure as some RSFs occurred several centuries after the onset of interstadial warming. Conversely, the timespan of the RSFs coincides with the period of maximum glacio-isostatic crustal uplift, suggesting that failure was triggered by uplift-driven seismic events acting on fractured rock masses. Implications of this and related research are: (1) that retreat of the last Pleistocene ice sheets across tectonically-stable mountainous terrains was succeeded by a period of enhanced rock-slope failure due to deglacial unloading and probably uplift-driven seismicity; (2) that the great majority of RSFs in the British Isles outside the limits of Loch Lomond Stadial (= Younger Dryas) glaciation are of Lateglacial (pre-Holocene) age; and (3) numerous RSFs must also have occurred inside Loch Lomond Stadial (LLS) glacial limits, but that runout debris was removed by LLS glaciers.PostprintPeer reviewe

Electron capture on iron group nuclei

We present Gamow-Teller strength distributions from shell model Monte Carlo studies of fp-shell nuclei that may play an important role in the pre-collapse evolution of supernovae. We then use these strength distributions to calculate the electron-capture cross sections and rates in the zero-momentum transfer limit. We also discuss the thermal behavior of the cross sections. We find large differences in these cross sections and rates when compared to the naive single-particle estimates. These differences need to be taken into account for improved modeling of the early stages of type II supernova evolution