An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer

Statistical Mechanics of Vibration-Induced Compaction of Powders

We propose a theory which describes the density relaxation of loosely packed, cohesionless granular material under mechanical tapping. Using the compactivity concept we develope a formalism of statistical mechanics which allows us to calculate the density of a powder as a function of time and compactivity. A simple fluctuation-dissipation relation which relates compactivity to the amplitude and frequency of a tapping is proposed. Experimental data of E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of initially deposited in a fluffy state powder evolves under carefully controlled tapping towards a random close packing (RCP) density. Ramping the vibration amplitude repeatedly up and back down again reveals the existence of reversible and irreversible branches in the response. In the framework of our approach the reversible branch (along which the RCP density is obtained) corresponds to the steady state solution of the Fokker-Planck equation whereas the irreversible one is represented by a superposition of "excited states" eigenfunctions. These two regimes of response are analyzed theoretically and a qualitative explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex

TDRSS orbit determination using short baseline differenced carrier phase

This paper discusses a covariance study on the feasibility of using station-differenced carrier phase on short baselines to track the TDRSS satellites. Orbit accuracies for the TDRSS using station-differenced carrier phase data and range data collected from White Sands, NM are given for various configurations of ground stations and range data precision. A one-sigma-position position accuracy of 25 meters can be achieved using two orthogonal baselines of 100 km for the station-differenced phase data and range data with 1 m accuracy. Relevant configuration parameters for the tracking system and important sources of error are examined. The ability of these data to redetermine the position after a station keeping maneuver is addressed. The BRTS system, which is currently used for TDRSS orbit determination, is briefly described and its errors are given for comparison

A deductive statistical mechanics approach for granular matter

We introduce a deductive statistical mechanics approach for granular materials which is formally built from few realistic physical assumptions. The main finding is an universal behavior for the distribution of the density fluctuations. Such a distribution is the equivalent of the Maxwell-Boltzmann's distribution in the kinetic theory of gasses. The comparison with a very extensive set of experimental and simulation data for packings of monosized spherical grains, reveals a remarkably good quantitative agreement with the theoretical predictions for the density fluctuations both at the grain level and at the global system level. Such agreement is robust over a broad range of packing fractions and it is observed in several distinct systems prepared by using different methods. The equilibrium distributions are characterized by only one parameter ($k$) which is a quantity very sensitive to changes in the structural organization. The thermodynamical equivalent of $k$ and its relation with the `granular temperature' are also discussed.Comment: 15 pages, 6 figure

Hope as a Source of Resilience in Later Adulthood

This research provided a preliminary investigation of how variations in trait and state hope are associated with positive adaptation to stress in later adulthood. Trait hope and neuroticism were measured by questionnaires and state hope, stress, and negative emotions were assessed daily for 45 days. Results from multilevel random coefficient modeling analyses suggested that daily hope provides protective benefits by keeping negative emotions low, while also contributing to adaptive recovery from stress. The dynamic linkages between daily hope, stress, and emotion were further moderated by individual differences in trait hope. Compared with those low in trait hope, high-hope individuals showed diminished stress reactivity and more effective emotional recovery

Spacecraft-spacecraft very long baseline interferometry. Part 1: Error modeling and observable accuracy

In Part 1 of this two-part article, an error budget is presented for Earth-based delta differential one-way range (delta DOR) measurements between two spacecraft. Such observations, made between a planetary orbiter (or lander) and another spacecraft approaching that planet, would provide a powerful target-relative angular tracking data type for approach navigation. Accuracies of better than 5 nrad should be possible for a pair of spacecraft with 8.4-GHz downlinks, incorporating 40-MHz DOR tone spacings, while accuracies approaching 1 nrad will be possible if the spacecraft incorporate 32-GHz downlinks with DOR tone spacing on the order of 250 MHz; these accuracies will be available for the last few weeks or months of planetary approach for typical Earth-Mars trajectories. Operational advantages of this data type are discussed, and ground system requirements needed to enable spacecraft-spacecraft delta DOR observations are outlined. This tracking technique could be demonstrated during the final approach phase of the Mars '94 mission, using Mars Observer as the in-orbit reference spacecraft, if the Russian spacecraft includes an 8.4-GHz downlink incorporating DOR tones. Part 2 of this article will present an analysis of predicted targeting accuracy for this scenario

Nonclassical shallow water flows

This paper deals with violent discontinuities in shallow water flows with large Froude number $F$. On a horizontal base, the paradigm problem is that of the impact of two fluid layers in situations where the flow can be modelled as two smooth regions joined by a singularity in the flow field. Within the framework of shallow water theory we show that, over a certain timescale, this discontinuity may be described by a delta-shock, which is a weak solution of the underlying conservation laws in which the depth and mass and momentum fluxes have both delta function and step functioncomponents. We also make some conjectures about how this model evolves from the traditional model for jet impacts in which a spout is emitted. For flows on a sloping base, we show that for flow with an aspect ratio of \emph{O}($F^{-2}$) on a base with an \emph{O(1)} or larger slope, the governing equations admit a new type of discontinuous solution that is also modelled as a delta-shock. The physical manifestation of this discontinuity is a small `tube' of fluid bounding the flow. The delta-shock conditions for this flow are derived and solved for a point source on an inclined plane. This latter delta-shock framework also sheds light on the evolution of the layer impact on a horizontal base

A model-based constraint on CO₂ fertilisation

We derive a constraint on the strength of CO2 fertilisation of the terrestrial biosphere through a “top-down” approach, calibrating Earth system model parameters constrained by the post-industrial increase of atmospheric CO2 concentration. We derive a probabilistic prediction for the globally averaged strength of CO2 fertilisation in nature, for the period 1850 to 2000 AD, implicitly net of other limiting factors such as nutrient availability. The approach yields an estimate that is independent of CO2 enrichment experiments. To achieve this, an essential requirement was the incorpo- ration of a land use change (LUC) scheme into the GENIE Earth system model. Using output from a 671-member ensemble of transient GENIE simulations, we build an emulator of the change in atmospheric CO2 concentration change since the preindustrial period. We use this emulator to sample the 28-dimensional input parameter space. A Bayesian calibration of the emulator output suggests that the increase in gross primary productivity (GPP) in response to a doubling of CO2 from preindustrial values is very likely (90 % confidence) to exceed 20 %, with a most likely value of 40–60 %. It is important to note that we do not represent all of the possible contributing mechanisms to the terrestrial sink. The missing processes are subsumed into our calibration of CO2 fertilisation, which therefore represents the combined effect of CO2 fertilisation and additional missing processes. If the missing processes are a net sink then our estimate represents an upper bound. We derive calibrated estimates of carbon fluxes that are consistent with existing estimates. The present-day land–atmosphere flux (1990–2000) is estimated at −0.7 GTC yr−1 (likely, 66 % confidence, in the range 0.4 to −1.7 GTC yr−1). The present-day ocean–atmosphere flux (1990–2000) is estimated to be −2.3 GTC yr−1 (likely in the range −1.8 to −2.7 GTC yr−1). We estimate cumulative net land emissions over the post-industrial period (land use change emissions net of the CO2 fertilisation and climate sinks) to be 66 GTC, likely to lie in the range 0 to 128 GTC