Highly precise Re-Os dating for molybdenite using alkaline fusion and NTIMS

The technique described in this paper represents the modification and combination of two previously existing methods, alkaline fusion and negative thermal ion mass spectrometry (NTIMS). We have used this technique to analyze repeatedly a homogeneous molybdenite powder used as a reference standard in our laboratory. Analyses were made over a period of 18 months, using four different calibrations of two different spike solutions. The age of this standard reproduces at a level of +/-0.13%. Each individual age analysis carries an uncertainty of about 0.4% that includes the uncertainty in the decay constant for (187)Re. This new level of resolution has allowed us to recognize real differences in ages for two grain-size populations of molybdenite from some Archean samples.     

On a stopping process for oscillatory integrals

In this paper we introduce a stopping process to analyze oscillatory integral operators with degenerate phases. The resulting bounds give smoothing properties for averages along variable families of curves inR ⁿ with two-sided torsion. Supported in part by the National Science Foundation under Grants DMS-92-04196 and DMS-91-04455.A01.     

Exotic states in long-range spin glasses

We consider Ising spin glasses onZ ^d with couplingsJ _xy =c _y–x Z _xy , where thec _y 's are nonrandom real coefficients and theZ _xy 's are independent, identically distributed random variables withE[Z _xy ]=0 andE[Z _xy ² ]=1. We prove that if _y |c _y |= while _y |c _y |²=, then (with probability one) there are uncountably many (infinite volume) ground states , each of which has the following property: forany temperatureT<, there is a Gibbs state supported entirely on (infinite volume) spin configurations which differ from only atfinitely many sites. This and related results are examples of the bizarre effects that can occur in disordered systems with coupling-dependent boundary conditions.Research supported in part by NSF Grants DMS-9196086 and 9209053Research supported in part by U.S. Department of Energy Grant No. DE-FG03-93ER25155     

Stochastic resonance: Linear response and giant nonlinearity

The response of a bistable noise-driven system to a weak periodic force is investigated using linear response theory (LRT) and by analogue electronic experiment. For quasithermal systems the response, and in particular its increase with increasing noise intensityD, are described by the fluctuationdissipation relations. For smallD the low-frequency susceptibility of the system() has been found in explicit form allowing for both forced oscillations about the states and periodic modulation of the probabilities of fluctuational transitions between the states. It is shown, both theoretically and experimentally, that a phase lag between the force and the response passes through a maximum whenD is tuned through the range where stochastic resonance (SR) occurs. A giant nonlinearity of the response is shown to arise for smallD and small frequencies of the driving force. It results in the signal induced by a sinusoidal force being nearly rectangular. The range of applicability of LRT is established.