The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

A plan for the characterization, calibration, and evaluation of LAPR-2

A new airborne Linear Array Pushbroom Radiometer (LAPR-II) was built. LAPR-II will use linear arrays of silicon detectors to acquire four channels of digital image data for spectral bands within the visible and near infrared portions of the spectrum (0.4 - 1.0 micrometers). The data will be quantized to 10 bits, and spectral filters for each channel will be changeable in flight. The instrument will initially be flown aboard a NASA/Wallops' aircraft, and off nadir pointing of LAPR-II will be possible. Together, the instrument and its platform will provide a flexible readily available source of digital image data for scientific experiments. If LAPR-II is to serve as a precise scientific instrument, the instrument's characteristics must be quantitatively described and the data must be calibrated with respect to absolute radiometric units. The LAPR-II is described and the work required to characterize the instrument's spectral response, radiometric response, and spatial resolution and to calibrate the response from the many detectors per array is outlined

1/fα1/f^\alpha noise and integrable systems

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f^2 power law. In this letter, we show that there is a family of well-known integrable systems, namely spin chains of Haldane-Shastry type, whose spectral fluctuations decay instead as 1/f^4. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.Comment: 5 pages, 3 figures, RevTe

Estimation of stratospheric input to the Arctic troposphere: 7Be and 10Be in aerosols at Alert, Canada

Concentrations of 7Be and 210Pb in 2 years of weekly high-volume aerosol samples collected at Alert, Northwest Territories, Canada, showed pronounced seasonal variations. We observed a broad winter peak in 210Pb concentration and a spring peak in 7Be. These peaks were similar in magnitude and duration to previously reported results for a number of stations in the Arctic Basin. Beryllium 10 concentrations (determined only during the first year of this study) were well correlated with those of 7Be; the atom ratio 10Be/7Be was nearly constant at 2.2 throughout the year. This relatively high value of 10Be/7Be indicates that the stratosphere must constitute an important source of both Be isotopes in the Arctic troposphere throughout the year. A simple mixing model based on the small seasonal variations of 10Be/7Be indicates an approximately twofold increase of stratospheric influence in the free troposphere in late summer. The spring maxima in concentrations of both Be isotopes at the surface apparently reflect vertical mixing in rather than stratospheric injections into the troposphere. We have merged the results of the Be-based mixing model with weekly O3 soundings to assess Arctic stratospheric impact on the surface O3 budget at Alert. The resulting estimates indicate that stratospheric inputs can account for a maximum of 10-15% of the 03 at the surface in spring and for less during the rest of the year. These estimates are most uncertain during the winter. The combination of Be isotopic measurements and O3 vertical profiles could allow quantification of the contributions of O3 from the Arctic stratosphere and lower latitude regions to the O3 budget in the Arctic troposphere. Although at present the lack of a quantitative understanding of the temporal variation of O3 lifetime in the Arctic troposphere precludes making definitive calculations, qualitative examples of the power of this approach are given

Navigating personal and relational concerns: the quest for equilibrium

The authors' personal-relational equilibrium model suggests that people come to seek equilibrium in their dedication to personal and relational concerns in that these 2 important needs cannot always be gratified simultaneously. The authors proposed that the experience of personal-relational disequilibrium motivates attempts to restore equilibrium and that achieving equilibrium promotes life satisfaction. Four studies revealed good support for the model. In Study 1, a manipulation of anticipated future disequilibrium (vs. equilibrium) as a result of overdedication to either the personal or relational domain caused reduced motivation to address concerns in that domain and increased motivation toward the complementary domain. In Study 2, narratives describing disequilibrium experiences (vs. equilibrium experiences) exhibited increased motivation to restore equilibrium and reduced life satisfaction. In Study 3, diary reports of everyday disequilibrium were associated with increased same-day motivation to restore equilibrium, reduced same-day life satisfaction, and increased next-day dedication of effort to the complementary domain. In Study 4, experiences of disequilibrium predicted reduced well-being 6 months later. Collectively, these findings extend knowledge of how people regulate themselves toward equilibrium in pursuing 2 fundamental human concerns

Rates of erosion and landscape change along the Blue Ridge escarpment, southern Appalachian Mountains, estimated from in situ cosmogenic 10Be

The Blue Ridge escarpment, located within the southern Appalachian Mountains of Virginia and North Carolina, forms a distinct, steep boundary between the lower-elevation Piedmont and higher-elevation Blue Ridge physiographic provinces. To understand better the rate at which this landform and the adjacent landscape are changing, we measured cosmogenic 10Be in quartz separated from sediment samples (n = 50) collected in thirty-two streams and from three exposed bedrock outcrops along four transects normal to the escarpment, allowing us to calculate erosion rates integrated over 104–105 years. These basin-averaged erosion rates (5.4–49 m My-1) are consistent with those measured elsewhere in the southern Appalachians and show a positive relationship between erosion rate and average basin slope. Erosion rates show no relationship with basin size or relative position of the Brevard fault zone, a fundamental structural element of the region. The cosmogenic isotopic data, when considered along with the distribution of average basin slopes in each physiographic province, suggest that the escarpment is eroding on average more rapidly than the Blue Ridge uplands, which are eroding more rapidly than the Piedmont lowlands. This difference in erosion rates by geomorphic setting suggests that the elevation difference between the uplands and lowlands adjacent to the escarpment is being reduced but at extremely slow rates

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

Zero-temperature generalized phase diagram of the 4d transition metals under pressure

We use an accurate implementation of density functional theory (DFT) to calculate the zero-temperature generalized phase diagram of the 4$d$ series of transition metals from Y to Pd as a function of pressure $P$ and atomic number $Z$. The implementation used is full-potential linearized augmented plane waves (FP-LAPW), and we employ the exchange-correlation functional recently developed by Wu and Cohen. For each element, we obtain the ground-state energy for several crystal structures over a range of volumes, the energy being converged with respect to all technical parameters to within $\sim 1$ meV/atom. The calculated transition pressures for all the elements and all transitions we have found are compared with experiment wherever possible, and we discuss the origin of the significant discrepancies. Agreement with experiment for the zero-temperature equation of state is generally excellent. The generalized phase diagram of the 4$d$ series shows that the major boundaries slope towards lower $Z$ with increasing $P$ for the early elements, as expected from the pressure induced transfer of electrons from $sp$ states to $d$ states, but are almost independent of $P$ for the later elements. Our results for Mo indicate a transition from bcc to fcc, rather than the bcc-hcp transition expected from $sp$-$d$ transfer.Comment: 28 pages and 10 figures. Submitted to Phys. Rev.

Cosmogenic Production of Be-7 and Be-10 in Water Targets

We have measured Be-10(t(sub 1/2) = 1.5 x 10(exp 6) years) and Be-7 (t(sub 1/2) = 53.28 days) concentrations in water targets exposed for 1 to 2 years at Echo Lake, Colorado (elevation = 3246 m) and at La Jolla, California (140 m). Neutron monitor data were used to normalize the measured concentrations in order to calculate production rates equivalent to the cosmic ray flux averaged over four solar cycles (43 years). The Be-7 production rates thus obtained correspond to 6.03 +/- 0.07 x 10(exp -6) atom/g.O/s at Echo Lake and 5.06 +/- 0.20 x 10(exp -7) atom/g.O/ s at La Jolla. The Be-10 production rates correspond to 3.14 +/- 0.18 x 10(exp -6) atom/g.O/s at Echo Lake and 2.68 +/- 0.47 x 10(exp -7) atom/g.O/s at La Jolla. When compared with Be-10 production rates determined in Be-10-saturated rocks from the Antarctic and with theoretical calculations based on meteorite and lunar sample data, we find that the million-year average production rate is about 14 - 17% greater than the present production rate averaged over the last four solar cycles. Comparison with production rates determined by measuring glacially polished rocks from the Sierra Nevada in California indicates that average production (based on a revised 13,000-year deglaciation age and a geographic latitude correction) is a about 11% greater than the average over the last four solar cycles. The measured Be-10/Be-7 production ratio in oxygen is 0.52 +/- 0.03 at Echo Lake and 0.55 +/- 0.07 at La Jolla