Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Quantification of complementarity in multi-qubit systems

Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation between classically incompatible properties, such as visibility of interference fringes and "which-way" information, but also between purely quantum mechanical properties, such as measures of entanglement. We discuss different complementarity relations for systems of 2-, 3-, or \textit{n} qubits. Using nuclear magnetic resonance techniques, we have experimentally verified some of these complementarity relations in a two-qubit system.Comment: 12 pages, 10 figures (A display error about the figures in the previous version

Application of constitutive friction laws to glacier seismicity

While analysis of glacial seismicity continues to be a widely used method for interpreting glacial processes, the underlying mechanics controlling glacial stick-slip seismicity remain speculative. Here, we report on laboratory shear experiments of debris-laden ice slid over a bedrock asperity under carefully controlled conditions. By modifying the elastic loading stiffness, we generated the first laboratory icequakes. Our work represents the first comprehensive lab observations of unstable ice-slip events and replicates several seismological field observations of glacier slip, such as slip velocity, stress drop, and the relationship between stress drop and recurrence interval. We also observe that stick-slips initiate above a critical driving velocity and that stress drop magnitude decreases with further increases in velocity, consistent with friction theory and rock-on-rock friction laboratory experiments. Our results demonstrate that glacier slip behavior can be accurately predicted by the constitutive rate-and-state friction laws that were developed for rock friction

Highly variable friction and slip observed at Antarctic ice stream bed

The slip of glaciers over the underlying bed is the dominant mechanism governing the migration of ice from land into the oceans, with accelerating slip contributing to sea-level rise. Yet glacier slip remains poorly understood, and observational constraints are sparse. Here we use passive seismic observations to measure both frictional shear stress and slip at the bed of the Rutford Ice Stream in Antarctica using 100,000 repetitive stick-slip icequakes. We find that basal shear stresses and slip rates vary from 10$^4$ to 10$^7$ Pa and 0.2 to 1.5 m per day, respectively. Friction and slip vary temporally over the order of hours, and spatially over 10s of metres, due to corresponding variations in effective normal stress and ice–bed interface material. Our findings suggest that the bed is substantially more complex than currently assumed in ice stream models and that basal effective normal stresses may be significantly higher than previously thought. Our observations can provide constraints on the basal boundary conditions for ice-dynamics models. This is critical for constraining the primary contribution of ice mass loss in Antarctica and hence for reducing uncertainty in sea-level rise projections

Short-wavelength collective modes in a binary hard-sphere mixture

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive gives misleading impression of new publicatio

The Greenland Ice Sheet Project 2 Depth-age Scale: Methods and Results

The Greenland Ice Sheet Project 2 (GISP2) depth-age scale is presented based on a multiparameter continuous count approach, to a depth of 2800 m, using a systematic combination of parameters that have never been used to this extent before. The ice at 2800 m is dated at 110,000 years B.P. with an estimated error ranging from 1 to 10% in the top 2500 m of the core and averaging 20% between 2500 and 2800 m. Parameters used to date the core include visual stratigraphy, oxygen isotopic ratios of the ice, electrical conductivity measurements, laser-light scattering from dust, volcanic signals, and major ion chemistry. GISP2 ages for major climatic events agree with independent ages based on varve chronologies, calibrated radiocarbon dates, and other techniques within the combined uncertainties. Good agreement also is obtained with Greenland Ice Core Project ice core dates and with the SPECMAP marine timescale after correlation through the δ18O of O2. Although the core is deformed below 2800 m and the continuity of the record is unclear, we attempted to date this section of the core on the basis of the laser-light scattering of dust in the ice

Five millennia of surface temperatures and ice core bubble characteristics from the WAIS Divide deep core, West Antarctica

Bubble number densities from the West Antarctic Ice Sheet (WAIS) Divide deep core in West Antarctica record relatively stable temperatures during the middle Holocene followed by late Holocene cooling. We measured bubble number density, shape, size, and arrangement on new samples of the main WAIS Divide deep core WDC06A from similar to 580m to similar to 1600 depth. The bubble size, shape, and arrangement data confirm that the samples satisfy the requirements for temperature reconstructions. A small correction for cracks formed after core recovery allows extension of earlier work through the brittle ice zone, and a site-specific calibration reduces uncertainties. Using an independently constructed accumulation rate history and a steady state bubble number density model, we determined a temperature reconstruction that agrees closely with other independent estimates, showing a stable middle Holocene, followed by a cooling of similar to 1.25 degrees C in the late Holocene. Over the last similar to 5 millennia, accumulation has been higher during warmer times by similar to 12%degrees C-1, somewhat stronger than for thermodynamic control alone, suggesting dynamic processes

Realistic Calculation of the hep Astrophysical Factor

The astrophysical factor for the proton weak capture on 3He is calculated with correlated-hyperspherical-harmonics bound and continuum wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v18 two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components, that include one- and many-body terms. All possible multipole transitions connecting any of the p-3He S- and P-wave channels to the 4He bound state are considered. The S-factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak energy, is predicted to be 10.1 10^{-20} keV b, a factor of five larger than the standard-solar-model value. The P-wave transitions are found to be important, contributing about 40 % of the calculated S-factor.Comment: 8 pages RevTex file, submitted to Phys. Rev. Let

The Ay Problem for p-3He Elastic Scattering

We present evidence that numerically accurate quantum calculations employing modern internucleon forces do not reproduce the proton analyzing power, A_y, for p-3He elastic scattering at low energies. These calculations underpredict new measured analyzing powers by approximately 30% at E_{c.m.} = 1.20 MeV and by 40% at E_{c.m.} = 1.69 MeV, an effect analogous to a well-known problem in p-d and n-d scattering. The calculations are performed using the complex Kohn variational principle and the (correlated) Hyperspherical Harmonics technique with full treatment of the Coulomb force. The inclusion of the three-nucleon interaction does not improve the agreement with the experimental data.Comment: Latex file, 4 pages, 2 figures, to be published on Phys. Rev. Let

Effects of thermal fluctuation and the receptor-receptor interaction in bacterial chemotactic signalling and adaptation

Bacterial chemotaxis is controlled by the conformational changes of the receptors, in response to the change of the ambient chemical concentration. In a statistical mechanical approach, the signalling due to the conformational changes is a thermodynamic average quantity, dependent on the temperature and the total energy of the system, including both ligand-receptor interaction and receptor-receptor interaction. This physical theory suggests to biology a new understanding of cooperation in ligand binding and receptor signalling problems. How much experimental support of this approach can be obtained from the currently available data? What are the parameter values? What is the practical information for experiments? Here we make comparisons between the theory and recent experimental results. Although currently comparisons can only be semi-quantitative or qualitative, consistency is clearly shown. The theory also helps to sort a variety of data.Comment: 26 pages, revtex. Journal version. Analysis on another set of data on adaptation time is adde