Constrained Reductions of 2D dispersionless Toda Hierarchy, Hamiltonian Structure and Interface Dynamics

Finite-dimensional reductions of the 2D dispersionless Toda hierarchy, constrained by the ``string equation'' are studied. These include solutions determined by polynomial, rational or logarithmic functions, which are of interest in relation to the ``Laplacian growth'' problem governing interface dynamics. The consistency of such reductions is proved, and the Hamiltonian structure of the reduced dynamics is derived. The Poisson structure of the rationally reduced dispersionless Toda hierarchies is also derivedComment: 18 pages LaTex, accepted to J.Math.Phys, Significantly updated version of the previous submissio

Diffusion-Limited Aggregation on Curved Surfaces

We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusion-limited-aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere ($K>0$) and pseudo-sphere ($K<0$), which approximate "bumps" and "saddles" in smooth surfaces, respectively. Although curvature affects the global morphology of the aggregates, the fractal dimension (in the curved metric) is remarkably insensitive to curvature, as long as the particle size is much smaller than the radius of curvature. We conjecture that all aggregates grown by conformally invariant transport on curved surfaces have the same fractal dimension as DLA in the plane. Our simulations suggest, however, that the multifractal dimensions increase from hyperbolic ($K0$) geometry, which we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig

A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation

We present a new class of exact solutions for the so-called {\it Laplacian Growth Equation} describing the zero-surface-tension limit of a variety of 2D pattern formation problems. Contrary to common belief, we prove that these solutions are free of finite-time singularities (cusps) for quite general initial conditions and may well describe real fingering instabilities. At long times the interface consists of N separated moving Saffman-Taylor fingers, with ``stagnation points'' in between, in agreement with numerous observations. This evolution resembles the N-soliton solution of classical integrable PDE's.Comment: LaTeX, uuencoded postscript file

Laplacian Growth and Whitham Equations of Soliton Theory

The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.Comment: 33 pages, 7 figures, typos corrected, new references adde

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.Comment: Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 200

The Current State of Performance Appraisal Research and Practice: Concerns, Directions, and Implications

On the surface, it is not readily apparent how some performance appraisal research issues inform performance appraisal practice. Because performance appraisal is an applied topic, it is useful to periodically consider the current state of performance research and its relation to performance appraisal practice. This review examines the performance appraisal literature published in both academic and practitioner outlets between 1985 and 1990, briefly discusses the current state of performance appraisal practice, highlights the juxtaposition of research and practice, and suggests directions for further research

Monitoring and evaluation of human resources for health: an international perspective

BACKGROUND: Despite the undoubted importance of human resources to the functions of health systems, there is little consistency between countries in how human resource strategies are monitored and evaluated. This paper presents an integrated approach for developing an evidence base on human resources for health (HRH) to support decision-making, drawing on a framework for health systems performance assessment. METHODS: Conceptual and methodological issues for selecting indicators for HRH monitoring and evaluation are discussed, and a range of primary and secondary data sources that might be used to generate indicators are reviewed. Descriptive analyses are conducted drawing primarily on one type of source, namely routinely reported data on the numbers of health personnel and medical schools as covered by national reporting systems and compiled by the World Health Organization. Regression techniques are used to triangulate a given HRH indicator calculated from different data sources across multiple countries. RESULTS: Major variations in the supply of health personnel and training opportunities are found to occur by region. However, certain discrepancies are also observed in measuring the same indicator from different sources, possibly related to the occupational classification or to the sources' representation. CONCLUSION: Evidence-based information is needed to better understand trends in HRH. Although a range of sources exist that can potentially be used for HRH assessment, the information that can be derived from many of these individual sources precludes refined analysis. A variety of data sources and analytical approaches, each with its own strengths and limitations, is required to reflect the complexity of HRH issues. In order to enhance cross-national comparability, data collection efforts should be processed through the use of internationally standardized classifications (in particular, for occupation, industry and education) at the greatest level of detail possible

Heating of nuclei with energetic anti-protons

International audienceHigh-energy γ rays associated with the decay of the giant dipole resonance have been measured for two fusion reactions leading to the 140Sm compound nucleus at an excitation energy of 71 MeV. The observed yield increases with the asymmetry in the ratios of the number of neutrons to protons in the entrance channel. This is interpreted as resulting from giant dipole phonons excited at the moment of collision in an N/Z asymmetric reaction

Direct visualization of phase-locking of large Josephson junction arrays by surface electromagnetic waves

Phase-locking of oscillators leads to superradiant amplification of the emission power. This is particularly important for development of THz sources, which suffer from low emission efficacy. In this work we study large Josephson junction arrays containing several thousands of Nb-based junctions. Using low-temperature scanning laser microscopy we observe that at certain bias conditions two-dimensional standing-wave patterns are formed, manifesting global synchronization of the arrays. Analysis of standing waves indicates that they are formed by surface plasmon type electromagnetic waves propagating at the electrode/substrate interface. Thus we demonstrate that surface waves provide an effective mechanism for long-range coupling and phase-locking of large junction arrays.Comment: 6 pages, 3 Figure

A Reconciled Estimate of Ice-Sheet Mass Balance

We combined an ensemble of satellite altimetry, interferometry, and gravimetry data sets using common geographical regions, time intervals, and models of surface mass balance and glacial isostatic adjustment to estimate the mass balance of Earth's polar ice sheets. We find that there is good agreement between different satellite methods-especially in Greenland and West Antarctica-and that combining satellite data sets leads to greater certainty. Between 1992 and 2011, the ice sheets of Greenland, East Antarctica, West Antarctica, and the Antarctic Peninsula changed in mass by -142 plus or minus 49, +14 plus or minus 43, -65 plus or minus 26, and -20 plus or minus 14 gigatonnes year(sup 1), respectively. Since 1992, the polar ice sheets have contributed, on average, 0.59 plus or minus 0.20 millimeter year(sup 1) to the rate of global sea-level rise