Nonlinear wavelength selection in surface faceting under electromigration

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as $t^{1/2}$. For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady-states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening {\it before} reaching a continuous family of stable non-equilibrium steady-states.Comment: 5 pages, 4 figures, submitte

Homalg: A meta-package for homological algebra

The central notion of this work is that of a functor between categories of finitely presented modules over so-called computable rings, i.e. rings R where one can algorithmically solve inhomogeneous linear equations with coefficients in R. The paper describes a way allowing one to realize such functors, e.g. Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra system. Once this is achieved, one can compose and derive functors and even iterate this process without the need of any specific knowledge of these functors. These ideas are realized in the ring independent package homalg. It is designed to extend any computer algebra software implementing the arithmetics of a computable ring R, as soon as the latter contains algorithms to solve inhomogeneous linear equations with coefficients in R. Beside explaining how this suffices, the paper describes the nature of the extensions provided by homalg.Comment: clarified some points, added references and more interesting example

Meeting the Sustainable Development Goals leads to lower world population growth

Here we show the extent to which the expected world population growth could be lowered by successfully implementing the recently agreed-upon Sustainable Development Goals (SDGs). The SDGs include specific quantitative targets on mortality, reproductive health, and education for all girls by 2030, measures that will directly and indirectly affect future demographic trends. Based on a multidimensional model of population dynamics that stratifies national populations by age, sex, and level of education with educational fertility and mortality differentials, we translate these goals into SDG population scenarios, resulting in population sizes between 8.2 and 8.7 billion in 2100. Because these results lie outside the 95% prediction range given by the 2015 United Nations probabilistic population projections, we complement the study with sensitivity analyses of these projections that suggest that those prediction intervals are too narrow because of uncertainty in baseline data, conservative assumptions on correlations, and the possibility of new policies influencing these trends. Although the analysis presented here rests on several assumptions about the implementation of the SDGs and the persistence of educational, fertility, and mortality differentials, it quantitatively illustrates the view that demography is not destiny and that policies can make a decisive difference. In particular, advances in female education and reproductive health can contribute greatly to reducing world population growth

Effect of hole doping on the London penetration depth in Bi2.15Sr1.85CaCu2O8+δ and Bi2.1Sr1.9Ca0.85Y0.15Cu2O8+δ

We report measurements of ac susceptibility and hence the in-plane London penetration depth on the same samples of Bi2.15Sr1.85CaCu2O8+δ and Bi2.1Sr1.9Ca0.85Y0.15Cu2O8+δ for many values of the hole concentration (p). These support the scenario in which the pseudogap weakens the superconducting response only for p≲0.19.We acknowledge funding from the EPSRC (U.K.), for the experimental facilities in Cambridge, and further financial support from The Royal Society, EURYI, and MEXT-CT-2006-039047. W.A. was supported by the Development and Promotion of Science and Technology Talents Project (D.P.S.T.), Thailand

Telerobotics: A simulation facility for university research

An experimental telerobotics (TR) simulation suitable for studying human operator (H.O.) performance is described. Simple manipulator pick-and-place and tracking tasks allowed quantitative comparison of a number of calligraphic display viewing conditions. A number of control modes could be compared in this TR simulation, including displacement, rate and acceleratory control using position and force joysticks. A homeomorphic controller turned out to be no better than joysticks; the adaptive properties of the H.O. can apparently permit quite good control over a variety of controller configurations and control modes. Training by optimal control example seemed helpful in preliminary experiments. An introduced communication delay was found to produce decrease in performance. In considerable part, this difficulty could be compensated for by preview control information. That neurological control of normal human movement contains a data period of 0.2 second may relate to this robustness of H.O. control to delay. The Ames-Berkeley enhanced perspective display was utilized in conjunction with an experimental helmet mounted display system (HMD) that provided stereoscopic enhanced views

Pressurization of Liquid Oxygen Containers Progress Report No. 7, Nov. 1963 - Nov. 1964

Pressurization of liquid oxygen containers - cryogenic fluid boiling under high and low gravity, liquid hydrogen boiling, injection cooling, and two-dimensional heat transfe

Criterion for polynomial solutions to a class of linear differential equation of second order

We consider the differential equations y''=\lambda_0(x)y'+s_0(x)y, where \lambda_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of degree n >0, then \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1}\hbox{and}\quad s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1},\quad n=1,2,.... Conversely (ii) if \lambda_n\lambda_{n-1}\ne 0 and \delta_n=0, then the differential equation has a polynomial solution of degree at most n. We show that the classical differential equations of Laguerre, Hermite, Legendre, Jacobi, Chebyshev (first and second kind), Gegenbauer, and the Hypergeometric type, etc, obey this criterion. Further, we find the polynomial solutions for the generalized Hermite, Laguerre, Legendre and Chebyshev differential equations.Comment: 12 page

Projection of Populations by Level of Educational Attainment, Age and Sex for 120 Countries for 2005-2050

Using demographic multi-state methods, this paper presents projections for the population of 120 countries (covering 93 percent of the world population in 2000) by age, sex and level of educational attainment for the years 2000 to 2050. The dataset produced gives the full educational attainment distributions for four categories (no education, primary, secondary and tertiary education) by five-year age groups, with definitions that are consistent with a previous reconstruction of educational attainment for the years 1970 to 2000. Based on empirical distributions of educational attainment by age and sex for the year 2000, the method moves along cohort lines while taking into account differentials in fertility and mortality by education level. The most extensive in time and geographical coverage to date, to our knowledge this work represents the first attempt to project future educational attainment trends based on a statistical model of historical international attainment growth. The resulting dataset provides valuable insights both on the feasibility of international education targets and on their implications for human capital and population size and age structure