Unequal relationships in high and low power distance societies: a comparative study of tutor - student role relations in Britain and China

This study investigated people's conceptions of an unequal role relationship in two different types of society: a high power distance society and a low power distance society. The study focuses on the role relationship of tutor and student. British and Chinese tutors and postgraduate students completed a questionnaire that probed their conceptions of degrees of power differential and social distance/closeness in this role relationship. ANOVA results yielded a significant nationality effect for both aspects. Chinese respondents judged the relationship to be closer and to have a greater power differential than did British respondents. Written comments on the questionnaire and interviews with 9 Chinese academics who had experienced both British and Chinese academic environments supported the statistical findings and indicated that there are fundamental ideological differences associated with the differing conceptions. The results are discussed in relation to Western and Asian concepts of leadership and differing perspectives on the compatibility/incompatibility of power and distance/closeness

Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.Comment: v

Forward Symplectic Integrators and the Long Time Phase Error in Periodic Motions

We show that when time-reversible symplectic algorithms are used to solve periodic motions, the energy error after one period is generally two orders higher than that of the algorithm. By use of correctable algorithms, we show that the phase error can also be eliminated two orders higher than that of the integrator. The use of fourth order forward time step integrators can result in sixth order accuracy for the phase error and eighth accuracy in the periodic energy. We study the 1-D harmonic oscillator and the 2-D Kepler problem in great details, and compare the effectiveness of some recent fourth order algorithms.Comment: Submitted to Phys. Rev. E, 29 Page

An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

Symplectic integrators with adaptive time steps

In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall into two categories. In the first, the time step is considered a function of time alone, \Delta=\Delta(t). In this case, backwards error analysis shows that while the algorithms remain symplectic, parametric instabilities arise because of resonance between oscillations of \Delta(t) and the orbital motion. In the second category the time step is a function of phase space variables \Delta=\Delta(q,p). In this case, the system of equations to be solved is analyzed by introducing a new time variable \tau with dt=\Delta(q,p) d\tau. The transformed equations are no longer in Hamiltonian form, and thus are not guaranteed to be stable even when integrated using a method which is symplectic for constant \Delta. We analyze two methods for integrating the transformed equations which do, however, preserve the structure of the original equations. The first is an extended phase space method, which has been successfully used in previous studies of adaptive time step symplectic integrators. The second, novel, method is based on a non-canonical mixed-variable generating function. Numerical trials for both of these methods show good results, without parametric instabilities or spurious growth or damping. It is then shown how to adapt the time step to an error estimate found by backward error analysis, in order to optimize the time-stepping scheme. Numerical results are obtained using this formulation and compared with other time-stepping schemes for the extended phase space symplectic method.Comment: 23 pages, 9 figures, submitted to Plasma Phys. Control. Fusio

The Longitudinal Stability of Intense Non-Relativistic Particle Bunches in Resistive Structures

The longitudinal stability of intense particle bunches is investigated theoretically in the limit of small wall resistivity compared to total reactance. It is shown that both in the absence of resistivity and to lowest order in the resistance that an intense bunch is stable against longitudinal collective modes. An expression is derived for the lowest order instability rate. Application of these results are made to drivers for heavy ion inertial fusion

Calcareous nannofossil data and magnetostratigraphy from the Atlantic and Tethys Oceans - An integrated approach to approximate the Jurassic/Cretaceous (J/K) boundary in low-latitudinal pelagic and hemipelagic sequences.

The Tithonian \u2013 Early Berriasian interval is characterized by a major calcareous nannofossil speciation event: several Cretaceous genera and species first appear and rapidly evolve (Bralower et al., 1989). Progressive increases in diversity, abundance and degree of calcification (Nannofossil Calcification Event \u2013 NCE; Bornemann et al., 2003) have also been documented. Integrated magneto- and calcareous nannofossil biostratigraphy across the Jurassic/Cretaceous (J/K) boundary have been independently investigated in Tethyan land sections (Torre de Busi and Foza, Southern Alps) and at Atlantic Ocean DSDP sites (534A, Blake Bahama Basin and 105, Hatteras Basin). Calcareous nannofossil biostratigraphy, absolute and relative abundances have been obtained using three different techniques: random settling slides (Geisen et al., 1999), simple smear slides and ultra-thin sections (7-8 \ub5m thick). Similar variations in nannofloral abundance and composition, including the NCE, have been documented in both Atlantic and Tethys oceans (low latitude associations). All known calcareous nannofossil Zones and corresponding Subzones, following the biostratigraphic scheme of Bralower et al. (1989), have been recognized: NJ-19b; NJ-20a, NJ-20b; NJK-A, NJK-B, NJK-C across J/K boundary, NJK-D; NK-1 In the Middle Tithonian the nannoliths taxa C. mexicana minor, C. mexicana mexicana, and P. beckmannii increase significantly in abundance (Bornemann et al., 2003; Tremolada et al., 2006): the maximum relative abundance is reached between the calcareous nannofossil Zone NJ-20B and early NJK-A (Atlantic Ocean) or NJK-B (Tethys Ocean), followed by a decrease through NJK-A and NJK-B. Nannoconids appear and rapidly evolve across the J/K boundary reaching high relative abundances in the lowermost Berriasian (from calcareous nannofossil Subzone NJK-C to NK-1). Quantitative and morphometric studies have identified new potential events. Relative abundances of the placolith genera Watznaueria and the nannolith genera Conusphaera show opposite trends, while morphometric analysis show a size increase of placoliths, nannoliths and nannoconids during NCEs both in the Atlantic and Tethyan sections: calibration with magnetostratigraphy indicate that these trends are useful as additional bio-horizons for locating the J/K boundary. Calcareous nannofossil zonations and abundance variations of tethyan Torre de Busi section have also been correlated with calpionellid biostratigraphy, which has been investigated on the same samples used for the calcareous nannofossil study. It has been possible to identify the Chitinoidella, Crassicollaria and Calpionella Zones across the J/K boundary (Remane, 1986;Pop, 1994b and Reh\ue1kov\ue1 and Michal\uedk, 1997). Six polarity chrons (from CM22 to CM17) have been identified in DSDP site 534A, and in the tethyan land sections. The speciation of highly-calcified and dissolution resistant calcareous nannofossil forms, and related remarkable abundance and size increases, and the relative trends between genera Watznaueria and Conusphaera could provide new reliable stratigraphic tools for the approximation of the J/K boundary in low latitudinal pelagic and hemipelagic sequences in the Atlantic and Tethyan Oceans. In conclusion integrated stratigraphy, derived from the correlation among several calcareous nannofossils events, capionellid zonation and magnetostratigraphic events, can be used to characterize the J/K boundary interval, and is believed essential for defining the Jurassic/Cretaceous boundary particularly in the absence of orthostratigraphic markers (e.g. ammonites). References: Bornemann, A., Aschwer, U. and Mutterlose, J., 2003. The impact of calcareous nannofossils on the pelagic carbonate accumulation across the Jurassic-Cretaceous boundary. Palaeogeography Palaeoclimatology Palaeoecology, 199(3-4): 187-228. Bown, P.R. and Cooper, M.K.E., 1998. Jurassic. In: P.R. Bown (Editor), Calcareous nannofossil stratigraphy. British Micropalaeontological Society Publications Series. Kluver Academic Publishers, Dordrecht, Boston, London, pp. 34-85. Bown, P.R., Lees, J.A. and Young, J.R., 2004. Calcareous nannoplankton evolution and diversity through time. In: H. Thierstein and J.R. Young (Editors), ), Coccolithophores - From Molecular Processes to Global Impact. Springer, Berlin, pp. 481-508. Bralower, T.J., Monechi, S. and Thierstein, H.R., 1989. Calcareous nannofossil Zonation of the Jurassic-Cretaceous Boundary Interval and Correlation with the Geomagnetic Polarity Timescale. Marine Micropaleontology, 14: 153-235. Geisen, M., Bollmann, J., Herrle, J.O., Mutterlose, J. and Young, J.R., 1999. Calibration of the random settling technique for calculation of absolute abundances of calcareous nannoplankton. Micropaleontology, 45(4): 437-442. Erba, E. and Quadrio, B., 1989. Biostratigrafia a Nannofossili Calcarei, Calpionellidi e Foramminiferi planctonici della Maiolica (Titoniano superiore - Aptiano) nelle Prealpi Bresciane (Italia settentrionale). Riv. It. Paleont. Strat. 93(1): 3-108 Danelian, T. and Johnson, K.G., 2001. Patterns of biotic changes in Middle Jurassic to Early Cretaceous Tethyan radiolaria. Marine Micropaleontology 43: 239-260 Pop, G., 1994b. Calpionellid evolutive events and their use in biostratigraphy. Rom. J. Stratigraphy, 76: 7-24. Reh\ue1kov\ue1, D. and Michal\uedk, J., 1997: Evolution and distribution of calpionellids- the most characteristic constituents of Lower Cretaceous Tethyan microplankton. Cretaceous Research, 18: 493-504 Remane, J., 1986: Calpionellids and the Jurassic-Cretaceous boundary. Acta Geologica Hungarica, 29: 15-26 Rais, P., 2007. Ph.D. Thesis Roth, P.H., 1983. Jurassic and Lower Cretaceous calcareous nannofossils in the western North Atlantic (site 534): biostratigraphy, preservation, and some observation on biogeography and paleoceanography. Init. Rep. DSDP 76: 587-621 Tremolada, F., Bornemann, A., Bralower, T.J., Koeberl, C. and van de Schootbrugge, B., 2006. Paleoceanographic changes across the Jurassic/Cretaceous boundary: The calcareous phytoplankton response. Earth and Planetary Science Letters, 241(3-4): 361-371. Weissert, H. and Channell, J.E.T., 1989. Tethyan carbonate carbon isotope stratigraphy across the Jurassic/Cretaceous boundary: an indicator of decelerated global carbon cycling?. Paleoceanography 4(4): 483-49

A consideration of the challenges involved in supervising international masters students

This paper explores the challenges facing supervisors of international postgraduate students at the dissertation stage of the masters programme. The central problems of time pressure, language difficulties, a lack of critical analysis and a prevalence of personal problems among international students are discussed. This paper makes recommendations for the improvement of language and critical thinking skills, and questions the future policy of language requirements at HE for international Masters students