Academic literature on the topic 'Van Kampen expansion'

- Peter Boomgaard, Christine Dobbin, Asian entrepreneurial minorities; Conjoint communities in the making of the world economy, 1570-1940. Richmond: Curzon Press, 1996, xiii + 246 pp. [Nordic Institute of Asian Studies Monograph Series 71.] - Ian Brown, Fukuda Shozo, With sweat and abacus; Economic roles of Southeast Asian Chinese on the eve of World War II, edited by George Hicks. Singapore: Select Books, 1995, xii + 246 pp. - Ian Brown, George Hicks, Chinese organisations in Southeast Asia in the 1930s. Singapore: Select Books, 1996, xv + 168 pp. - Matthew I. Cohen, Laurie J. Sears, Shadows of empire; Colonial discourse and Javanese tales. Durham/London: Duke University Press, 1996, xxi + 349 pp. - J. van Goor, Anthony Reid, Southeast Asia in the age of commerce 1450-1680. Vol. II: Expansion and crisis. New Haven/London: Yale University Press, 1993, xv + 390 pp. - J. van Goor, Anthony Reid, Southeast Asia in the age of commerce 1450-1680. Vol. I: The lands below the winds. New Haven/London: Yale University Press, 1988, xvi + 275 pp. - David Henley, Saya S. Shiraishi, Young heroes; The Indnesian family in politics. Ithaca/New York: Southeast Asia Program, Cornell University, Southeast Asia Program Publications, 1997, 183 pp. [Studies on Southeast Asia 22.] - Gerrit Knaap, P. Jobse, Bronnen betreffende de Midden-Molukken 1900-1942. Den Haag: Instituut voor Nederlandse Geschiedenis, 1997. 4 volumes. Rijks Geschiedkundige Publicatiën, Kleine Serie, 81, 82, 83, 84. Volume 1 bewerkt door P. Jobse, 2 en 3 door Ch.F. van Fraassen, 4 door Ch.F van Fraassen en P. Jobse. xii + 578, xii + 578, xii + 711, x + 655, xi + 261 pp., Ch. F. van Fraassen (eds.) - Indro Nugroho-Heins, Clara Brakel-Papenhuyzen, Classical Javanese dance; The Surakarta tradition and its terminology. Leiden: KITLV Press, 1995, xi + 252 pp. [Verhandelingen 155.] - László Sluimers, Shigeru Sato, War, nationalism and peasants; Java under the Japanese occupation, 1942-1945. Armonk, New York: Sharpe, St. Leonards: Allen and Unwin, 1994. xx + 280 pp. [ASAA Southeast Asia Publication Series.] - Karel Steenbrink, P.N. Holtrop, Een bundel opstellen over de Zending van de Gereformeerde Kerken in Nederland ter gelegenheid van de honderdjarige hedenking van de Synode van Middelburg 1896. Kampen: Werkgroep voor de Geschiedenis van de Nederlandse Zending en Overzeese Kerken, 1996, 199 pp. - Jaap Timmer, Aletta Biersack, Papuan borderlands; Huli, Duna, and Ipili perspectives on the Papua New Guinea Highlands. Ann Arbor: University of Michigan Press, 1995, xii + 440 pp., bibliography, index.

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle.

The spatial evolution of the velocity in a turbulent fluid is shown to consist of a mean strain rate plus a noise term whose mean-square amplitude is dependent upon the local velocity. Assuming the independence of different length scales allows one to eliminate the effect of cubic and higher moments of the velocity upon the evolution of the two-point probability density function for the velocity, analogous to the system-size expansion of the master equation (N. G. van Kampen. Adv. Chem. Phys. 34, 245 (1976); R. Kubo, K. Matsuo, and K. Kitahara. J. Stat. Phys. 9, 51 (1973); M. Suzuki. Adv. Chem. Phys. 46, 198 (1981)). Furthermore, for the velocity structures that exhibit the most internal correlation (i.e., the flow fields that are most likely to be observed) the mean strain rate drops out, leaving only the nonlinear diffusion term. In other words, the dependence of the two-point velocity statistics upon length scale or separation is found to be governed by the gradients of the stress (rather than of the velocity, as is usually assumed.) This provides a new approach for predicting the dominant patterns observed in turbulent flows and a new means of characterizing or classifying different structures, namely, by their nonlinear diffusion coefficient. As a physically relevant example, the isotropic case with algebraic nonlinearity is considered.

- Tim Behrend, Nancy K. Florida, Javanese literature in Surakarta manuscripts; Volume 2; Manuscripts of the Mangkunagaran palace. Ithaca, New York: Cornell University Southeast Asia Program, 2000, 575 pp. - Harold Brookfield, Judith M. Heimann, The most offending soul alive; Tom Harrisson and his remarkable life. Honolulu: University of Hawai’i Press, 1998, 468 pp. - Harold Brookfield, Victor T. King, Rural development and social science research; Case studies from Borneo. Phillips, Maine: Borneo Research Council, 1999, xiii + 359 pp. [Borneo Research Council Proceedings Series 6.] - J.G. de Casparis, Roy E. Jordaan, The Sailendras in Central Javanese history; A survey of research from 1950 to 1999. Yogyakarta: Penerbitan Universitas Sanata Dharma, 1999, iv + 108 pp. - H.J.M. Claessen, Francoise Douaire-Marsaudon, Les premiers fruits; Parenté, identité sexuelle et pouvoirs en Polynésie occidentale (Tonga, Wallis et Futuna). Paris: Éditions de la Maison des Sciences de l’Homme, 1998, x + 338 pp. - Matthew Isaac Cohen, Andrew Beatty, Varieties of Javanese religion; An anthropological account. Cambridge: Cambridge University Press, 1999, xv + 272 pp. [Cambridge Studies in Social and Cultural Anthropology 111.] - Matthew Isaac Cohen, Sylvia Tiwon, Breaking the spell; Colonialism and literary renaissance in Indonesia. Leiden: Department of Languages and Cultures of Southeast Asia and Oceania, University of Leiden, 1999, vi + 235 pp. [Semaian 18.] - Freek Colombijn, Victor T. King, Anthropology and development in South-East Asia; Theory and practice. Kuala Lumpur: Oxford University Press, 1999, xx + 308 pp. - Bernhard Dahm, Cive J. Christie, A modern history of South-East Asia; Decolonization, nationalism and seperatism. London: Tauris, 1996, x + 286 pp. - J. van Goor, Leonard Blussé, Pilgrims to the past; Private conversations with historians of European expansion. Leiden: Research School CNWS, 1996, 339 pp., Frans-Paul van der Putten, Hans Vogel (eds.) - David Henley, Robert W. Hefner, Market cultures; Society and morality in the new Asian capitalisms. Boulder, Colorado: Westview Press, 1998, viii + 328 pp. - David Henley, James F. Warren, The Sulu zone; The world capitalist economy and the historical imagination. Amsterdam: VU University Press for the Centre for Asian Studies, Amsterdam (CASA), 1998, 71 pp. [Comparative Asian Studies 20.] - Huub de Jonge, Laurence Husson, La migration maduraise vers l’Est de Java; ‘Manger le vent ou gratter la terre’? Paris: L’Harmattan/Association Archipel, 1995, 414 pp. [Cahier d’Archipel 26.] - Nico Kaptein, Mark R. Woodward, Toward a new paradigm; Recent developments in Indonesian Islamic thought. Tempe: Arizona State University, Program for Southeast Asian Studies, 1996, x + 380 pp. - Catharina van Klinken, Gunter Senft, Referring to space; Studies in Austronesian and Papuan languages. Oxford: Clarendon Press, 1997, xi + 324 pp. - W. Mahdi, J.G. de Casparis, Sanskrit loan-words in Indonesian; An annotated check-list of words from Sanskrit in Indonesian and Traditional Malay. Jakarta: Badan Penyelenggara Seri NUSA, Universitas Katolik Indonesia Atma Jaya, 1997, viii + 59 pp. [NUSA Linguistic Studies of Indonesian and Other Languages in Indonesia 41.] - Henk Maier, David Smyth, The canon in Southeast Asian literatures; Literatures of Burma, Cambodia, Indonesia, Laos, Malaysia, the Philippines, Thailand and Vietnam. Richmond: Curzon, 2000, x + 273 pp. - Toon van Meijl, Robert J. Foster, Social reproduction and history in Melanesia; Mortuary ritual, gift exchange, and custom in the Tanga islands. Cambridge: Cambridge University Press, 1995, xxii + 288 pp. - J.A. de Moor, Douglas Kammen, A tour of duty; Changing patterns of military politics in Indonesia in the 1990’s. Ithaca, New York: Southeast Asia Program, Cornell University, 1999, 98 pp., Siddharth Chandra (eds.) - Joke van Reenen, Audrey Kahin, Rebellion to integration; West Sumatra and the Indonesian polity, 1926-1998. Amsterdam University Press, 1999, 368 pp. - Heather Sutherland, Craig J. Reynolds, Southeast Asian Studies: Reorientations. Ithaca: Southeast Asia Program, Cornell University, 1998, 70 pp. [The Frank H. Golay Memorial Lectures 2 and 3.], Ruth McVey (eds.) - Nicholas Tarling, Patrick Tuck, The French wolf and the Siamese lamb; The French threat to Siamese independence, 1858-1907. Bangkok: White Lotus, 1995, xviii + 434 pp. [Studies in Southeast Asian History 1.] - B.J. Terwiel, Andreas Sturm, Die Handels- und Agrarpolitik Thailands von 1767 bis 1932. Passau: Universität Passau, Lehrstuhl für Südostasienkunde, 1997, vii + 181 pp. [Passauer Beiträge zur Südostasienkunde 2.] - René S. Wassing, Koos van Brakel, A passion for Indonesian art; The Georg Tillmann collection at the Tropenmuseum Amsterdam. Amsterdam. Royal Tropical Institute/Tropenmuseum, 1996, 128 pp., David van Duuren, Itie van Hout (eds.) - Edwin Wieringa, J. de Bruin, Een Leidse vriendschap; De briefwisseling tussen Herman Bavinck en Christiaan Snouck Hurgronje, 1875-1921. Baarn: Ten Have, 1999, 192 pp. [Passage 11.], G. Harinck (eds.)

We compare initial value and eigenvalue problems for two-dimensional perturbations of the inviscid shear flow in a channel. Singular solutions, known in plasma physics as van Kampen (vK) modes, are constructed. They form a complete set of eigenfunctions for decomposition of any initial perturbation for stable wavy perturbations. A pair of discrete modes appears to ensure completeness in the unstable case. Expansion coefficients for eigenmodes are found, and equivalence of temporal evolution obtained with the help of the evolutionary equation for vorticity and expansion over eigenmodes is presented. This alternative description of the evolution using vK-modes is analogous to ones found earlier in plasma and in stellar dynamics. In particular, for stable wavy perturbations, an initial state decays first exponentially due to Landau damping, then algebraically. It has been established (numerically and analytically) that the final decay law is $t^{-1}$.Also we numerically demonstrate that Landau-damped perturbations are not true eigenmodes, but rather a superposition of vK-modes with a real frequency which does not retain its shape over time. However, solution on a contours in the complex plane may exhibit properties of a true eigenmode, i.e., decay without changing its spatial form. Energy redistribution between perturbation and the flow, in stable and unstable regimes, is analyzed.

AbstractInfluenza is an infectious disease with obvious periodic changes over time. It is of great practical significance to explore the non-environment-related factors that cause this regularity for influenza control and individual protection. In this paper, based on the randomness of population number and the heterogeneity of population contact, we have established a stochastic infectious disease model about influenza based on the degree of the network, and obtained the power spectral density function by using the van Kampen expansion method of the master equation. The relevant parameters are obtained by fitting the influenza data of sentinel hospitals. The results of the numerical analysis show that: (1) for the infected, the infection period of patients who go to the sentinel hospitals is particularly different from the others who do not; (2) for all the infected, there is an obvious nonlinear relationship between their infection period and the visiting rate of the influenza sentinel hospitals, the infection rate and the degree. Among them, only the infection period of patients who do not go to the sentinel hospitals decreased monotonously with the infection rate (increased monotonously with the visiting rate), while the rest had a non-monotonic relationship.

Experimental studies have shown that the protein abundance in living cells varies from few tens to several thousands molecules per species. Molecular fluctuations roughly scale as the inverse square root of the number of molecules due to the random timing of reactions. It is hence expected that intrinsic noise plays an important role in the dynamics of biochemical networks. The Chemical Master Equation is the accepted description of these systems under well-mixed conditions. Because analytical solutions to this equation are available only for simple systems, one often has to resort to approximation methods. A popular technique is an expansion in the inverse volume to which the reactants are confined, called van Kampen's system size expansion. Its leading order terms are given by the phenomenological rate equations and the linear noise approximation that quantify the mean concentrations and the Gaussian fluctuations about them, respectively. While these approximations are valid in the limit of large molecule numbers, it is known that physiological conditions often imply low molecule numbers. We here develop systematic approximation methods based on higher terms in the system size expansion for general biochemical networks. We present an asymptotic series for the moments of the Chemical Master Equation that can be computed to arbitrary precision in the system size expansion. We then derive an analytical approximation of the corresponding time-dependent probability distribution. Finally, we devise a diagrammatic technique based on the path-integral method that allows to compute time-correlation functions. We show through the use of biological examples that the first few terms of the expansion yield accurate approximations even for low number of molecules. The theory is hence expected to closely resemble the outcomes of single cell experiments.

The classical approach to population dynamics is deterministic in nature: the concentrations of the interacting constituents are assumed to be continuous variables. Alternatively, one can proceed with a stochastic modelling, respecting the intrinsic granularity of the scrutinized system. Starting for a microscopic, hence inherently stochastic, formulation of the inspected model, one can rigorously recover the underlying deterministic picture and assess the role played by finite size corrections via the celebrated van Kampen expansion. At the conventional order of approximation, also called linear noise approximation, the van Kampen analysis yields a Fokker-Planck equation for the distribution of fluctuations. This machinery can be for instance applied to explain the emergence of the so-called quasi-cycles, regular time oscillations of the concentrations, which result from a resonant amplification of the stochastic noise. This possibility is discussed in the first part of the thesis with reference to problem of intracellular calcium dynamics. Then, we have considered the van Kampen expansion beyond the Gaussian order of approximation. The method has been challenged for a selection models and its predictive ability tested versus numerical simulations. In practice, when accounting for higher order corrections, one obtains a generalized Fokker-Planck equation which depends explicitly on N, the size of the system. This enables us to write down a system of ODEs for the unknown moments of the distribution of fluctuations. The sought distribution is eventually recovered by Fourier inversion. The analysis that we have carried out testifies on the adequacy of the van Kampen expansion also when the weak noise hypothesis breaks down or, equivalently, when the characteristic size of the population is small. To complete the study we have also drawn a quantitative comparison between the WKB and the generalized van Kampen expansion, working with a stochastic version of the logistic equations. In the second part of the thesis we have studied reaction-diffusion systems of both stochastic and deterministic inspiration. As an interesting ingredient we have considered the effect of the microscopic competition for the available space, imposing a finite carrying capacity constraint into the microscopic formulation of the models. This is presumably relevant when the interacting species are densely packed in space, in a regime that is often referred to as to the molecular crowding. We studied in particular the conditions for the emergence of stochastic spatially extended patterns and the interplay between Turing like patterns and the cross diffusion due to crowding.