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Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit
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- Joseph T. Parker, Paul J. Dellar
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- Journal:
- Journal of Plasma Physics / Volume 81 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 03 February 2015, 305810203
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We study Landau damping in the 1+1D Vlasov–Poisson system using a Fourier–Hermite spectral representation. We describe the propagation of free energy in Fourier–Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov–Poisson system. This captures Landau damping via Hou–Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.
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- By Dale C. Allison, John Barton, Pierre-Maurice Bogaert, Jonathan G. Campbell, James Carleton Paget, J. F. Coakley, John J. Collins, Kristin De Troyer, Gilles Dorival, Mark Edwards, J. K. Elliott, Mark W. Elliott, Wolf-Peter Funk, Thomas Graumann, Lucy Grig, Carol Harrison, C. T. R. Hayward, Michael J. Hollerich, William Horbury, Larry W. Hurtado, Jan Joosten, Adam Kamesar, Chris Keith, Geoffrey Khan, Wolfram Kinzig, Winrich Löhr, David C. Parker, Gerard Rouwhorst, Joachim Schaper, William M. Schniedewind, Günter Stemberger, Emanuel Tov, Eugene Ulrich, Joseph Verheyden, James W. Watts, Peter J. Williams, Frances M. Young
- Edited by James Carleton Paget, University of Cambridge, Joachim Schaper, University of Aberdeen
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- Book:
- The New Cambridge History of the Bible
- Published online:
- 05 May 2013
- Print publication:
- 09 May 2013, pp x-xi
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. 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Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
- Print publication:
- 20 September 2010, pp xi-xliv
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Settling Behavior of Alumina Dispersions and Resultant Green Body Characteristics: Solvent, Binder, and Dispersant Competition in Model Systems
- Anthony A. Parker, Mei-Yuan Tsai, Girma Biresaw, Todd T. Stanzione, George H. Armstrong, Joseph J. Marcinko
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- MRS Online Proceedings Library Archive / Volume 249 / 1991
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- 25 February 2011, 273
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- 1991
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The chemical functionality of binders, dispersants, and solvents will influence competitive adsorption/desorption behavior on alumina powder, and hence will affect both slurry and ultimate green tape properties. Given that multiple competitive interactions are common to most dispersions, it is usually difficult to ascertain mechanisms from simple settling density experiments. However, this problem can be partially overcome with the choice of model systems that minimize the number of competitive processes. This criterion is met to a first approximation with a model system of toluene solvent, polystyrene binder, and a C8 aliphatic dispersant with an anchor group of variable functionality. Plateau adsorption concentrations from settling experiments in toluene show that surface coverage for efficient dispersants is typically achieved at about 6μmoles/m2. Less efficient dispersants adsorb at higher plateau concentrations, and are eventually displaced after repeated washing steps in toluene. The settling densities of dispersions prepared with C8 dispersants are consistently higher than densities achieved in toluene alone, and as seen in a case study with n-octylsilane, the settling densities are independent of the presence of polystyrene. Green bodies cast from a polystyrene/Al2O3 slurry also show increased densities in the presence of n-octylsilane dispersant. However, despite the apparent low levels of interaction between polystyrene and n-octylsilane in the dispersion state, solid state NMR and dynamic mechanical results show that the solid state molecular motional behavior of polystyrene is strongly affected by the presence of n-octylsilane dispersant.
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