1,420 research outputs found
Systematic derivation of a rotationally covariant extension of the 2-dimensional Newell-Whitehead-Segel equation
An extension of the Newell-Whitehead-Segel amplitude equation covariant under
abritrary rotations is derived systematically by the renormalization group
method.Comment: 8 pages, to appear in Phys. Rev. Letters, March 18, 199
Selection, Stability and Renormalization
We illustrate how to extend the concept of structural stability through
applying it to the front propagation speed selection problem. This
consideration leads us to a renormalization group study of the problem. The
study illustrates two very general conclusions: (1) singular perturbations in
applied mathematics are best understood as renormalized perturbation methods,
and (2) amplitude equations are renormalization group equations.Comment: 38 pages, LaTeX, two PostScript figures available by anonymous ftp to
gijoe.mrl.uiuc.edu (128.174.119.153) files /pub/front_kkfest_fig
Application Of High Speed And High Performance Fluid Film Bearings In Rotating Machinery.
Tutorialpg. 209-234Some of the critical parameters in the design and application of high performance fluid film bearings are emphasized. The limitations and problems associated with high speed and highly loaded bearings will be discussed. Examples of bearing failures, the symptoms associated with these failures, and their impact on the machine performance will be shown. Some of the common failure mechanisms will also be described with suggestions on how to eliminate the failures or reduce their consequences by changes to some of the bearing design features. New developments in bearing technology and testing specifically designed to address some of these limitations will be demonstrated. Case studies and analysis will be used in many common and newly developed turbomachinery equipment to help illustrate some of the key attributes in the design and application of high performance fluid film bearings and squeeze film dampers
The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
Perturbative renormalization group theory is developed as a unified tool for
global asymptotic analysis. With numerous examples, we illustrate its
application to ordinary differential equation problems involving multiple
scales, boundary layers with technically difficult asymptotic matching, and WKB
analysis. In contrast to conventional methods, the renormalization group
approach requires neither {\it ad hoc\/} assumptions about the structure of
perturbation series nor the use of asymptotic matching. Our renormalization
group approach provides approximate solutions which are practically superior to
those obtained conventionally, although the latter can be reproduced, if
desired, by appropriate expansion of the renormalization group approximant. We
show that the renormalization group equation may be interpreted as an amplitude
equation, and from this point of view develop reductive perturbation theory for
partial differential equations describing spatially-extended systems near
bifurcation points, deriving both amplitude equations and the center manifold.Comment: 44 pages, 2 Postscript figures, macro \uiucmac.tex available at macro
archives or at ftp://gijoe.mrl.uiuc.edu/pu
Renormalization Group Method Applied to Kinetic Equations: roles of initial values and time
The so-called renormalization group (RG) method is applied to derive kinetic
and transport equations from the respective microscopic equations. The derived
equations include Boltzmann equation in classical mechanics, Fokker-Planck
equation, a rate equation in a quantum field theoretical model. Utilizing the
formulation of the RG method which elucidates the important role played by the
choice of the initial conditions, the general structure and the underlying
assumptions in the derivation of kinetic equations in the RG method is
clarified. It is shown that the present formulation naturally leads to the
choice for the initial value of the microscopic distribution function at
arbitrary time to be on the averaged distribution function to be
determined. The averaged distribution function may be thought as an integral
constant of the solution of microscopic evolution equation; the RG equation
gives the slow dynamics of the would-be initial constant, which is actually the
kinetic equation governing the averaged distribution function. It is further
shown that the averaging as given above gives rise to a coarse-graining of the
time-derivative which is expressed with the initial time , thereby leads
to time-irreversible equations even from a time-reversible equation. It is
shown that a further reduction of Boltzmann equation to fluid dynamical
equations and the adiabatic elimination of fast variables in Fokker-Planck
equation are also performed in a unified way in the present method.Comment: The detailed derivations are added to section 5 (fluiddynamical limit
of Boltzmann equation) and to Appendix B (Adiabatic elimination of fast
variables in Fokker-Planck equation) which is moved to the text as a section.
Other minor corrections are made all over the text including typo
Renormalization Group Theory for Global Asymptotic Analysis
We show with several examples that renormalization group (RG) theory can be
used to understand singular and reductive perturbation methods in a unified
fashion. Amplitude equations describing slow motion dynamics in nonequilibrium
phenomena are RG equations. The renormalized perturbation approach may be
simpler to use than other approaches, because it does not require the use of
asymptotic matching, and yields practically superior approximations.Comment: 13 pages, plain tex + uiucmac.tex (available from babbage.sissa.it),
one PostScript figure appended at end. Or (easier) get compressed postscript
file by anon ftp from gijoe.mrl.uiuc.edu (128.174.119.153), file
/pub/rg_sing_prl.ps.
Cronoestratigrafía del volcanismo con énfasis en ignimbritas desde hace 25 Ma en el SO del Perú – Implicaciones para la evolución de los Andes centrales
El sur del Perú representa el segundo campo ignimbrítico de los Andes con un área que sobrepasa los 25 000 km2 y volúmenes de casi 5000 km3. Se prresenta la extensión, la estratigrafía y la cronología de 12 ignimbritas que afloran en el área de los cañones profundos de los Ríos Ocoña–Cotahuasi–Marán y Colca (OCMC). La cronología de las ignimbritas a lo largo de los últimos 25 Myr está basada en 74 dataciones 40Ar/39Ar and U/Pb. Antes de 9 Ma, ocho ignimbritas con gran volumen fueron producidas cada 2.4 Myr. Después de 9 Ma, el periodo de reposo entre cada ignimbrita de volumen pequeño a moderado ha disminuido hasta 0.85 Myr. Esta cronología de las ignimbritas y de las lavas del Neógeno y Cuaternario ayuda a revisar la nomenclatura de las formaciones volcánicas utilizadas para la Carta Geológica Nacional. Además las unidades volcánicas identificadas son herramientas para reconstruir la evolución geológica del flanco occidental de los Andes Centrales durante su levantamiento desde hace 25 Ma. Junto con la cronoestratigrafía de estas unidades, datos geomorfológicos obtenidos en las cuencas y sobre otros depósitos de los cañones OCMC ayudan a precisar la historia de la incisión del flanco occidental de los Andes Centrales desde hace 25 Ma. Finalmente la cronología de depósitos de avalancha de escombros y de terrazas rocosas basada en cosmogénicos (Be10) permite precisar la evolución de los cañones durante el Pleistoceno y el Holoceno
Self-Stabilizing Byzantine Resilient Topology Discovery and Message Delivery
Traditional Byzantine resilient algorithms use vertex disjoint paths to ensure message delivery in the presence of up to f Byzantine nodes. The question of how these paths are identified is related to the fundamental problem of topology discovery. Distributed algorithms for topology discovery cope with a never ending task, dealing with frequent changes in the network topology and unpredictable transient faults. Therefore, algorithms for topology discovery should be self-stabilizing to ensure convergence of the topology information following any such unpredictable sequence of events. We present the first such algorithm that can cope with Byzantine nodes. Starting in an arbitrary global state, and in the presence of f Byzantine nodes, each node is eventually aware of all the other non-Byzantine nodes and their connecting communication links. Using the topology information, nodes can, for example, route messages across the network and deliver messages from one end user to another. We present the first deterministic, cryptographic-assumptions-free, self-stabilizing, Byzantine-resilient algorithms for network topology discovery and end-to-end message delivery. We also consider the task of r-neighborhood discovery for the case in which and the degree of nodes are bounded by constants. The use of r-neighborhood discovery facilitates polynomial time, communication and space solutions for the above tasks. The obtained algorithms can be used to authenticate parties, in particular during the establishment of private secrets, thus forming public key schemes that are resistant to man-in-the-middle attacks of the compromised Byzantine nodes. A polynomial and efficient end-to-end algorithm that is based on the established private secrets can be employed in between periodical re-establishments of the secrets
Immunity toward H1N1 influenza hemagglutinin of historical and contemporary strains suggests protection and vaccine failure
Evolution of H1N1 influenza A outbreaks of the past 100 years is interesting and significantly complex and details of H1N1 genetic drift remains unknown. Here we investigated the clinical characteristics and immune cross-reactivity of significant historical H1N1 strains. We infected ferrets with H1N1 strains from 1943, 1947, 1977, 1986, 1999, and 2009 and showed each produced a unique clinical signature. We found significant cross-reactivity between viruses with similar HA sequences. Interestingly, A/FortMonmouth/1/1947 antisera cross-reacted with A/USSR/90/1977 virus, thought to be a 1947 resurfaced virus. Importantly, our immunological data that didn't show cross-reactivity can be extrapolated to failure of past H1N1 influenza vaccines, ie. 1947, 1986 and 2009. Together, our results help to elucidate H1N1 immuno-genetic alterations that occurred in the past 100 years and immune responses caused by H1N1 evolution. This work will facilitate development of future influenza therapeutics and prophylactics such as influenza vaccines.published_or_final_versio
Structural Stability and Renormalization Group for Propagating Fronts
A solution to a given equation is structurally stable if it suffers only an
infinitesimal change when the equation (not the solution) is perturbed
infinitesimally. We have found that structural stability can be used as a
velocity selection principle for propagating fronts. We give examples, using
numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure
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