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 $t_0$ 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 $t_0$, 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 $2f + 1$ 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 $r$ 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