Relevant bibliographies by topics / Scaling asymptotics

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Scaling asymptotics'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Scaling asymptotics"

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Paoletti, Roberto. "Local scaling asymptotics in phase space and time in Berezin–Toeplitz quantization." International Journal of Mathematics 25, no. 06 (June 2014): 1450060. http://dx.doi.org/10.1142/s0129167x14500608.

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This paper deals with the local semiclassical asymptotics of a quantum evolution operator in the Berezin–Toeplitz scheme, when both time and phase space variables are subject to appropriate scalings in the neighborhood of the graph of the underlying classical dynamics. Global consequences are then drawn regarding the scaling asymptotics of the trace of the quantum evolution as a function of time.
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Riley, N. "Scaling, self-similarity, and intermediate asymptotics." European Journal of Mechanics - B/Fluids 17, no. 3 (May 1998): 389–90. http://dx.doi.org/10.1016/s0997-7546(98)80266-5.

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PAOLETTI, ROBERTO. "SCALING ASYMPTOTICS FOR QUANTIZED HAMILTONIAN FLOWS." International Journal of Mathematics 23, no. 10 (October 2012): 1250102. http://dx.doi.org/10.1142/s0129167x12501029.

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In recent years, the near diagonal asymptotics of the equivariant components of the Szegö kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.
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Hashorva, Enkelejd, and Anthony G. Pakes. "Tail asymptotics under beta random scaling." Journal of Mathematical Analysis and Applications 372, no. 2 (December 2010): 496–514. http://dx.doi.org/10.1016/j.jmaa.2010.07.045.

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Szpak, Nikodem. "Asymptotics from Scaling for Nonlinear Wave Equations." Communications in Partial Differential Equations 35, no. 10 (September 2010): 1876–90. http://dx.doi.org/10.1080/03605300903540935.

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VENEZIANO, DANIELE. "LARGE DEVIATIONS OF MULTIFRACTAL MEASURES." Fractals 10, no. 01 (March 2002): 117–29. http://dx.doi.org/10.1142/s0218348x02000872.

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We analyze the extremes of stationary multifractal measures using large deviation theory. We consider various cases involving discrete multiplicative cascades: scalar or vector cascades with dependent or independent generators, bare or dressed measures, and marginal (single-point) or joint (multi-point) extremes. In each case, we obtain the scaling behavior of the probability of large deviations as the resolution of the cascade diverges. Existing rough exponential limits for scalar cascades are confirmed, whereas for other cases our scaling relationships differ from previously published results. For scalar cascades, we refine the rough limits by obtaining the asymptotic pre-factor to the exponential term. Based on these refined asymptotics, we propose a variant to the Probability Distribution/Multiple Scaling (PDMS) technique to estimate the co-dimension function c(γ).
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PAOLETTI, ROBERTO. "LOCAL TRACE FORMULAE AND SCALING ASYMPTOTICS IN TOEPLITZ QUANTIZATION." International Journal of Geometric Methods in Modern Physics 07, no. 03 (May 2010): 379–403. http://dx.doi.org/10.1142/s021988781000435x.

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A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here, we give a local version of this result for a class of Toeplitz operators related to continuous groups of symmetries on quantizable compact symplectic manifolds. The local trace formula involves certain scaling asymptotics along the clean fixed locus of the Hamiltonian flow of the symbol, reminiscent of the scaling asymptotics of the equivariant components of the Szegö kernel along the diagonal.
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Ignat, Tatiana I. "Asymptotics for nonlocal evolution problems by scaling arguments." Differential Equations & Applications, no. 4 (2013): 613–26. http://dx.doi.org/10.7153/dea-05-36.

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Calka, Pierre, and J. E. Yukich. "Variance asymptotics and scaling limits for Gaussian polytopes." Probability Theory and Related Fields 163, no. 1-2 (November 14, 2014): 259–301. http://dx.doi.org/10.1007/s00440-014-0592-6.

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Calka, Pierre, and J. E. Yukich. "Variance asymptotics and scaling limits for random polytopes." Advances in Mathematics 304 (January 2017): 1–55. http://dx.doi.org/10.1016/j.aim.2016.08.006.

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Dissertations / Theses on the topic "Scaling asymptotics"

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CAMOSSO, SIMONE. "Scaling asymptotics of Szego kernels under commuting Hamiltonian actions." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/77488.

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Let M be a connected d-dimensional complex projective manifold, and let A be a holomorphic positive Hermitian line bundle on M, with normalized curvature. Let G be a compact and connected Lie group of dimension d(G), and let T be a compact torus T of dimension d(T). Suppose that both G and T act on M in a holomorphic and Hamiltonian manner, that the actions commute, and linearize to A. If X is the principal circle-bundle associated to A, then this set-up determines commuting unitary representations of G and T on the Hardy space H(X) of X, which may then be decomposed over the irreducible representations of the two groups. If the moment map for the T-action is nowhere zero, all isotypical components for the torus are finite-dimensional, and thus provide a collection of finite-dimensional G-modules. Given a non-zero integral weight n(T) for T, we consider the isotypical components associated to the multiples kn(T), k that goes to infinity, and focus on how their structure as G-modules is reflected by certain local scaling asymptotics on X (and M). More precisely, given a fixed irreducible character n(G) of G, we study the local scaling asymptotics of the equivariant Szegő projectors associated to n(G) and kn(T), for k that goes to infinity, investigating their asymptotic concentration along certain loci defined by the moment maps.
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Haug, Nils Adrian. "Asymptotics and scaling analysis of 2-dimensional lattice models of vesicles and polymers." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/30706.

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The subject of this thesis is the asymptotic behaviour of generating functions of different combinatorial models of two-dimensional lattice walks and polygons, enumerated with respect to different parameters, such as perimeter, number of steps and area. These models occur in various applications in physics, computer science and biology. In particular, they can be seen as simple models of biological vesicles or polymers. Of particular interest is the singular behaviour of the generating functions around special, so-called multicritical points in their parameter space, which correspond physically to phase transitions. The singular behaviour around the multicritical point is described by a scaling function, alongside a small set of critical exponents. Apart from some non-rigorous heuristics, our asymptotic analysis mainly consists in applying the method of steepest descents to a suitable integral expression for the exact solution for the generating function of a given model. The similar mathematical structure of the exact solutions of the different models allows for a unified treatment. In the saddle point analysis, the multicritical points correspond to points in the parameter space at which several saddle points of the integral kernels coalesce. Generically, two saddle points coalesce, in which case the scaling function is expressible in terms of the Airy function. As we will see, this is the case for Dyck and Schröder paths, directed column-convex polygons and partially directed self-avoiding walks. The result for Dyck paths also allows for the scaling analysis of Bernoulli meanders (also known as ballot paths). We then construct the model of deformed Dyck paths, where three saddle points coalesce in the corresponding integral kernel, thereby leading to an asymptotic expression in terms of a bivariate, generalised Airy integral.
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Kishi, Tatsuro. "Scaling laws for turbulent relative dispersion in two-dimensional energy inverse-cascade turbulence." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263445.

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Hoffmann, Franca Karoline Olga. "Keller-Segel-type models and kinetic equations for interacting particles : long-time asymptotic analysis." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/269646.

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This thesis consists of three parts: The first and second parts focus on long-time asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling approaches. (1) Keller–Segel-type aggregation-diffusion equations: We study a Keller–Segel-type model with non-linear power-law diffusion and non-local particle interaction: Does the system admit equilibria? If yes, are they unique? Which solutions converge to them? Can we determine an explicit rate of convergence? To answer these questions, we make use of the special gradient flow structure of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the asymptotic behaviour of solutions. (2) Hypocoercivity techniques for a fibre lay-down model: We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in non-woven textile production. Further, we prove convergence to equilibrium with an explicit rate. This part of the thesis is an extension of previous work which considered the case of a stationary conveyor belt. Adding the movement of the belt, the global equilibrium state is not known explicitly and a more general hypocoercivity estimate is needed. Although we focus here on a particular application, this approach can be used for any equation with a similar structure as long as it can be understood as a certain perturbation of a system for which the global Gibbs state is known. (3) Scaling approaches for collective animal behaviour models: We study the multi-scale aspects of self-organised biological aggregations using various scaling techniques. Not many previous studies investigate how the dynamics of the initial models are preserved via these scalings. Firstly, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local kinetic 1D and 2D models to simpler models existing in the literature. Secondly, we investigate how some of the kinetic spatio-temporal patterns are preserved via these scalings using asymptotic preserving numerical methods.
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Hobert, Anne [Verfasser], Axel [Akademischer Betreuer] Munk, Axel [Gutachter] Munk, and Tatyana [Gutachter] Krivobokova. "Semiparametric Estimation of Drift, Rotation and Scaling in Sparse Sequential Dynamic Imaging: Asymptotic theory and an application in nanoscale fluorescence microscopy / Anne Hobert ; Gutachter: Axel Munk, Tatyana Krivobokova ; Betreuer: Axel Munk." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2019. http://d-nb.info/1203875312/34.

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Gianfelici, Alessandro. "A linear O(N) model: a functional renormalization group approach for flat and curved space." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8343/.

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In questa tesi sono state applicate le tecniche del gruppo di rinormalizzazione funzionale allo studio della teoria quantistica di campo scalare con simmetria O(N) sia in uno spaziotempo piatto (Euclideo) che nel caso di accoppiamento ad un campo gravitazionale nel paradigma dell'asymptotic safety. Nel primo capitolo vengono esposti in breve alcuni concetti basilari della teoria dei campi in uno spazio euclideo a dimensione arbitraria. Nel secondo capitolo si discute estensivamente il metodo di rinormalizzazione funzionale ideato da Wetterich e si fornisce un primo semplice esempio di applicazione, il modello scalare. Nel terzo capitolo è stato studiato in dettaglio il modello O(N) in uno spaziotempo piatto, ricavando analiticamente le equazioni di evoluzione delle quantità rilevanti del modello. Quindi ci si è specializzati sul caso N infinito. Nel quarto capitolo viene iniziata l'analisi delle equazioni di punto fisso nel limite N infinito, a partire dal caso di dimensione anomala nulla e rinormalizzazione della funzione d'onda costante (approssimazione LPA), già studiato in letteratura. Viene poi considerato il caso NLO nella derivative expansion. Nel quinto capitolo si è introdotto l'accoppiamento non minimale con un campo gravitazionale, la cui natura quantistica è considerata a livello di QFT secondo il paradigma di rinormalizzabilità dell'asymptotic safety. Per questo modello si sono ricavate le equazioni di punto fisso per le principali osservabili e se ne è studiato il comportamento per diversi valori di N.
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Gratton, Michel. "Comportement d'un composite 3D carb/carb : méso-modélisation pour la prévision de la réponse sous choc." Cachan, Ecole normale supérieure, 1998. http://www.theses.fr/1998DENS0004.

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Ce travail, mené en collaboration avec l'aérospatiale Les Mureaux et le centre d'études de Gramat, concerne la modélisation de matériaux composites tridirectionnels carbone/carbone sous sollicitations fortement dynamiques. Pour ce type de sollicitations, la notion de matériau homogène équivalent est inadaptée. L'objet de ce travail est de tester l'aptitude d'une modélisation a l'échelle des constituants mésoscopique (torons de fibres et blocs de matrice), a reproduire la réponse du matériau sous choc. Le matériau est tout d'abord identifie a l'échelle de ses méso-constituants. A cette fin, divers essais quasi-statiques sont réalisés et une modélisation sans effet de vitesse du comportement des constituants est alors proposée. Elle prend en compte des mécanismes d'endommagement, de compaction et d'anélasticité. Une technique de changement d'échelle, basée sur les développements asymptotiques adaptée aux matériaux périodiques, est utilisée. Associée à une analyse de sensibilité et à une hiérarchisation des mécanismes non-linéaires, elle permet de déterminer les paramètres locaux du modèle a partir des réponses globales du matériau. Afin de tester le méso-modèle ainsi identifie, une partie des informations est exploitée dans un logiciel de dynamique simplifie. Ce dernier permet de simuler les essais d'impact plaque/plaque suivant une direction de torons. Des essais de compression dynamique et des essais d'écaillage (réalisés par le ceg) sont ainsi bien reproduits. Les simulations montrent des modes distincts de propagation d'ondes dans les torons et dans la matrice ainsi que des phénomènes de transferts de charges. Des essais i pulsionnels, mal reproduits par simulation, ouvrent de nombreuses perspectives, notamment sur la nécessite de compléter la modélisation du comportement des méso-constituants par une sensibilité a la vitesse de déformation.
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Gao, Long. "Throughput and Delay Analysis in Cognitive Overlaid Networks." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7531.

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Consider a cognitive overlaid network (CON) that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio (CR) technologies. The primary tier consists of randomly distributed primary radios (PRs) of density n, which have an absolute priority to access the spectrum. The secondary tier consists of randomly distributed CRs of density m = n^y with y greater than or equal to 1, which can only access the spectrum opportunistically to limit the interference to PRs. In this dissertation, the fundamental limits of such a network are investigated in terms of the asymptotic throughput and packet delay performance when m and n approaches infinity. The following two types of CONs are considered: 1) selfish CONs, in which neither the primary tier nor the secondary tier is willing to route the packets for the other, and 2) supportive CONs, in which the secondary tier is willing to route the packets for the primary tier while the primary tier does not. It is shown that in selfish CONs, both tiers can achieve the same throughput and delay scaling laws as a stand-alone network. In supportive CONs, the throughput and delay scaling laws of the primary tier could be significantly improved with the aid of the secondary tier, while the secondary tier can still achieve the same throughput and delay scaling laws as a stand-alone network. Finally, the throughput and packet delay of a CON with a small number of nodes are investigated. Specifically, we investigate the power and rate control schemes for multiple CR links in the same neighborhood, which operate over multiple channels (frequency bands) in the presence of PRs with a delay constraint imposed on data transmission. By further considering practical limitations in spectrum sensing, an efficient algorithm is proposed to maximize the average sum-rate of the CR links over a finite time horizon under the constraints on the CR-to-PR interference and the average transmit power for each CR link. In the proposed algorithm, the PR occupancy of each channel is modeled as a discrete-time Markov chain (DTMC). Based on such a model, a novel power and rate control strategy based on dynamic programming (DP) is derived, which is a function of the spectrum sensing output, the instantaneous channel gains for the CR links, and the remaining power budget for the CR transmitter. Simulation results show that the proposed algorithm leads to a significant performance improvement over heuristic algorithms.
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Apostolakis, John. "Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers." Thesis, 1994. https://thesis.library.caltech.edu/7649/1/Apostolakis-j-1994.pdf.

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We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

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Hobert, Anne. "Semiparametric Estimation of Drift, Rotation and Scaling in Sparse Sequential Dynamic Imaging: Asymptotic theory and an application in nanoscale fluorescence microscopy." Doctoral thesis, 2019. http://hdl.handle.net/11858/00-1735-0000-002E-E5B3-9.

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Books on the topic "Scaling asymptotics"

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Scaling, self-similarity, and intermediate asymptotics. Cambridge: Cambridge University Press, 1996.

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Leal, L. Gary. Laminar flow and convective transport processes: Scaling principles and asymptotic analysis. Boston: Butterworth-Heinemann, 1992.

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Barenblatt, Grigory Isaakovich. Scaling, Self-Similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics. Cambridge University Press, 2014.

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Brenner, Howard. Laminar Flow and Convective Transport Processes: Scaling Principles and Asymptotic Analysis. Elsevier Science & Technology Books, 2016.

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Book chapters on the topic "Scaling asymptotics"

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Garza-López, R. A., and J. J. Kozak. "Asymptotic Scaling for Euclidean Lattices." In Understanding Complex Systems, 579–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-34070-3_43.

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Badii, R., M. Finardi, and G. Broggi. "Unfolding Complexity and Modelling Asymptotic Scaling Behavior." In NATO ASI Series, 259–75. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4757-0172-2_12.

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Toussaint, D., S. A. Gottlieb, A. D. Kennedy, J. Kuti, S. Meyer, B. J. Pendleton, and R. L. Sugar. "Monte Carlo Investigations of Asymptotic Scaling in QCD." In NATO ASI Series, 399–410. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4613-1909-2_41.

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Ogasawara, Haruhiko. "Applications of Asymptotic Expansion in Item Response Theory Linking." In Statistical Models for Test Equating, Scaling, and Linking, 261–80. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-98138-3_16.

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Castillo, Luciano, and Xia Wang. "The Asymptotic Profiles In Forced Convection Turbulent Boundary Layers." In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, 191–94. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-94-007-0997-3_33.

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Gerasimenko, V. I., and Yu Yu Fedchun. "On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior." In Springer Proceedings in Mathematics & Statistics, 165–82. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12145-1_10.

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Scheichl, B., and A. Kluwick. "Asymptotic Theory of Turbulent Bluff-Body Separation: A Novel Shear Layer Scaling Deduced from an Investigation of the Unsteady Motion." In IUTAM Symposium on Unsteady Separated Flows and their Control, 135–50. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-1-4020-9898-7_11.

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Crestetto, Anaïs, Nicolas Crouseilles, and Mohammed Lemou. "Asymptotic-Preserving Scheme Based on a Finite Volume/Particle-In-Cell Coupling for Boltzmann-BGK-Like Equations in the Diffusion Scaling." In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, 827–35. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05591-6_83.

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Bothner, Thomas, Percy Deift, Alexander Its, and Igor Krasovsky. "On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II." In Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics, 213–34. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0_12.

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"Self-similarity and intermediate asymptotics." In Scaling, 52–68. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9780511814921.005.

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Conference papers on the topic "Scaling asymptotics"

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Trivini, Aurora. "Asymptotic Scaling and Monte Carlo Data." In XXIIIrd International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2005. http://dx.doi.org/10.22323/1.020.0036.

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Mirazita, M. "Onset of asymptotic scaling in deuteron photodisintegration." In FEW-BODY PROBLEMS IN PHYSICS: The 19th European Conference on Few-Body Problems in Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1932927.

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Ferro, Marco, Bengt E. G. Fallenius, and Jens H. M. Fransson. "On the scaling of turbulent asymptotic suction boundary layers." In Tenth International Symposium on Turbulence and Shear Flow Phenomena. Connecticut: Begellhouse, 2017. http://dx.doi.org/10.1615/tsfp10.1070.

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Wang, Xia, and Luciano Castillo. "The Asymptotic Temperature Profile for Forced Convection Turbulent Boundary Layers With and Without Pressure Gradient." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45451.

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Similarity analysis of the equations of motion is used in order to study forced convection turbulent boundary layers with and without pressure gradient. New scalings are found for both the inner and the outer temperature profiles, respectively. It is shown that by normalizing the temperature profiles using the new scalings, the effects from the Pe´clet number and pressure gradient can be removed completely from the profiles. Therefore, the asymptotic solutions can be obtained even at the finite Pe´clet number. Moreover, using the Near-Asymptotic principle, a power law solution is derived for the temperature profile in the overlap region. This power law solution is a consequence of the fact that the boundary layer depends on two different temperature scalings.
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Phoenix, S. Leigh, and Irene J. Beyerlein. "Strength Distribution and Size Effects for the Fracture of Fibrous Composite Materials." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0706.

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Abstract Random network models have recently been developed in the physics literature to explain the strength and size effect in heterogeneous materials. Applications have included the breakdown of random fuse networks, dielectric breakdown and brittle fracture. Unfortunately, conventional scaling approaches of statistical mechanics have yielded incorrect predictions, and new approaches have been proposed which build on field enhancement occurring near the tips of critical, random clusters together with the statistical theory of extremes. New distributions and size scalings for strength have been proposed and supported through Monte Carlo simulation. Here we consider an idealized, one-dimensional model for the failure of such networks where elements of constant strength may be initially present or absent at random. Our idealized rule for local stress redistribution near breaks reflects features we find in a discrete mechanics model that has limiting forms consistent with continuum theories for cracks. We obtain rigorous asymptotic results for the strength distribution and size effect with constants and exponents that are known. The validity of various analytical approximations in the literature is then discussed.
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Muzychka, Y. S., and M. M. Yovanovich. "Unsteady Viscous Flows and Stokes's First Problem." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14301.

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Unsteady viscous flows and Stokes's first problem are examined. Three problems are considered: unsteady Couette flow, unsteady Poiseuille flow, and unsteady boundary layer flow. The relationship between these three fundamental unsteady flows and Stokes' first problem is illustrated. Scaling principles are used to deduce the short time and long time characteristics of these three problems. Asymptotic analysis is used to obtain exact short and long time characteristics and to show the relationship of each problem to Stokes's first problem for short times. Finally, compact robust models are developed for all values of time using the Churchill-Usagi asymptotic correlation method to combine the short and long time characteristics.
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7

Schmitt, John. "Mechanical Models for Insect Locomotion: Parameter Studies." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1756.

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Abstract Motivated by experimental studies of insects, we develop a three-degree-of-freedom, energetically conservative, rigid body model with a pair of elastic legs in intermittent contact with the ground. The resulting piecewise-holonomic mechanical system exhibits periodic gaits whose neutral and asymptotic stability characteristics are due to intermittent foot contact, and are largely determined by geometrical criteria. We study how dynamics depend on physical parameters such as mass, moment of inertia, leg length, leg stiffness, and leg touchdown angle. We develop exact and approximate scaling relations that predict gait scaling in response to individual parameter changes, and suggest that the model is relevant to the understanding of locomotion dynamics across species.
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Wong, T. T. Y., M. S. Aly, and K. Han. "Scaling and asymptotic compensation techniques for early-time response calculation by transform methods." In IEEE Antennas and Propagation Society International Symposium 1992 Digest. IEEE, 1992. http://dx.doi.org/10.1109/aps.1992.221854.

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9

Ciucu, Florin. "On the scaling of non-asymptotic capacity in multi-access networks with bursty traffic." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6034027.

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10

Cruise, James. "A scaling framework for the many flows asymptotic, through large deviations: invited presentation, extended abstract." In 4th International ICST Conference on Performance Evaluation Methodologies and Tools. ICST, 2009. http://dx.doi.org/10.4108/icst.valuetools2009.8004.

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