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Energy and speed exploration in digital CMOS circuits in the near-threshold regime for very-wide voltage-frequency scaling

Stangherlin, Kleber Hugo
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Dissertação Formato: application/pdf
Português
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This thesis assesses the benefits and drawbacks associated with a very wide range of frequency when operation at near-threshold is considered. Scaling down the supply voltage in digital CMOS circuits presents great benefits in terms of power reduction. Such scaling comes with a performance penalty, hence in digital synchronous circuits the reduction in frequency of operation follows, for a given circuit layout, the VDD reduction. Minimum-energy operation of digital CMOS circuits is commonly associated to the sub-VT regime, carrying huge performance and variability penalties. This thesis shows that it is possible to achieve 8X higher energy-efficiency with a very-wide range of dynamic voltage-frequency scaling, from nominal voltages down to the lower boundary of near-VT operation. As part of this study, a CMOS digital cell-library for such wide range of frequencies was developed. The cell-library is exercised in a 65nm commercial PDK and targets near-VT operation, mitigating the variability effects without compromising the design in terms of area and energy at strong inversion. For near-VT or sub-VT operation the cells have to be designed with few stacked transistors. Our study shows that acceptable performance in terms of static-noise margins is obtained for a constrained set of cells...

Statistical properties of a dissipative kicked system: Critical exponents and scaling invariance

Oliveira, Diego F. M.; Robnik, Marko; Leonel, Edson Denis
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 723-728
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A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action. (C) 2012 Elsevier B.V. All rights reserved.

Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

Vollet, Dimas R.; Donatti, Dario A.; Ruiz, Alberto Ibanez; Vicente, Fábio Simões de
Fonte: Wiley-Blackwell Publicador: Wiley-Blackwell
Tipo: Artigo de Revista Científica Formato: 949-954
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Dynamical scaling properties in fractal structures were investigated from small-angle X-ray scattering (SAXS) data of the kinetics of aggregation in silica-based gelling systems. For lack of a maximum in the SAXS intensity curves, a characteristic correlation distance xi was evaluated by fitting a particle scattering factor model valid for polydisperse coils of linear chains and f-functional branched polycondensates in solution, so the intensity at q = xi-1, I(xi-1, t), was considered to probe dynamical scaling properties. The following properties have been found: (i) the SAXS intensities corresponding to different times t, I(q, t), are given by a time-independent function F(q xi) = I(q, t)xi-D /Q, where the scattering invariant Q has been found to be time-independent; (ii) xi exhibited a power-law behavior with time as xi similar or equal to t alpha, the exponent alpha being close to 1 but diminishing with temperature; (iii) I(xi-1, t) exhibited a time dependence given by I(xi-1, t) similar or equal to t beta, with the exponent beta found to be around 2 but diminishing with temperature, following the same behavior as the exponent alpha. In all cases...

Scaling properties of the fermi-ulam accelerator model

Da Silva, Jafferson Kamphorst Leal; Ladeira, Denis Gouvêa; Leonel, Edson D.; McClintock, P. V E; Kamphorst, Sylvie O.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 700-707
Português
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The chaotic low energy region (chaotic sea) of the Fermi-Ulam accelerator model is discussed within a scaling framework near the integrable to non-integrable transition. Scaling results for the average quantities (velocity, roughness, energy etc.) of the simplified version of the model are reviewed and it is shown that, for small oscillation amplitude of the moving wall, they can be described by scaling functions with the same characteristic exponents. New numerical results for the complete model are presented. The chaotic sea is also characterized by its Lyapunov exponents.

Efficacy of Carisolv™ as an adjunctive therapy to scaling and root planing on subgingival calculus removal

Grisi, Daniela C.; Salvador, Sérgio Luiz de Souza; Marcantonio, Rosemary Adriana Chierici
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Artigo de Revista Científica Formato: 213-218
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The purpose of this study was to evaluate the effectiveness of subgingival application of Carisolv™ gel as an adjunctive therapy to scaling and root planing (SRP) on calculus removal compared to conventional instrumentation. Forty-five teeth requiring extraction due to severe periodontal disease were randomized to the following treatments: 1) SRP alone; 2) placebo gel + SRP; 3) Carisolv™ gel + SRP. Either test or placebo gel was applied subgingivally for 1 min and then the root were instrumented until a smooth and calculus-free surface was achieved. Instrumentation time and the number of strokes required were recorded. After extraction, the efficacy of root surface instrumentation was measured by percentage of remaining calculus. There was no statistically significant difference (p>0.05) between the treatment groups regarding either time required for instrumentation or the percentage of residual calculus. The subgingival application of Carisolv™ gel prior to SRP did not provide any additional benefit to root instrumentation compared to scaling and root planing alone.

Dynamical properties of a dissipative discontinuous map: A scaling investigation

Aguilar-Sanchez, R.; Leonel, Edson D.; Mendez-Bermudez, J. A.
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica Formato: 3216-3222
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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Processo FAPESP: 12/23688-5; The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action < I-2 > as a function of the n-th iteration of the map as well as the parameters K and gamma, controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K >> 1. In this regime and for large initial action I-0 >> K, we prove that dissipation produces an exponential decay for the average action < I >. Also, for I-0 congruent to 0, we describe the behavior of < I-2 > using a scaling function and analytically obtain critical exponents which are used to overlap different curves of < I-2 > onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action omega. (C) 2013 Elsevier B.V. All rights reserved.

Scaling of semivariograms and the kriging estimation of field-measured properties

Vieira,S. R.; Tillotson,P. M.; Biggar,J. W.; Nielsen,D. R.
Fonte: Sociedade Brasileira de Ciência do Solo Publicador: Sociedade Brasileira de Ciência do Solo
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/1997 Português
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Two methods were evaluated for scaling a set of semivariograms into a unified function for kriging estimation of field-measured properties. Scaling is performed using sample variances and sills of individual semivariograms as scale factors. Theoretical developments show that kriging weights are independent of the scaling factor which appears simply as a constant multiplying both sides of the kriging equations. The scaling techniques were applied to four sets of semivariograms representing spatial scales of 30 x 30 m to 600 x 900 km. Experimental semivariograms in each set successfully coalesced into a single curve by variances and sills of individual semivariograms. To evaluate the scaling techniques, kriged estimates derived from scaled semivariogram models were compared with those derived from unscaled models. Differences in kriged estimates of the order of 5% were found for the cases in which the scaling technique was not successful in coalescing the individual semivariograms, which also means that the spatial variability of these properties is different. The proposed scaling techniques enhance interpretation of semivariograms when a variety of measurements are made at the same location. They also reduce computational times for kriging estimations because kriging weights only need to be calculated for one variable. Weights remain unchanged for all other variables in the data set whose semivariograms are scaled.

Generalized z-scaling and pp collisions at RHIC

Tokarev,Mikhail; Zborovsky,Imrich
Fonte: Sociedade Brasileira de Física Publicador: Sociedade Brasileira de Física
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2007 Português
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New generalization of the z-scaling in inclusive particle production is proposed. The scaling variable z is expressed in terms of the momentum fractions x1 and x2 of the incoming protons. Explicit dependence of z on the momentum fractions y a and y b of the scattered and recoil constituents carried by the inclusive particle and recoil object is included. The scaling function psi (z) for charged and identified hadrons produced in proton-proton collisions is constructed. The scheme allows unique description of data on inclusive cross sections of charged hadrons, pions, kaons, antiprotons and lambdas produced at RHIC energies. The obtained results suggest that the z-scaling may be used as a tool for searching for new physics phenomena of particle production in high transverse momentum and high multiplicity region at proton-proton colliders RHIC and LHC.

Phylogenetically informed analysis of the allometry of mammalian basal metabolic rate supports neither geometric nor quarter-power scaling

White, C.; Blackburn, T.; Seymour, R.
Fonte: Soc Study Evolution Publicador: Soc Study Evolution
Tipo: Artigo de Revista Científica
Publicado em //2009 Português
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The form of the relationship between the basal metabolic rate (BMR) and body mass (M) of mammals has been at issue for almost seven decades, with debate focusing on the value of the scaling exponent (b, where BMR is proportional to M(b)) and the relative merits of b= 0.67 (geometric scaling) and b= 0.75 (quarter-power scaling). However, most analyses are not phylogenetically informed (PI) and therefore fail to account for the shared evolutionary history of the species they consider. Here, we reanalyze the most rigorously selected and comprehensive mammalian BMR dataset presently available, and investigate the effects of data selection and phylogenetic method (phylogenetic generalized least squares and independent contrasts) on estimation of the scaling exponent relating mammalian BMR to M. Contrary to the results of a non-PI analysis of these data, which found an exponent of 0.67-0.69, we find that most of the PI scaling exponents are significantly different from both 0.67 and 0.75. Similarly, the scaling exponents differ between lineages, and these exponents are also often different from 0.67 or 0.75. Thus, we conclude that no single value of b adequately characterizes the allometric relationship between body mass and BMR.; Craig R. White...

Niedrig-skalierende Møller-Plesset Störungstheorie zweiter Ordnung unter Verwendung von Auxiliarbasen und quantenchemische Berechnung von NMR-Verschiebungen supramolekularer Systeme; Low-Order Scaling Second-Order Møller-Plesset Perturbation Theory Using Auxiliary Basis Sets and Quantum-Chemical Calculation of NMR Chemical Shifts for Supramolecular Systems

Zienau, Jan
Fonte: Universidade de Tubinga Publicador: Universidade de Tubinga
Tipo: Dissertação
Português
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Neben der ab-initio Berechnung von NMR-Verschiebungen für supramolekulare Systeme befasst sich die vorliegende Dissertation mit der Effiziensteigerung von kürzlich entwickelten linear-skalierenden Methoden im Rahmen der ab-initio Quantenchemie. In diesem Zusammenhang konnte der bei größeren Basissätzen auftretende große Vorfaktor des Rechenzeitaufwandes der in unserer Gruppe entwickelten linear-skalierenden AO-MP2- (Atomorbital-basierte Møller-Plesset Störungstheorie zweiter Ordnung) Methode, welche rigorose Integralschranken verwendet, verkleinert werden. Diese Vorfaktor-Reduktion wird durch Approximation auftretender Integrale unter Verwendung einer Auxiliarbasis im Rahmen des Resolution of the Identity- (RI-) Verfahrens erreicht. Die RI-Approximation wurde weiterhin auf eine ebenfalls linear-skalierende Abwandlung der AO-MP2-Methode angewendet, welche mit einer Cholesky-Zerlegung der bei AO-MP2 auftretenden Pseudodichtematrizen arbeitet (Cholesky-decomposed density-based MP2, CDD-MP2) und durch Beschränkung der Laufindizes auf den besetzten/virtuellen Subraum vor allem für große Basissätze einen inhärent kleineren Vorfaktor als AO-MP2 aufweist. Durch Einführung der RI-Näherung konnte hier eine weitere wesentliche Effizienzsteigerung erzielt werden. Sowohl bei AO-MP2 als auch bei CDD-MP2 wurde die RI-Approximation zunächst nur für die Coulomb-artige Integralkontraktion implementiert. Obwohl beide entwickelten RI-basierten Methoden (RI-AO-MP2 und RI-CDD-MP2) für Basissätze wie SVP und cc-pVTZ gegenüber AO-MP2 beziehungsweise CDD-MP2 einen verkleinerten Vorfaktor aufweisen...

Linear skalierende Møller-Plesset-Störungstheorie zur Berechnung der Elektronenkorrelation in großen Molekülen; Linear-scaling Møller-Plesset Perturbation Theory for the Calculation of Electron Correlation in Large Molecules

Doser, Bernd
Fonte: Universidade de Tubinga Publicador: Universidade de Tubinga
Tipo: Dissertação
Português
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Die Berechnung der Elektronenkorrelation mit konventionellen ab-initio-Methoden ist aufgrund des starken Anstiegs des Rechenaufwands mit der Systemgröße auf kleine Moleküle beschränkt. Die Møller-Plesset-Störungstheorie zweiter Ordnung (MP2), welche in Bezug auf den Rechenaufwand die günstigste Korrelationsmethode darstellt, zeigt bereits einen Anstieg des Rechenaufwandes mit der fünften Potenz der Systemgröße, so dass dieser bei Verdopplung der Systemgröße auf das 32-fache ansteigt. Um die Anwendbarkeit des MP2-Verfahrens auf große Moleküle zu erweitern, wurde eine linear skalierende Methode entwickelt, bei der sich der Rechenaufwand direkt proportional zur Systemgröße verhält. Grundlage ist der in den 1990er Jahren von Almlöf und Häser entwickelte Laplace- Ansatz, mit dem die Kopplung an kanonische Molekülorbitale aufgehoben werden kann. Kanonische Molekülorbitale erstrecken sich typischerweise über das gesamte Molekül und lassen somit keine Reduktion des Skalenverhaltens zu. Dagegen ermöglichen die von Natur aus lokalen Atomorbitale (AO) oder auch lokalisierte Molekülorbitale die Reduktion auf ein lineares Skalenverhalten. Die Verwendung rigoroser Integralschranken, die durch eine Kombination aus einer Cauchy-Schwarz- und einer multipolbasierten Abschätzung realisiert wurden...

Small-Time Scaling Behavior of Internet Backbone Traffic

Ribeiro, Vinay Joseph; Zhang, Zhi-Li; Moon, Sue; Diot, Christophe; Ribeiro, Vinay Joseph; Zhang, Zhi-Li; Moon, Sue; Diot, Christophe
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
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Journal Paper; We perform an extensive wavelet analysis of Internet backbone traffic signals to observe and understand the causes of small-time (sub-seconds) scaling phenomena present in them. We observe that for a majority of the traffic traces, the (second-order) scaling exponents at small time scales (1ms - 100ms) are fairly close to 0.5, indicating that traffic fluctuations at these time scales are (nearly) uncorrelated. Some traces, however, do exhibit moderately large scaling exponents (approximately 0.7) at small time scales. In addition, the traces manifest mostly monofractal behaviors at small time scales. To identify the network causes of the observed scaling behavior, we analyze the flow composition of the traffic along two dimensions -- flow size and flow density. Our study points to the dense flows (i.e., flows with bursts of densely clustered packets) as the correlation-causing factor in small time scales, and reveals that the traffic composition in terms of proportions of dense vs. sparse flows plays a major role in influencing the small-time scalings of aggregate traffic. Since queuing inside routers is strongly influenced by traffic fluctuations at small time-scales, our observations and results have significant implications in networking modeling...

Mineral scaling in geothermal fields: A review

Ngothai, Y.; Yanagisawa, N.; Pring, A.; Rose, P.; O'Neill, B.; Brugger, J.
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Conference paper
Publicado em //2010 Português
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Geothermal power is an established energy source in several countries, for example New Zealand and Iceland. However the proposed geothermal operations in South Australia occurs at a much greater depth (5 km) and the heat source is radioactive decay rather than volcanism. A number of issues relating to the geochemistry of geothermal fluids are required to be considered and explored to ensure safe, economic energy production from geothermal fields. Low pH and saline waters, at temperatures much greater than 200oC, are highly corrosive, and it is vital to prevent the generation of scales as the brines are transported to the surface. This paper provides a review on silica, calcite and metal sulphide scaling at various geothermal fields. The solubility of silica and calcite as a function of temperature and/or pressure were discussed and how it affects scaling at various locations in the geothermal plant.; Yung Ngothai, Norio Yanagisawa, Allan Pring, Peter Rose, Brian O'Neill and Joël Brugger

Allometric scaling of mammalian metabolism

White, C.; Seymour, R.
Fonte: Company of Biologists Ltd Publicador: Company of Biologists Ltd
Tipo: Artigo de Revista Científica
Publicado em //2005 Português
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The importance of size as a determinant of metabolic rate (MR) was first suggested by Sarrus and Rameaux over 160 years ago. Max Rubner's finding of a proportionality between MR and body surface area in dogs (in 1883) was consistent with Sarrus and Rameaux's formulation and suggested a proportionality between MR and body mass (Mb) raised to the power of 2/3. However, interspecific analyses compiled during the first half of the 20th century concluded that mammalian basal MR (BMR, ml O2 h-1) was proportional to Mb3/4, a viewpoint that persisted for seven decades, even leading to its common application to non-mammalian groups. Beginning in 1997, the field was re-invigorated by three new theoretical explanations for 3/4-power BMR scaling. However, the debate over which theory accurately explains 3/4-power scaling may be premature, because some authors maintain that there is insufficient evidence to adopt an exponent of 3/4 over 2/3. If progress toward understanding the non-isometric scaling of BMR is ever to be made, it is first essential to know what the relationship actually is. We re-examine previous investigations of BMR scaling by standardising units and recalculating regression statistics. The proportion of large herbivores in a data set is positively correlated both with the scaling exponent (b...

Computational approach to scaling and criticality in planar Ising models

Dudalev, Mikhail
Fonte: Universidade Nacional da Austrália Publicador: Universidade Nacional da Austrália
Tipo: Thesis (PhD); Doctor of Philosophy (PhD)
Português
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In this thesis, we study the critical behaviour of the two-dimensional Ising model on the regular lattices. Using the numerical solution of the model on the square, triangular and honeycomb lattices we compute the universal scaling function, which turns out to be identical on each of the lattices, in addition to being identical to the scaling function of the Ising Field Theory, computed previously by Fonseca and Zamolodchikov. To cope with the lattice contributions we carefully examined series expansions of the lattice free energy derivatives. We included the non-scaling regular part of the free energy as well as non-linear Aharony-Fisher scaling elds, which all have non-universal expansions. Using as many of the previously known exact results as possible, we were able to t the unknown coe cients of the scaling function expansion and obtain some non-universal coe cients. In contrast to the IFT approach of Fonseca and Zamolodchikov, all coe cients were obtained independently from separate datasets, without using dispersion relations. These results show that the Scaling and Universality hypotheses, with the help of the Aharony-Fisher corrections, hold on the lattice to very high precision and so there should be no doubt of their validity. For all numerical computations we used the Corner Transfer Matrix Renormalisation Group (CTMRG) algorithm...

Scaling-Up the Impact of Good Practices in Rural Development : A Working Paper to Support Implementation of the World Bank’s Rural Development Strategy

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Economic & Sector Work :: Rural Development Assessment; Economic & Sector Work
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A key thrust in the implementation of the Bank's new rural development strategy is identifying and "scaling-up good practice investments and innovations in rural development." Historically, successful World Bank projects have been one-time investments without strategies for leveraging projects to a larger scale or to broader coverage to increase efficiency and developmental impact in a country or region. The Bank believes that scaling-up good practices must become an integral part of national rural development strategies to reduce rural poverty and support broad-based rural development. This working paper, written in support of the Bank's rural development strategy, is intended to contribute to the development of a framework for thinking about scaling-up. The paper begins with a review of the literature on scaling-up in rural development and other contexts to develop an understanding of basic concepts and terms. Drawing from the literature review and interviews, the authors develop a working definition of the term scaling-up and a provisional framework for analyzing experiences of scaling-up in rural development. Then...

Scaling relations of branching pulsatile flow

Silva, Carla; Reis, A. Heitor
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Português
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Apparently complex flow structures obey to scaling relations that enable to make it viable the study of their configuration and flow dynamics. This is the case of flow structures that exhibit several branching levels and are thought to perform optimally. Here we present scaling relations of diameters and lengths of branching cylindrical channels with pulsatile flows, and compare them with other relations published in the literature. It is shown that, under constant global volume of the flow tree, and for zero pulse frequency these scaling relations reduce to Murrays's law of consecutive diameters. Optimal scaling depends on pulse frequency, distensibility of the channel walls, and asymmetry of the daughter vessels. In case that in addition to global volume of the flow tree, the pressure head is also kept constant, a similar scaling law of channel lengths emerges that holds together with the law of diameter scaling. The effect of channel distensibility is shown to be somehow important, such that for achieving optimal performance (lowest impedance) channels with lower relative distensibility must have their diameter increased. Results are compared with those of other models for the case of some arteries.

A conceptual model to approach the scaling process of social entreprises: The case of Cozinha com Alma

Figueiredo, Marta
Fonte: NSBE - UNL Publicador: NSBE - UNL
Tipo: Dissertação de Mestrado
Publicado em /01/2014 Português
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A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics; The positive results of the past two years and the strong desire to expand social impact led the co-founders of the social takeaway Cozinha com Alma (CcA) to start planning the organization’s scaling strategy. Considering the complexities and challenges of the social enterprises’ scaling process, this Work Project aims to approach the scaling process of CcA by creating a conceptual model to guide social organizations this strategic decision-process. This theoretical framework was then applied and tested to CcA's current scaling issue in order to assess the organization's business model and readiness to expand with the purpose to define the most promising growing path.

Interspecies Scaling in Blast Neurotrauma

Wood, Garrett Wayne
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2015 Português
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Between October 2001 and May 2012 approximately 70% of U.S. military personnel killed in action and 75% wounded in action were the direct result of exposure to an explosion. As of 2008, it was estimated that close to 20% of all Operation Iraqi Freedom and Operation Enduring Freedom (OIF/OEF) veterans had sustained some form of traumatic brain injury (TBI). Further, blast exposure is also a civilian problem due to the increased usage of explosives in terrorist attacks. Blast injury research has historically focused on the pulmonary system and the other air-containing organs which have been shown through extensive experimentation to be susceptible to blast overpressure injury. A shift in injury pattern during recent conflicts is characterized by decreased incidence of pulmonary injuries with an increase in TBI thought to be associated with blast exposure. This increase in observation of blast TBI has resulted in a large research effort to understand mechanisms and thresholds. However, due to the relatively sudden shift, much of this research is being conducted without a proper understanding and consideration of blast mechanics and interspecies scaling effects.

This dissertation used experimental and computational finite element (FE) analysis to investigate some large questions surrounding blast TBI research. An experimental investigation was conducted to determine the effects of modern thoracic body armor usage on blast pressure exposure seen by the body. To improve FE modeling capabilities...

Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development

Di Matteo, Tiziana; Aste, Tomaso; Dacorogna, Michel
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
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The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte Carlo studies and a computation of the scaling in the frequency domain.