988 resultados para exponential function


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The wettability of thin poly(methyl methacrylate) (PMMA) films on a silicon wafer with a native oxide layer exposed to solvent vapors is dependent on the solvent properties. In the nonsolvent vapor, the film spread on the substrate with some protrusions generated on the film surface. In the good solvent vapor, dewetting happened. A new interface formed between the anchored PMMA chains and the swollen upper part of the film. Entropy effects caused the upper movable chains to dewet on the anchored chains. The rim instability depended on the surface tension of solvent (i.e., the finger was generated in acetone vapor (gamma(acetone) = 24 mN/m), not in dioxane vapor (gamma(dioxane) = 33 mN/m)). The spacing (lambda) that grew as an exponential function of film thickness h scaled as similar to h(1.31) whereas the mean size (D) of the resulting droplets grew linearly with h.

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In this paper, BPO4-xSiO(2) (X: SiO2/BPO4 molar ratio, 0-70%) and BPO4-xAl(2)O(3) (X: Al2O3/BPO4 molar ratio, 0-20%) powder samples were prepared by the Pechini-type sol-gel (PSG) process using glycerol and poly(ethylene glycol) as additives. The structure and optical properties of the resulting samples were characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy, field emission scanning electron microscopy (FESEM), diffuse reflection spectra, photoluminescence (PL) excitation and emission spectra, kinetic decay, and X-ray photoelectron spectra (XPS), respectively. It was found that the Pechini-type sol-gel-derived BPO4-xSiO(2) annealed at 1000 degrees C and BPO4-xAl(2)O(3) annealed at 960 degrees C exhibited bright bluish-white emissions centered at 428 and 413 nm, respectively. The luminescence decay curve analysis indicates that each sample has two kinds of lifetimes (more than 0.4 ms and less than 10 ns) and two types of kinetic decay behaviors, which can be fitted into a double-exponential function and a single-exponential function, respectively.

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The perturbation method is developed to deal with the effective nonlinear dielectric responses of weakly nonlinear graded composites, which consist of the graded inclusion with a linear dielectric function of spatial variables of inclusion material. For Kerr-like nonlinear graded composites, as an example in two dimensions, we have used the perturbation method to solve the boundary value problems of potentials, and studied the effective responses of nonlinear graded composites, where a cylindrical inclusion with linear dielectric function and nonlinear dielectric constant is randomly embedded in a homogeneous host with linear and nonlinear dielectric constants. For the exponential function and the power-law dielectric profiles of cylindrical inclusions, in the dilute limit, we have derived the formulae of effective nonlinear responses of both graded nonlinear composites.

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Effective dielectric responses of graded cylindrical composites are investigated when an external uniform field is applied to the composites. Considering linear random composites of cylindrical particles with a specific dielectric function, which varies along the radial direction of the particles, we have studied three cases of dielectric profiles: exponential function, linear and power-law profiles. For each case, the effective dielectric response of graded composites is given on the basis of exact solutions of the local potentials of composites in the dilute limit. For a larger volume fraction, we have proposed an effective medium approximation to estimate the effective dielectric response.

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The effective thermal conductivity of graded composites with contact resistance on the inclusion surface is investigated. As an example, we have considered the graded composite media with a spherical particle embedded in a homogeneous matrix, where the thermal conductivity of spherical inclusion is an exponential function k(i) = c exp(betar) (where r is the inside distance of a point in particle from the center of the spherical particle in a spherical coordinate). For both heat contact resistance and perfect contact cases, we have given a reasonable effective medium approximation to calculate the effective conductivity. (C) 2003 Elsevier B.V. All rights reserved.

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Thus far, grassland ecosystem research has mainly been focused on low-lying grassland areas, whereas research on high-altitude grassland areas, especially on the carbon budget of remote areas like the Qinghai-Tibetan plateau is insufficient. To address this issue, flux of CO2 were measured over an alpine shrubland ecosystem (37 degrees 36'N, 101 degrees 18'E; 325 above sea level [a. s. l.]) on the Qinghai-Tibetan Plateau, China, for 2 years (2003 and 2004) with the eddy covariance method. The vegetation is dominated by formation Potentilla fruticosa L. The soil is Mol-Cryic Cambisols. To interpret the biotic and abiotic factors that modulate CO2 flux over the course of a year we decomposed net ecosystem CO2 exchange (NEE) into its constituent components, and ecosystem respiration (R-eco). Results showed that seasonal trends of annual total biomass and NEE followed closely the change in leaf area index. Integrated NEE were -58.5 and -75.5 g C m(-2), respectively, for the 2003 and 2004 years. Carbon uptake was mainly attributed from June, July, August, and September of the growing season. In July, NEE reached seasonal peaks of similar magnitude (4-5 g C m(-2) day(-1)) each of the 2 years. Also, the integrated night-time NEE reached comparable peak values (1.5-2 g C m(-2) day(-1)) in the 2 years of study. Despite the large difference in time between carbon uptake and release (carbon uptake time < release time), the alpine shrubland was carbon sink. This is probably because the ecosystem respiration at our site was confined significantly by low temperature and small biomass and large day/night temperature difference and usually soil moisture was not limiting factor for carbon uptake. In general, R-eco was an exponential function of soil temperature, but with season-dependent values of Q(10). The temperature-dependent respiration model failed immediately after rain events, when large pulses of R-eco were observed. Thus, for this alpine shrubland in Qinghai-Tibetan plateau, the timing of rain events had more impact than the total amount of precipitation on ecosystem R-eco and NEE.

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The unsaturated expansive soil is a hotspot and difficulty in soil mechanics inland and outland. The expansive soil in our China is one of the widest in distributing and greatest in area, and the disaster of expansive soil happens continually as a result. The soil mechanics test, monitor, numerical simulation and engineering practice are used to research swell and shrinkage characteristic, edge strength characteristic and unsaturated strength characteristic of Mengzi expansive soil. The seep and stability of the slope for expansive soil associated with fissure are analyzed and two kinds of new technique are put forward to be used in expansive soil area, based on disaster mechnics proposed of the slope.The technique of reinforcement in road embankment is optimized also. Associated with engineering geology research of Mengzi expansive soil, mineral composition, chemical composition, specific area and cation content, dissolubility salt and agglutinate, microcosmic fabric characteristic, cause of formation and atmosphere effect depth are analyzed to explain the intrinsic cause and essence of swell and shrinkage for expansive soil. The rule between swell-shrinkage and initial state, namely initial water content, initial dry density and initial pressure, can be used to construction control. Does Response model is fit to simulate the rule, based on ternary regression analysis. It has great meaning to expansive soil engineering in area with salt or alkali. The mechanics under CD, CU and GCU of expansive soil is researched by edge surface theory to explain the remarkable effect of consolidation pressure, initial dry density, initial water content, cut velocity, drainage and reinforcement to the edge strength characteristic. The infirm hardening stress strain curves can be fitted with hyperbola model and the infirm softening curves can be fitted with exponential model. The normalization theory can be used to reveal the intrinsic unity of the otherness which is brought by different methods to the shear strength of the same kinds of samples. The unsaturated strain softening characteristic and strength envelope of remolding samples are researched by triaxial shear test based on suction controlled, the result of which is simulated by exponential function. The strength parameters of the unsaturated samples are obtained to be used in the unsaturated seep associated with rainfall. The elasticity and plasticity characters of expansive soil are researched to attain the model parameters by using modified G-A model. The humidification destroy characteristic of expansive soil is discussed to research the disaster mechanism of the slope with the back pressure increasing and suction decreasing under bias pressure consolidation. The indoor and outdoor SWCCs are measured to research the effect factors and the rule between different stress and filling environment. The moisture absorption curves can express the relationship between suction and water content in locale. The SWCCs of Mengzi expansive soil are measured by GDS stress path trixial system. The unsaturated infiltration function is gained to research seep and stability of the slope of expansive soil. The rainfall infiltration and ability of slope considering multifarious factors are studied by analyzing fissure cause of Mengzi expansive soil. The mechanism of the slope disaster is brought forward by the double controlling effect between suction and fissure. Two new kinds of technique are put forward to resolve disaster of expansive soil and the technique of reinforcement on embankment is optimized, which gives a useful help to solving engineering trouble.

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Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/H s and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs > 12 m and Hmax > 16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs > 5.5 m or Hmax > 8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

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Observations of extreme ultraviolet (EUV) emission from an X-class solar flare that occurred on 2011 February 15 at 01: 44 UT are presented, obtained using the EUV Variability Experiment (EVE) on board the Solar Dynamics Observatory. The complete EVE spectral range covers the free-bound continua of H I (Lyman continuum), He I, and He II, with recombination edges at 91.2, 50.4, and 22.8 nm, respectively. By fitting the wavelength ranges blueward of each recombination edge with an exponential function, light curves of each of the integrated continua were generated over the course of the flare, as was emission from the free-free continuum (6.5-37 nm). The He II 30.4 nm and Ly alpha 121.6 nm lines, and soft X-ray (SXR; 0.1-0.8 nm) emission from GOES are also included for comparison. Each free-bound continuum was found to have a rapid rise phase at the flare onset similar to that seen in the 25-50 keV light curves from RHESSI, suggesting that they were formed by recombination with free electrons in the chromosphere. However, the free-free emission exhibited a slower rise phase seen also in the SXR emission from GOES, implying a predominantly coronal origin. By integrating over the entire flare the total energy emitted via each process was determined. We find that the flare energy in the EVE spectral range amounts to at most a few percent of the total flare energy, but EVE gives us a first comprehensive look at these diagnostically important continuum components.

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A ~si MAS NMR study of spin-lattice relaxation behaviour in paramagnetic-doped crystalline silicates was undertaken, using synthetic magnesium orthosilicate (forsterite) and synthetic zinc orthosilicate (willemite) doped with 0.1% to 20% of Co(II), Ni(II), or CU(II), as experimental systems. All of the samples studied exhibited a longitudinal magnetization return to the Boltzmann distribution of nuclear spin states which followed a stretched-exponential function of time: Y=exp [- (tjTn) n], O

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Rationale: Central cannabinoid systems have been implicated in appetite control through the respective hyperphagic and anorectic actions of CB1 agonists and antagonists. The motivational changes underlying these actions remain to be determined, but may involve alterations to food palatability. Objectives: The mode of action of cannabinoids on ingestion was investigated by examining the effects of exogenous and endogenous agonists, and a selective CB1 receptor antagonist, on licking microstructure in rats ingesting a palatable sucrose solution. Methods: Microstructural analyses of licking for a 10% sucrose solution was performed over a range of agonist and antagonist doses administered to non-deprived, male Lister hooded rats. Results: Delta(9)-tetrahydrocannabinol (0.5, 1 and 3 mg/kg) and anandamide (1 mg/kg and 3 mg/kg) significantly increased total number of licks. This was primarily due to an increase in bout duration rather than bout number. There was a nonsignificant increase in total licks following administration of 2-arachidonoyl glycerol (0.2, 1.0 and 2.0 mg/kg), whereas administration of the CB1 antagonist SR141716 (1 mg/kg and 3 mg/kg) significantly decreased total licks. All drugs, with the exception of anandamide, significantly decreased the intra-bout lick rate. An exponential function fitted to the cumulative lick rate curves for each drug revealed that all compounds altered the asymptote of this function without having any marked effects on the exponent. Conclusions: These data are consistent with endocannabinoid involvement in the mediation of food palatability.

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Grasslands restoration is a key management tool contributing to the long-term maintenance of insect populations, providing functional connectivity and mitigating against extinction debt across landscapes. As knowledge of grassland insect communities is limited, the lag between the initiation of restoration and the ability of these new habitats to contribute to such processes is unclear. Using ten data sets, ranging from 3 to 14 years, we investigate the lag between restoration and the establishment of phytophagous beetle assemblages typical of species rich grasslands. We used traits and ecological characteristics to determine factors limiting beetle colonisation, and also considered how food-web structure changed during restoration. For sites where seed addition of host-plants occurred the success in replicating beetle assemblages increased over time following a negative exponential function. Extrapolation beyond the existing data set tentatively suggested that success would plateau after 20 years, representing a c. 60% increase in assemblage similarity to target grasslands. In the absence of seed addition, similarity to the target grasslands showed no increase over time. Where seed addition was used the connectance of plant-herbivore food webs decreased over time, approaching values typical of species rich grasslands after c. 7 years. This trend was, however, dependent on the inclusion of a single site containing data in excess of 6 years of restoration management. Beetles not capable of flight, those showing high degrees of host-plant specialisation and species feeding on nationally rare host plants take between 1 and 3 years longer to colonise. Successful grassland restoration is underpinned by the establishment of host-plants, although individual species traits compound the effects of poor host-plant establishment to slow colonisation. The use of pro-active grassland restoration to mitigate against future environmental change should account for lag periods in excess of 10 years if the value of these habitats is to be fully realised.

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Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.

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In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

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We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.