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991.
The paper deals with the effect of dimensionless non-Newtonian coefficient on the thermal stability of a reactive viscous liquid in steady flow between parallel heated plates. It is assumed that the liquid is symmetrically heated and the flow fully developed. Approximate analytical solution is obtained for the velocity of the flow and the criterion for which this solution is valid is determined. After the velocity distribution is known, the temperature distribution may be calculated. Disappearance of criticality (transition values) are obtained in the following cases: (i) bimolecular (ii) Arrhenius and (iii) sensitized temperature dependence. We have observed that non-linear effect from velocity and temperature fields introduced decaying for the transitional values of the dimensionless central temperature. Other effects of this non-linearity are reported. The results help to enhance understanding of the interplay between Newtonian and non-Newtonian thermal explosions. 相似文献
992.
A correction of the 2D KdV equation of Djordjevic & Redekopp in exponentially stratified fluid* 总被引:1,自引:0,他引:1
To further study the fission laws of initial internal solitons on the continental shelf/slope, we rederive and correct the 2D KdV equation of Djordjevic & Redekopp for exponentially stratified fluid (or ocean) and with two-dimensional topography. Through a combination of theoretical study and numerical experiments, we show that solitons in the odd vertical modes can fission. However, because of the corrections, the fission conditions are different from those of Djordjevic & Redekopp. The even modes cannot fission unless the initial internal solitons propagate from shallow sea to deep sea. This conclusion is entirely opposite to that of Djordjevic & Redekopp.The project supported by the National Natural Science Foundation of China (40276008) and the Grant of Key Laboratory of Marine Science and Numerical Modeling, SOA (0201(2003))The English text was polished by Keren Wang. 相似文献
993.
We consider the steady-state solutions for the exothermic chemical reaction, taking the diffusion of the reactant in a slab into account and assuming an Arrhenius temperature dependence with variable pre-exponential factor. We solve the resulting nonlinear boundary value problem using both numerical and analytical methods. This new analytical solution for the Frank-Kamenetskii parameter δ, as it is in terms of Bernoulli’s numbers, is in accordance with the numerical integration provided the activation energy parameter ε (1) is very small and for ε→0 it goes to the well-known Frank-Kamenetskii case. We determine numerically the transitional values of δ, ε and the dimensionless central temperature θm. 相似文献
994.
Samuel N. Stechmann Andrew J. Majda 《Theoretical and Computational Fluid Dynamics》2006,20(5-6):377-404
When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear waves of simplified tropical climate models with convective parameterizations. In this paper’s simplified tropical climate model, convection is parameterized by a nonlinear precipitation term, and the nonlinearity gives rise to precipitation front solutions. Precipitation fronts are solutions where the spatial domain is divided into two regions, and the precipitation (and other model variables) changes abruptly at the boundary of the two regions. In one region the water vapor is below saturation and there is no precipitation, and in the other region the water vapor is above saturation level and precipitation is nonzero. The boundary between the two regions is a free boundary that moves at a constant speed. It is shown that only certain front speeds are allowed. The three types of fronts that exist for this model are drying fronts, slow moistening fronts, and fast moistening fronts. Both types of moistening fronts violate Lax’s stability criterion, but they are robustly realizable in numerical experiments that use finite relaxation times. Remarkably, here it is shown that all three types of fronts are robustly realizable analytically for finite relaxation time. All three types of fronts may be physically unreasonable if the front spans an unrealistically large physical distance; this depends on various model parameters, which are investigated below. From the viewpoint of applied mathematics, these model equations exhibit novel phenomena as well as features in common with the established applied mathematical theories of relaxation limits for conservation laws and waves in reacting gas flows. 相似文献
995.
Samuel A. Meek Antonin Poisson Guy Guelachvili Theodor W. Hänsch Nathalie Picqué 《Applied physics. B, Lasers and optics》2014,114(4):573-578
We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.1 μm. High power per comb mode (>10?7 W/mode) is obtained over a broad spectral span (>750 nm, >790 cm?1). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer. 相似文献
996.
Samuel Monnier 《Communications in Mathematical Physics》2014,325(1):41-72
In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows one to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper. 相似文献
997.
Dana Mendelson Asaf Nachmias Samuel S. Watson 《Communications in Mathematical Physics》2014,329(1):29-56
We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy–Smirnov formula. We use this result to obtain new upper and lower bounds of ${e^{O(\sqrt{{\rm log}\,{\rm log} R})}\, R^{-1/3}}$ for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R ?1/3+o(1). 相似文献
998.
Susana Álvarez-Díez J. Samuel Baixauli-Soler María Belda-Ruiz 《Central European Journal of Operations Research》2014,22(2):237-262
Greek letters, in particular delta and vega based on the Black–Scholes model (BS), have been widely used to estimate the sensitivity of CEO wealth to changes in stock price (delta) and stock return volatility (vega) and to evaluate the executive stock options (ESOs) granted on the basis of performance and risk. However, the BS model does not take into account the main features of ESOs and therefore the delta and vega values it produces are not valid. The Cvitanic–Wiener–Zapatero model (CWZ) is an alternative model to Black–Scholes for valuing ESOs. It has a closed formula and considers the main features of ESOs. We carry out a sensitivity analysis to show that research on option-based compensation and its risk-taking effects is not robust in ESO pricing models. The sensitivity analysis consists of comparing the impact of the common parameters of the BS and CWZ models, as well as the effect of the specific parameters of the CWZ model, on the sensitivity of CEO wealth to stock price and stock volatility. Additionally, using panel data methodology, we develop an empirical analysis to illustrate the influence of stock return volatility and different corporate policies on both CEO wealth sensitivities. 相似文献
999.
Molecules encountering silica interfaces interact primarily with the hydroxyl groups that terminate the bulk structure. When the nominal surface density is very low, these "silanols" are presumed to be isolated. Nevertheless, silicas that are highly dehydroxylated by pretreatment at 800 °C react with Ga(CH(3))(3) at room temperature to give primarily disilanolate-bridged digallium sites, [(CH(3))(2)Ga(μ-OSi≡)](2). The EXAFS at the Ga K-edge shows a prominent Ga-Ga scattering path, regardless of whether an excess or a limiting amount of Ga(CH(3))(3) is used. Some dimers are formed by the concerted reaction of Ga(CH(3))(3) with an "isolated" silanol and an adjacent siloxane bond. These grafting sites are proposed to be hydroxyl-substituted 2-rings, formed by condensation within a vicinal Q(2)-Q(3) pair. Other dimers are formed by reaction of Ga(CH(3))(3) with vicinal Q(3)-Q(3) pairs which have not condensed, even at 800 °C. In a computational model for the dimer sites, the O-O distance is <2.6 ?, which is far shorter than the calculated mean interhydroxyl separation for the thermally treated silicas (12.2 ?). This highly nonrandom distribution of surface silanols, in combination with the coupled reaction of "isolated" silanols and strained siloxane bonds, accounts for the preferential formation of grafted site pairs rather than isolated grafted sites when silica surfaces are chemically modified. 相似文献
1000.
Nucleated polymerisation processes are involved in many growth phenomena in nature, including the formation of cytoskeletal filaments and the assembly of sickle hemoglobin and amyloid fibrils. Closed form rate equations have, however, been challenging to derive for these growth phenomena in cases where secondary nucleation processes are active, a difficulty exemplified by the highly non-linear nature of the equation systems that describe monomer dependent secondary nucleation pathways. We explore here the use of fixed point analysis to provide self-consistent solutions to such growth problems. We present iterative solutions and discuss their convergence behaviour. We establish a range of closed form results for linear growth processes, including the scaling behaviours of the maximum growth rate and of the reaction end-point. We further show that a self-consistent approach applied to the master equation of filamentous growth allows the determination of the evolution of the shape of the length distribution including the mean, the standard deviation, and the mode. Our results highlight the power of fixed-point approaches in finding closed form self-consistent solutions to growth problems characterised by the highly non-linear master equations. 相似文献