Analytical Expressions In Order Research Articles

Accounting for mudflow genesis in preliminary assessment of the maximum volume of solid mudflow sediments in the North Caucasus

The area of investigation was subject to multifactor analysis of the relationship between the maximum amount of mudflow solid sediments (W) and parameters such as the mudflow basin area (S), average channel slope (α), and mudflow channel length (L). They were used to obtain analytical expressions in order to approximate the W(S, L, α) relation based on the mudflow genesis and source height. Statistical data on mudflow manifestations in different basins in the North Caucasus covering more than fifty years were used to obtain the analytical expressions in order to assess the maximum volume of mudflow solid sediments.

State-to-State Quantum Mechanical Calculations of Rate Coefficients for the D+ + H2 → HD + H+ Reaction at Low Temperature

The dynamics of the D(+) + H2 → HD + H(+) reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models.

Exact Solution of Out-of-Plane Problems of an Arch with Varying Curvature and Cross Section

This paper deals with the exact solution of the differential equations for the out-of-plane behavior of an arch with varying curvature and cross section. The differential equations include the shear deformation effect. The cross section of the arch is doubly symmetric. Due to the double symmetry, in-plane and out-of-plane behavior will be uncoupled. However, a coupling of the out-of-plane bending and the torsional response will exist and will be discussed in this study. The governing differential equations of planar arches loaded perpendicular to their plane are solved exactly by using the initial value method. The analytical expressions of the fundamental matrix can be obtained for some cases. It is also possible to use these analytical expressions in order to obtain the displacements and the stress resultants for an arch with any loading and boundary conditions. The examples given in the literature are solved and the results are compared. The analytical expressions of the results are given for some examples.

Semi-analytical modeling of a PWR lower head failure under severe accident conditions using an axisymetrical shell theory

The USNRC/SNL OLHF program was carried out within the framework of an OECD project. This program consisted of four one-fifth scale experiments of a reactor pressure vessel (RPV) lower head failure (LHF) under well controlled internal pressure and large throughwall temperature differentials; the objectives were to characterize the mode, timing and size of a possible PWR lower head failure in the event of a core meltdown accident. These experiments should also lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all ex-vessel events. A large quantity of escaping corium may lead to direct heating of the containment or ex-vessel steam explosion. These are important issues due to their potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, a 2D semi-analytical model has been developed and used to simulate these experiments. The aim of this effort is to develop a simplified but well predicting code that can be then implemented in European integral severe accident computer codes (ASTEC, ICARE/CATHARE). This paper presents the detailed mathematical formulation of this simplified method which is used to interpret the experimental results. The axi-symmetric shell theory under internal pressure proposed by Timoshenko has been utilised. The solution to the equilibrium equations is presented, with particular attention to the Rabotnov analytical formula. The radius and the polar angle of the deformed structure have been written as analytical expressions in order to take the large displacements and large strains into account using our mathematical formulation. The Norton type creep law and the Kachanov damage law have been used. Several failure criteria were used in the calculations and their effect on the numerical results is discussed. This 2D semi-analytical model gives very satisfactory results when compared, with the experimental and numerical results that were presented recently in the Benchmark calculations based on the first test of the OLHF program. The performance of this model is also illustrated by its capacity to accurately simulate the deformation of the lower head, including the variation of wall thickness.

Magneto-optical transverse Kerr effect in multilayers

We present detailed theoretical and experimental analysis of the magneto-optic transverse Kerr effect in magnetic multilayers. The theoretical model is based upon a phenomenological permittivity tensor. From the general result, suitable only for numerical calculations, we derive several approximate analytical expressions in order to make a qualitative discussion. The theoretical predictions are compared with experimental results in Y/Co bilayers, and the good agreement found allows for an accurate determination of the magneto-optical constants of the material. Then, the theoretical model is applied to make a detailed study of interface magnetism in ${\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}$ alloys, and to perform numerical simulations in Co/Cu and Fe/Cu multilayers. The results in multilayers highlight the complex behavior of the magneto-optic transverse Kerr effect, in which the contributions of the individual layers are never strictly additive. This nonlinearity is found to be strongly dependent on the $3d$ magnetic metal present and could be used to probe the alignment of the layers even in a configuration of vanishing magnetic moment.

Limb-darkening coefficients of illuminated atmospheres

The eect of mutual illumination in a close bi- nary on the limb-darkening coecients is studied using the UMA (Uppsala Model Atmosphere) code in convective line-blanketed atmospheres illuminated by line-blanketed fluxes, for 3 700 K <T e < 7 000 K and 7 000 K <T h < 12 000 K. The results show that the limb-darkening coef- cients of illuminated atmospheres are signicantly dif- ferent from the non-illuminated ones and mostly depend on four parameters: the amount of incident energy, the illumination direction, the eective temperature of the il- luminated star and the temperature of the illuminating one. We present bolometric, monochromatic and passband specic coecients and we give, for the latter, analytical expressions in order to easily account for the eect in light curve synthesis programs.

Molecular gas-flow over convex bodies: a physico-mathematical model for heat transfer calculation

This paper deals with a physico-mathematical model for the heat-flux over a convex body in near-free molecular flow regime. The model depends on the characteristic global physical quantity of the state of the external flux and upon two phenomenological parameters which represent the physico-chemical conditions of the gas-surface pair. The presence of these two parameters, which is due to the construction of the model by means of the theory of scattering kernels, gives the model a certain arbitrariness. To remove this limitation the model has been further identified in the sense that these parameters have been determined for a particular gas-surface pair by comparison with experimental results on a cylindrical body. The model has then been applied to a sphere in order to determine the Stanton number. Finally, these results have been approximated in terms of analytical expressions in order to simplify the model itself.