On a problem of S.L. Sobolev

In his famous works of 1930 [1,2] Sergey L. Sobolev has proposed a construction of the solution of the Cauchy problem for the hyperbolic equation of the second order with variable coefficients in Rş. Although Sobolev did not construct the fundamental solution, his construction was modified later by Romanov (2002) and Smirnov (1964) to obtain the fundamental solution. However, these works impose a restrictive assumption of the regularity of geodesic lines in a large domain. In addition, it is unclear how to realize those methods numerically. In this paper a simple construction of a function, which is associated in a clear way with the fundamental solution of the acoustic equation with the variable speed in 3-d, is proposed. Conditions on geodesic lines are not imposed. An important feature of this construction is that it lends itself to effective computations.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

On the Rayleigh-Plateau instability

In this paper,we study the surface instability of a cylindrical pore in the absence of stress. This instability is called the Rayleigh-Plateau instabilty. We consider the model developed by Spencer et ...     

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

Intensity‐based estimation of extreme loss event probability and value at risk

We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self‐exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability. Copyright © 2012 John Wiley & Sons, Ltd.     

Thermomechanical formulation of ductile damage coupled to nonlinear isotropic hardening and multiplicative viscoplasticity

In this paper, we present a thermomechanical framework which makes use of the internal variable theory of thermodynamics for damage-coupled finite viscoplasticity with nonlinear isotropic hardening. Damage evolution, being an irreversible process, generates heat. In addition to its direct effect on material's strength and stiffness, it causes deterioration of the heat conduction. The formulation, following the footsteps of Simó and Miehe (1992), introduces inelastic entropy as an additional state variable. Given a temperature dependent damage dissipation potential, we show that the evolution of inelastic entropy assumes a split form relating to plastic and damage parts, respectively. The solution of the thermomechanical problem is based on the so-called isothermal split. This allows the use of the model in 2D and 3D example problems involving geometrical imperfection triggered necking in an axisymmetric bar and thermally triggered necking of a 3D rectangular bar.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

Metabonomic analysis of serum reveals antifatigue effects of Yi Guan Jian on fatigue mice using gas chromatography coupled to mass spectrometry

Yi Guan Jian (YGJ), one of the most commonly used traditional Chinese medicines, has been reported to possess significant antifatigue effects. However, the mechanisms underlying its antifatigue effects remain largely unresolved. In this study, a metabonomics approach, involving gas chromatography coupled to mass spectrometry and a multivariate statistical technique, was developed to estimate the extent to which YGJ alleviated the exhausting swimming‐induced fatigue of mice. High‐dose treatment with YGJ significantly extended the swimming time of fatigued mice. Significant alterations of metabolites involving amino acids, organic acids and carbohydrates were observed in the serum of fatigued mice, which were reversed by YGJ treatment while biochemical indexes returned to normal. These metabolic changes suggest that the antifatigue effect of YGJ is associated with the impairement of amino acid, organic acids and carbohydrates. It also appears that YGJ can induce significant metabolic alterations independent of the exhausting swimming‐induced metabolic changes. The significantly altered metabolites induced by YGJ intervention include l‐ 2‐amino‐acetoacetate, taurine, fumaric acid, malic acid, oxoadipic acid and l‐ aspartate, all of which are associated with antifatigue properties. This suggests that YGJ exerts chemopreventive effects via antifatigue mechanisms.