Large deviation principle for the fourth-order stochastic heat equations with fractional noises

In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method.     

Higher order global solution and normalized flux for singularly perturbed reaction-diffusion problems

In this paper a computational technique is proposed for obtaining a higher order global solution and global normalized flux of singularly perturbed reaction-diffusion two-point boundary-value problems. The HOC (higher order compact) finite difference scheme developed in Gracia et al. (2001) [4] and which is constructed on an appropriate piecewise uniform Shishkin mesh, has been considered to find an almost fourth order convergent solution at mesh points. Using these values, piecewise cubic interpolants based approximations for solution and normalized flux in whole domain have been defined. It has been shown that the global solution and the global normalized flux are also uniformly convergent. Moreover, for the global solution, the order of uniform convergence in the whole domain is optimal, i.e., it is the same as this one obtained at mesh points, whereas, for the global normalized flux, the uniform convergence is almost third order, except at midpoints of the mesh, where it is also almost fourth order. Theoretical error bounds have been provided along with some numerical examples, which corroborate the efficiency of the proposed technique to find good approximations to the global solution and the global normalized flux.     

A note on a non-standard problem for an equation with a delay term

In this note we investigate the continuous dependence of the solutions for a theory of heat conduction with a delay term. We use energy arguments to obtain the continuous dependence results and spectral arguments to prove the non-uniqueness result. The extension to the thermoelastic problem is also pointed out.     

Metric and ultrametric spaces of resistances

Consider an electrical circuit, each edge e of which is an isotropic conductor with a monomial conductivity function . In this formula, y_e is the potential difference and current in e, while μ_e is the resistance of e; furthermore, r and s are two strictly positive real parameters common for all edges. In particular, the case r=s=1 corresponds to the standard Ohm’s law.In 1987, Gvishiani and Gurvich [A.D. Gvishiani, V.A. Gurvich, Metric and ultrametric spaces of resistances, in: Communications of the Moscow Mathematical Society, Russian Math. Surveys 42 (6 (258)) (1987) 235-236] proved that, for every two nodes a,b of the circuit, the effective resistance μ_a,b is well-defined and for every three nodes a,b,c the inequality holds. It obviously implies the standard triangle inequality μ_a,b≤μ_a,c+μ_c,b whenever s≥r. For the case s=r=1, these results were rediscovered in the 1990s. Now, after 23 years, I venture to reproduce the proof of the original result for the following reasons:

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It is more general than just the case r=s=1 and one can get several interesting metric and ultrametric spaces playing with parameters r and s. In particular, (i) the effective Ohm resistance, (ii) the length of a shortest path, (iii) the inverse width of a bottleneck path, and (iv) the inverse capacity (maximum flow per unit time) between any pair of terminals a and b provide four examples of the resistance distances μ_a,b that can be obtained from the above model by the following limit transitions: (i) r(t)=s(t)≡1, (ii) r(t)=s(t)→∞, (iii) r(t)≡1,s(t)→∞, and (iv) r(t)→0,s(t)≡1, as t→∞. In all four cases the limits μ_a,b=lim_t→∞μ_a,b(t) exist for all pairs a,b and the metric inequality μ_a,b≤μ_a,c+μ_c,b holds for all triplets a,b,c, since s(t)≥r(t) for any sufficiently large t. Moreover, the stronger ultrametric inequality μ_a,b≤max(μ_a,c,μ_c,b) holds for all triplets a,b,c in examples (iii) and (iv), since in these two cases s(t)/r(t)→∞, as t→∞.

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Communications of the Moscow Math. Soc. in Russ. Math. Surveys were (and still are) strictly limited to two pages; the present paper is much more detailed.Although a translation in English of the Russ. Math. Surveys is available, it is not free in the web and not that easy to find.

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The last but not least: priority.

     

Phonon Dispersion in Polyadenylic Acid

A study of the normal modes of vibration and their dispersion in polyadenylic acid based on the Urey–Bradley force field is reported. It gives a better interpretation of FTIR spectra as compared with the valence force field. Characteristic features of dispersion curves such as regions of high density‐of‐states, repulsion, and character mixing of dispersive modes are discussed. Predictive valuzes of heat capacity as a function of temperature are reported.     

金属磁记忆效应的第一性原理计算与实验研究

为研究铁磁材料应力集中区域金属磁记忆信号的产生机理及其变化规律, 采用基于密度泛函理论的第一性原理平面波赝势法, 建立了磁记忆效应的磁力学模型; 计算分析了力与磁记忆自发漏磁信号的定量变化关系. 研究结果表明:力作用导致晶格畸变是磁记忆自发漏磁信号产生的根本原因; 常温下, 磁记忆信号随应力近似线性变化的规律与X70钢管水压爆破实验结果具有很好的一致性. 研究结果有助于金属磁记忆检测机理的研究. 关键词： 金属磁记忆 第一性原理 漏磁信号     

基于比例积分控制原理预测钻井全过程原始地层温度的新方法研究

应用比例积分控制原理将瞬态传热模型预测结果与出口 温度实测数据逐步进行反馈可准确预测原始静态地层温度. 为此, 本文基于井下各控制组件质量、动量及能量守恒原理, 建立了实际井身结构与钻具组合条件下循环和停止循环期间井筒-地层温度分布全瞬态传热模型, 应用全隐式有限差分法进行求解, 并引入比例积分控制原理对比分析实测温度与预测温度的误差范围进而精确、 快速获取原始地层温度. 结合一口深井基础数据计算表明, 套管下入深度改变了井筒-地层间热交换效率, 进而影响了近井壁地层温度分布状况; 同时, 钻井过程中循环和停止循环作业过程改变了井下各控制组件的初始条件与边界条件, 致使近井壁原始地层温度分布距离产生变化. 建立的数学模型和研究方法可为石油钻井、地热井开采及地球深部原始地层温度信息准确、 经济、快速获取提供理论基础. 关键词： 原始地层温度 循环与停止循环 瞬态传热模型 比例积分控制原理     

大型回热换热器的降温实验

大型低温配件的降温试验复杂和多变,文中针对大型回热换热器的降温进行了研究。将回热换热器置于特制的冷箱内,利用液氮作为冷源,氦气做为载冷剂为换热器提供降温条件;隔膜压缩机为循环氦气提供循环压力。试验前将换热器上面布置9支传感器,传感器所采集的数据自动记录并保存在上位机内,同时绘制降温曲线,为大型回热换热器的降温研究提供了数据。     

Smectic A-Nematic and Nematic-Isotropic Liquid Transitions in 8CB Liquid Crystal: Comparative Analysis

A differential heat flux calorimeter has been used to study the Smectic A-Nematic and Nematic-Isotropic Liquid transitions in 8CB liquid crystal. The Faktor and Hanks model under our working conditions enables us to distinguish first-order from second-order transitions by analysis of differential signal. The critical exponent values obtained justify the proportionality between Cp evolution and the normalized differential signal (differential signal divided by the scanning rate).