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81.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
82.
Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering
a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms.
The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions
of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible
magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body
(of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface
is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses
the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide
local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest
models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest
problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals,
and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science,
fracture, physical chemistry, and low-temperature physics. 相似文献
83.
In squeeze flow rheometry, the main problem is the boundary condition between the squeezed material and the plates. Therefore, the crucial assumption is to know the location and the shape of the sample part where wall slip may or may not occur. This question is investigated from experimental results. For this, squeeze flow experiments are carried out to visualize the flow pattern at the walls. Influence of boundary conditions is particularly studied using different plate surface condition. As a result, with wall slipping conditions, we propose a flow modelling divided into two zones: a circular central zone of the sample sticks on the plates and, beyond that zone, the sample slips at the plates with friction. 相似文献
84.
不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。 相似文献
85.
讨论了关节柔性且系统参数不确定的漂浮基空间机器人系统的动力学建模过程、运动轨迹跟踪控制算法设计及系统柔性振动的主动抑制问题。利用系统动量、动量矩守恒关系和拉格朗日法对系统动力学进行分析,并建立系统动力学方程。基于奇异摄动法将系统分解为表示系统刚性运动部分的慢变子系统和表示系统柔性运动部分的快变子系统。针对慢变子系统提出了一种自适应滑模控制算法。该控制算法是由基于滑模面的等效控制项、自适应控制项和PID反馈控制项组成。因此,它集合了滑模控制、自适应算法和PID技术的优点,且弥补了三种算法各自的缺点。该控制算法能够有效地补偿系统的转动误差和不确定参数,提高控制系统的精度。针对快变子系统,提出基于速度差值的反馈控制算法来抑制柔性关节引起的系统柔性振动,保证系统的稳定性。最后,通过仿真实验证明了提出的混合控制算法的有效性。 相似文献
86.
We present an exact timestepping method for Brownian motion that does not require Gaussian random variables to be generated. Time is incremented in steps that are exponentially-distributed random variables; boundaries can be explicitly accounted for at each timestep. The method is illustrated by numerical solution of a system of diffusing particles. 相似文献
87.
Hacer Guzlek Ines I.R. Baptista Philip L. Wood Andrew Livingston 《Journal of chromatography. A》2010,1217(40):6230-6240
Literature lists a number of counter-current chromatography (CCC) models that can predict the retention time and to a certain extent the peak width of a solute eluting from a CCC column. The approach described in this paper distinguishes itself from previous reports by relating all model parameters directly to column dimensions and experimental settings. Most importantly, this model can predict a chromatogram from scratch without resorting to traditional calibration using empirical values. The model validation with experimental results obtained across a range of CCC instruments demonstrated that the solute retention time, peak width, and peak resolution could be predicted within reasonable accuracy. Additionally, the effect of several process parameters, such as mobile phase flow rate, rotational speed of the column or β-value, showed that the model is robust and applicable to a wide range of CCC instruments. Overall, this model proved to be a useful tool for parameter estimation and, most significantly, separation optimisation. 相似文献
88.
H. Frahm C. Rödenbeck 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(3):409-414
We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic
field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a
single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the
low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases
of spin ladder systems away from the soluble line in a magnetic field.
Received 17 November 1998 and Received in final form 22
January 1999 相似文献
89.
We give necessary and sufficient conditions for the almost sure relative stability of the overshoot of a random walk when
it exits from a two-sided symmetric region with curved boundaries. The boundaries are of power-law type, ±rn
b
, r > 0, n = 1, 2,..., where 0 ≤ b < 1, b≠ 1/2. In these cases, the a.s. stability occurs if and only if the mean step length of the random walk is finite and non-zero,
or the step length has a finite variance and mean zero.
相似文献
90.
Jean-Francois Bisson Hideki Yagi Takakimi Yanagitani Alexander Kaminskii Yuri N. Barabanenkov Ken-Ichi Ueda 《Optical Review》2007,14(1):1-13
Grain boundaries play a key role in determining several key properties of polycrystalline laser ceramics. Heat transfer measurements
at low temperature constitute a good tool to probe grain boundaries. We review the results of heat transfer measurements in
polycrystalline Y3Al5O12 garnets as well as Y2O3 and Lu2O3 sesquioxide materials obtained by self-energy-driven sintering of nano-particles. The average phonon mean free path in Y3Al5O12 was found to be significantly larger than the average grain size and to scale with temperature as T
−2 at low temperature. Existing models describing the interaction between phonons and grain boundaries are reviewed. Correct
temperature dependence of the mean free path and order of magnitude of scattering rates were found by assuming the existence
of a grain boundary layer having acoustic properties different from those of the bulk. A different temperature dependence
of phonon mean free path was found for the sesquioxides and was ascribed to the stronger elastic anisotropy of these materials.
The thermal resistance associated to the grain boundaries of laser ceramics was found to be lower than in other dense polycrystalline
ceramic materials reported in the literature. 相似文献