Variational piecewise constant level set methods for shape optimization of a two-density drum

We apply the piecewise constant level set method to a class of eigenvalue related two-phase shape optimization problems. Based on the augmented Lagrangian method and the Lagrange multiplier approach, we propose three effective variational methods for the constrained optimization problem. The corresponding gradient-type algorithms are detailed. The first Uzawa-type algorithm having applied to shape optimization in the literature is proven to be effective for our model, but it lacks stability and accuracy in satisfying the geometry constraint during the iteration. The two other novel algorithms we propose can overcome this limitation and satisfy the geometry constraint very accurately at each iteration. Moreover, they are both highly initial independent and more robust than the first algorithm. Without penalty parameters, the last projection Lagrangian algorithm has less severe restriction on the time step than the first two algorithms. Numerical results for various instances are presented and compared with those obtained by level set methods. The comparisons show effectiveness, efficiency and robustness of our methods. We expect our promising algorithms to be applied to other shape optimization and multiphase problems.     

On the existence of thermodynamics for the generalized random energy model

Derrida's generalized random energy model is considered. Almost sure andL ^p convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn is discussed.     

Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model

Using a recently developed multiscale simulation methodology, we describe the equilibrium behaviour of bilayer membranes under the influence of curvature-inducing proteins using a linearized elastic free energy model. In particular, we describe how the cooperativity associated with a multitude of protein–membrane interactions and protein diffusion on a membrane-mediated energy landscape elicits emergent behaviour in the membrane phase. Based on our model simulations, we predict that, depending on the density of membrane-bound proteins and the degree to which a single protein molecule can induce intrinsic mean curvature in the membrane, a range of membrane phase behaviour can be observed including two different modes of vesicle-bud nucleation and repressed membrane undulations. A state diagram as a function of experimentally tunable parameters to classify the underlying states is proposed.     

Study and optimization of the ultrasound-enhanced cleaning of an ultrafiltration ceramic membrane through a combined experimental–statistical approach

Membrane fouling is one of the main drawbacks of ultrafiltration technology during the treatment of dye-containing effluents. Therefore, the optimization of the membrane cleaning procedure is essential to improve the overall efficiency. In this work, a study of the factors affecting the ultrasound-assisted cleaning of an ultrafiltration ceramic membrane fouled by dye particles was carried out. The effect of transmembrane pressure (0.5, 1.5, 2.5 bar), cross-flow velocity (1, 2, 3 m s⁻¹), ultrasound power level (40%, 70%, 100%) and ultrasound frequency mode (37, 80 kHz and mixed wave) on the cleaning efficiency was evaluated. The lowest frequency showed better results, although the best cleaning performance was obtained using the mixed wave mode.A Box–Behnken Design was used to find the optimal conditions for the cleaning procedure through a response surface study. The optimal operating conditions leading to the maximum cleaning efficiency predicted (32.19%) were found to be 1.1 bar, 3 m s⁻¹ and 100% of power level.Finally, the optimized response was compared to the efficiency of a chemical cleaning with NaOH solution, with and without the use of ultrasound. By using NaOH, cleaning efficiency nearly triples, and it improves up to 25% by adding ultrasound.     

Experimental design to measure the anchoring energy on substrate surface by using the alternating-current bridge

The anchoring property of the substrate surface of liquid crystal cells plays an important role in display and nondisplay fields. This property directly affects the deformation of liquid crystal molecules to change the phase difference through liquid crystal cells. In this paper, a test method based on the alternating-current bridge is proposed to determine the capacitance of liquid crystal cells and thus measure the anchoring energy of the substrate surface. The anchoring energy can be obtained by comparing the capacitance–voltage curves of twisted nematic liquid crystal cells with different anchoring properties in experimental and theoretical results simulated on the basis of Frank elastic theory. Compared with the other methods to determine the anchoring energy, our proposed method requires a simple treatment of liquid crystal cells and allows easy and high-accuracy measurements, thereby expanding the test ideas on the performance parameters of liquid crystal devices.     

线性三原子分子转动-振动能谱的李群处理方法

本文利用李代数方法与二次量子化理论计算了线性三原子分子的转动-振动能谱.结果表明,如果将分子的转动与振动均看作是谐振子,则可以导致这种分子的转动-振动能谱公式.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Exact solution of the Klein‐Gordon equation for the PT‐symmetric generalized Woods‐Saxon potential by the Nikiforov‐Uvarov method

The exact solution of the one‐dimensional Klein‐Gordon equation of the ????‐symmetric generalized Woods‐Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s‐states are also investigated for different types of complex generalized Woods‐Saxon potentials.     

利用Gupta势结合遗传算法研究ConCu55－n(n=0—55)混合团簇的结构演化及基态能量

采用半经验的Gupta多体势结合遗传算法对Co_nCu_55－n(n=0—55)混合团簇的基态结构和能量进行了研究,发现这些混合团簇的基态结构是在Co₅₅,Cu₅₅单质团簇(Mackay二十面体)的基础之上发生的畸变;从n=0(Cu₅₅)开始,Co原子从中心到表面,从棱到顶点依次、连续替换Cu原子;基态结构与键能较大键的数目及其平均键长有关;Co₁₃Cu₄₂具有最稳定的结构,13个Co原子全部位于团簇内部形成Mackay二十面体对整个团簇的稳定性有显著影响. 关键词： 团簇 结构和能量 Gupta势 遗传算法