1. Liquid–Liquid Phase Transitions Consider a fluid confined into a container Ω ⊂ R . Assume that the total mass of the fluid is m, so that admissible density distributions u : Ω→ R satisfy the constraint ∫ Ω u(x) dx = m. The total energy is given by the functional u 7→ ∫ Ω W (u(x)) dx, where W : R→ [0,∞) is the energy per unit volume. Assume that W supports two phases a < b, that is, W is a do...

Department of Mechanical Engineering, The Hong Kong Polytechnic University Hung Home, Kowloon, Hong Kong, SAR of China Email address: [email protected]. Abstract This paper examines the influence of the internal resistance of a Helmholtz resonator on the noise control in a small enclosure. The absorptive process mainly occurring within the neck of a Helmholtz resonator provides the resonator w...

in the present study, mixed convection laminar flow around an adiabatic body in a lid-driven enclosure filled with nanofluid using variable thermal conductivity and variable viscosity is numerically investigated. the fluid around the body in the enclosure is a water-based nanofluid containing al2o3 nanoparticles. the vertical enclosure’s walls are maintained at constant cold temperature and the...

We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in L2(R2) with an attractive interaction supported on a closed curve Γ, formally given by −∆ − αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread Γ in R3, homogeneously charged but not conducting, and we ask a...

The portable generators are the main means of compensating the shortage of national electricity power as in Iraq. However, their noise causes a huge disturbance, uncomforting and loss of concentration of the nearby resident. This problem requires a solution because most shops and residential houses use generators. Covering method is a simple and relatively low cost one for reduction of generato...

We present the first of two articles on the small volume fraction limit of a nonlocal Cahn–Hilliard functional introduced to model microphase separation of diblock copolymers. Here we focus attention on the sharp-interface version of the functional and consider a limit in which the volume fraction tends to zero but the number of minority phases (called particles) remains O(1). Using the languag...

We study, by means of Γ-convergence, the asymptotic behaviour of a variational problem modeling a dislocation ensemble moving on a slip plane through a discrete array of obstacles. The variational problem is a two dimensional phase transition type energy given by a non local term and a non linear potential which penalizes non integer values. In this paper we consider a regime corresponding to a...

Three enclosures (10 x 10 x 1.5-1.3 m in depth) were set beside Dianch Lake, Kunming, People's Republic of China, for the period from July 28 to August 26, 2002. The enclosures were filled with cyanobacterial (Microcystis aeruginosa) water bloom-containing lake water. Lake sediment that contained macrophytes and water chestnut seeds was spread over the entire bottom of each enclosure. Initially...

This note completely resolves the asymptotic development of order 2 by Γ-convergence of the mass-constrained Cahn–Hilliard functional, by showing that one of the critical assumptions of the authors’ previous work [10] is unnecessary.