Bending of rectangular plates subject to non-uniform pressure distributions relevant to containment structures

Rectangular planform silos are often used where there is need for simple construction or space restrictions. The flexibility of the flat plate walls leads to a horizontal variation in wall pressure across each wall, with much reduced pressures at the mid‐side. There is a clear and systematic relationship between the wall flexural stiffness relative to the stiffness of the stored solid and the pressure pattern on the wall which is now well proven. Since the centre of each wall is subject to significantly reduced pressures, it may be expected that the bending moments in the wall will much lower, permitting the use of a thinner wall. In turn, the thinner wall is then more flexible and leads to a further redistribution of the pressures. This paper is the first to examine the structural consequences of these pressure changes. The horizontal variation of the wall pressure is well captured by a hyperbolic form, with much reduced mid‐side pressures and raised corner pressures, characterised by a single parameter “alpha” that determines the strength of this redistribution. This parameter α is naturally dependent on the relative wall and solid stiffness. In this study, the value of α is varied between the uniform pressure condition α = 0 and a high value (α=3). The highest values occur when a stiff solid is stored in a silo with very flexible walls. Wall plates of different aspect ratio are investigated representing conditions in a square or rectangular silo. The finite element predictions show that great savings can be made in the design of these structures by exploiting the reduced deflections and reduced stresses that arise when realistic patterns of pressure are adopted. The results presented here are suitable for transformation into design rules for the Eurocode standards EN 1993‐1‐7 [1] and EN 1993‐4‐1 [2]

Equilibrium states in open quantum systems

The aim of the paper is to study the question whether or not equilibrium states exist in open quantum systems that are embedded in at least two environments and are described by a non-Hermitian Hamilton operator $\cal H$. The eigenfunctions of $\cal H$ contain the influence of exceptional points (EPs) as well as that of external mixing (EM) of the states via the environment. As a result, equilibrium states exist (far from EPs). They are different from those of the corresponding closed system. Their wavefunctions are orthogonal although the Hamiltonian is non-Hermitian.Comment: 12 page

Exceptional points and double poles of the S matrix

Exceptional points and double poles of the S matrix are both characterized by the coalescence of a pair of eigenvalues. In the first case, the coalescence causes a defect of the Hilbert space. In the second case, this is not so as shown in prevoius papers. Mathematically, the reason for this difference is the bi-orthogonality of the eigenfunctions of a non-Hermitian operator that is ignored in the first case. The consequences for the topological structure of the Hilbert space are studied and compared with existing experimental data.Comment: 9 pages, no figure

Binary Stars in Planetary Nebulae

When a star like the sun dies, it swells into a red giant and then expels its outer layers to form a planetary nebula. Eventually the outer layers leave the leftover core and it becomes a white dwarf. The cause of the many exotic shapes in the planetary nebulae is unknown; however, it is thought that binary stars may play a role in the shaping process. In this project we are studying the central stars of planetary nebulae to see if they vary in brightness, and to see if that variability is due to the central star having a binary companion. Data is collected with the SARA North and SARA South telescopes. We have recently found the central star of the planetary nebula PN G337.0+08.4 to vary with a period of 0.2959 days (7.102 hours). We have data for this object in green (V), red (R), and blue (B) filters. The data strongly indicates that the central star does have a binary companion. Using a binary star modeling program we have found several possible sets of physical parameters for the binary central star of the planetary nebula PN G337.0+08.4