Efficient shock capturing for isentropic flows using arithmetic averaging

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.

An analysis of arithmetic averaging in approximate Riemann solvers with an application to steady, supercritical flows

An analysis of various arithmetic averaging procedures for approximate Riemann solvers is made with a specific emphasis on efficiency and a jump capturing property. The various alternatives discussed are intended for future work, as well as the more immediate problem of steady, supercritical free-surface flows. Numerical results are shown for two test problems.

An efficient numerical method for compressible flows of a real gas using arithmetic averaging

An efficient numerical method is presented for the solution of the Euler equations governing the compressible flow of a real gas. The scheme is based on the approximate solution of a specially constructed set of linearised Riemann problems. An average of the flow variables across the interface between cells is required, and this is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual square root averaging. The scheme is applied to a test problem for five different equations of state.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Self-assembly of a designed amyloid peptide containing the functional thienylalanine unit

The self-assembly of a peptide based on a sequence from the amyloid beta peptide but incorporating the non-natural amino acid beta-2-thienylalanine (2-Thi) has been investigated in aqueous and methanol solutions. The peptide AAKLVFF was used as a design motif, replacing the phenylalanine residues (F) with 2-Thi units to yield (2-Thi)(2-Thi)VLKAA. The 2-Thi residues are expected to confer interesting electronic properties due to charge delocalization and pi-stacking. The peptide is shown to form beta-sheet-rich amyloid fibrils with a twisted morphology, in both water and methanol solutions at sufficiently high concentration. The formation of a self-assembling hydrogel is observed at high concentration. Detailed molecular modeling using molecular dynamics methods was performed using NOE constraints provided by 2D-NMR experiments. The conformational and charge properties of 2-Thi were modeled using quantum mechanical methods, and found to be similar to those previously reported for the beta-3-thienylalanine analogue. The molecular dynamics simulations reveal well-defined folded structures (turn-like) in dilute aqueous solution, driven by self-assembly of the hydrophobic aromatic units, with charged lysine groups exposed to water.

Perspex machine X: software development

The Perspex Machine arose from the unification of computation with geometry. We now report significant redevelopment of both a partial C compiler that generates perspex programs and of a Graphical User Interface (GUI). The compiler is constructed with standard compiler-generator tools and produces both an explicit parse tree for C and an Abstract Syntax Tree (AST) that is better suited to code generation. The GUI uses a hash table and a simpler software architecture to achieve an order of magnitude speed up in processing and, consequently, an order of magnitude increase in the number of perspexes that can be manipulated in real time (now 6,000). Two perspex-machine simulators are provided, one using trans-floating-point arithmetic and the other using transrational arithmetic. All of the software described here is available on the world wide web. The compiler generates code in the neural model of the perspex. At each branch point it uses a jumper to return control to the main fibre. This has the effect of pruning out an exponentially increasing number of branching fibres, thereby greatly increasing the efficiency of perspex programs as measured by the number of neurons required to implement an algorithm. The jumpers are placed at unit distance from the main fibre and form a geometrical structure analogous to a myelin sheath in a biological neuron. Both the perspex jumper-sheath and the biological myelin-sheath share the computational function of preventing cross-over of signals to neurons that lie close to an axon. This is an example of convergence driven by similar geometrical and computational constraints in perspex and biological neurons.

Unit-cell approximation for diblock−copolymer brushes grafted to spherical particles

This paper examines the equilibrium phase behavior of thin diblock-copolymer films tethered to a spherical core, using numerical self-consistent field theory (SCFT). The computational cost of the calculation is greatly reduced by implementing the unit-cell approximation (UCA) routinely used in the study of bulk systems. This provides a tremendous reduction in computational time, permitting us to map out the phase behavior more extensively and allowing us to consider far larger particles. The main consequence of the UCA is that it omits packing frustration, but evidently the effect is minor for large particles. On the other hand, when the particles are small, the UCA calculation can be readily followed up with the full SCFT, the comparison to which conveniently allows one to quantitatively assess the effect of packing frustration.

The automatic layout model in the sequencing of construction activities of multi-objective diaphragm wall unit by using self-learning neural network

Foundation construction process has been an important key point in a successful construction engineering. The frequency of using diaphragm wall construction method among many deep excavation construction methods in Taiwan is the highest in the world. The traditional view of managing diaphragm wall unit in the sequencing of construction activities is to establish each phase of the sequencing of construction activities by heuristics. However, it conflicts final phase of engineering construction with unit construction and effects planning construction time. In order to avoid this kind of situation, we use management of science in the study of diaphragm wall unit construction to formulate multi-objective combinational optimization problem. Because the characteristic (belong to NP-Complete problem) of problem mathematic model is multi-objective and combining explosive, it is advised that using the 2-type Self-Learning Neural Network (SLNN) to solve the N=12, 24, 36 of diaphragm wall unit in the sequencing of construction activities program problem. In order to compare the liability of the results, this study will use random researching method in comparison with the SLNN. It is found that the testing result of SLNN is superior to random researching method in whether solution-quality or Solving-efficiency.