Hexagonal Mesh Research Articles

Neutron Spectrum Calculation Code HARPY for Hexagonal Assembly.

Abstract Hexagonal assemblies are used in a high conversion light water reactor (HCLVVR) and a nuclear reactor for cancer therapy. A cross section generation code for hexagonal assemblies is needed to design these cores precisely. For this purpose, a two-dimensional spectrum calculation code HARPY which can treat a hexagonal assembly has been developed. The HARPY code consists of a nodal code for pin-cell coupling in hexagonal geometry and a hexagonal mesh SN transport code and calculates detailed neutron spectra of fuel cells in the assembly. Verification calculations have been performed on a small hexagonal assembly by using SRAC and a Monte Carlo code GMVP to check the calculational accuracy of HARPY. The comparisons of k ∞'s, rod worths and pin power distributions have shown good agreement. This shows the adequacy of HARPY calculation.

The adsorption and desorption of CdI2 on InSb(001): observation of an epitaxial orientational relationship

A LEED, AES and ARUPS study has been made of CdI2 adsorbed on the clean In-rich InSb(001) c(8*2) reconstructed surface at room temperature. A chemisorbed p(2*1) structure formed which consisted of a double layer of iodine atoms with cadmium atoms between them. It is suggested that this surface consists of linear I-Cd-I molecules aligned perpendicularly to the surface. Continued adsorption caused growth of an orientational relationship epitaxial layer of CdI2. The epitaxial layer had the basal plane of the layered CdI2 material parallel to the InSb(001) surface, with the hexagonal mesh of the CdI2 at an angle of approximately=7 degrees to the square net of the substrate. On heating to approximately=400 K the epitaxial layer desorbed leaving a p(2*1) structure identical to that formed during adsorption. The p(2*1) was stable to 433 K beyond which further loss of Cd and I caused a change to a (1*1) structure. This structure is thought to consist of a (1*1) monolayer of iodine with Cd below the iodine layer, possibly incorporated into the substrate. Heating to 500 K caused complete loss of iodine and cadmium from the surface and the formation of a clean, Sb-rich surface.

Delivery of time-critical messages using a multiple copy approach

Reliable and timely delivery of messages between processing nodes is essential in distributed real-time systems. Failure to deliver a message within its deadline usually forces the system to undertake a recovery action, which introduces some cost (or overhead) to the system. This recovery cost can be very high, especially when the recovery action fails due to lack of time or resources. Proposed in this paper is a scheme to minimize the expected cost incurred as a result of messages failing to meet their deadlines. The scheme is intended for distributed real-time systems, especially with a point-to-point interconnection topology. The goal of minimizing the expected cost is achieved by sending multiple copies of a message through disjoint routes and thus increasing the probability of successful message delivery within the deadline. However, as the number of copies increases, the message traffic on the network increases, thereby increasing the delivery time for each of the copies. There is therefore a tradeoff between the number of copies of each message and the expected cost incurred as a result of messages missing their deadlines. The number of copies of each message to be sent is determined by optimizing this tradeoff. Simulation results for a hexagonal mesh and a hypercube topology indicate that the expected cost can be lowered substantially by the proposed scheme.

Mayfly: A general-purpose, scalable, parallel processing architecture

TheMayfly is a scalable general-purpose parallel processing system being designed at HP Laboratories, in collaboration with colleagues at the University of Utah. The system is intended to efficiently support parallel variants of modern programming languages such as Lisp, Prolog, and Object Oriented Programming models. These languages impose a common requirement on the hardware platform to supportdynamic system needs such as runtime type checking and dynamic storage management. The main programming language for the Mayfly is a concurrent dialect of Scheme. The system is based on a distributed-memory model, and communication between processing elements is supported by message passing. The initial prototype of Mayfly will consist of 19 identical processing elements interconnected in a hexagonal mesh structure. In order to achieve the goal of scalable performance, each processing element is a parallel processor as well, which permits the application code, runtime operating system, and communication to all run in parallel. A 7 processing element subset of the prototype is presently operational. This paper describes the hardware architecture after a brief background synopsis of the software system structure.

Traffic routing for multicomputer networks with virtual cut-through capability

The problem of selecting routes for interprocess communication in a network with virtual cut-through capability while balancing the network load and minimizing the number of times that a message gets buffered is addressed. The approach taken is to formulate the route selection problem as a minimization problem, with a link cost function that depends upon the traffic through the link. The form of this cost function is derived based on the probability of establishing a virtual cut-through route. It is shown that this route selection problem is NP-hard, and an approximate algorithm is developed which tries to incrementally reduce the cost by rerouting traffic. The performance of this algorithm is evaluated for the hypercube and the C-wrapped hexagonal mesh, example networks for which virtual cut-through switching support has been developed. >

Investigations of the small-scale flat field response of microchannel plate detectors in the far and extreme ultraviolet

High signal-to-noise flat field images taken in the extreme and far ultraviolet with photon-counting microchannel plate (MCP) detectors are presented. Small spatial scale (<1 mm) modulations of the flat field, in particular the hexagonal mesh pattern and dead spots, are discussed. It is shown that the hexagonal modulation at the multifiber bundle boundaries of the MCPs is due to a differential nonlinearity in the mapping of input photon position to readout pixel and is caused by the rear plates of the MCP stack. Possible mechanisms for the nonlinearity, including hexagonal gain variations, are presented.

Performance analysis of virtual cut-through switching in HARTS: a hexagonal mesh multicomputer

The authors present a formal analysis of virtual cut-through in a C-wrapped hexagonal mesh multicomputer, called the HARTS (hexagonal architecture for real-time systems). In virtual cut-through, packets arriving at an intermediate node are forwarded to the next node in the route without buffering if a circuit can be established to the next node. The hexagonal mesh is first characterized using a combinatorial analysis to determine the probability that a packet will establish a cut-through at an intermediate node. Given this parameter the probability distribution function for packet delivery times in HARTS is derived. The delivery times obtained from the analytic model are then compared against results collected from a simulator of the routing hardware designed for use in HARTS. The results from both the analytic model and the simulator further reinforce the choice of the virtual cut-through routing scheme for use in HARTS. >

HARTS: a distributed real-time architecture

The design, implementation, and evaluation of a distributed real-time architecture called HARTS (hexagonal architecture for real-time systems) are discussed, emphasizing its support of time-constrained, fault-tolerant communications and I/O (input/output) requirements. HARTS consists of shared-memory multiprocessor nodes, interconnected by a wrapped hexagonal mesh. This architecture is intended to meet three main requirements of real-time computing: high performance, high reliability, and extensive I/O. The high-level and low-level architecture is described. The evaluation of HARTS, using modeling and simulation with actual parameters derived from its implementation, is reported. Fault-tolerant routing, clock synchronization and the I/O architecture are examined. >

Segregation of some mesh-derived textures evaluated by free viewing

Beginning with a hexagonal mesh, a family of equiluminous geometric textures can be formed by rotating each line segment by a fixed amount. Such textures vary both in line orientation and in the sizes of the intervening spaces or “holes”. In the Fourier domain the textures have the same discrete two-dimensional frequency components but the amplitudes vary. The segregation of texture pairs as figures in grounds has been assessed for free viewing by the ratings of 10 subjects. Line segment orientation information alone cannot explain the results. Linear regression techniques were used to examine the correlation between the subjects' ratings and physical differences between figures and grounds. Significant correlations were found with (a) the amplitudes of the low-frequency Fourier harmonics of the textures and (b) maximum hole size, but not with the third harmonics or line segment orientation. Patterns composed of mirror-image pairs are very poorly discriminated; in these cases line orientation information may be used.

A distributed I/O architecture for HARTS

The issue of I/O device access in HARTS — a distributed real-time computer system under construction at the Real-Time Computing Laboratory (RTCL), The University of Michigan — is explicitly addressed. Several candidate solutions are introduced, explored, and evaluated according to cost and complexity, reliability, and performance: (1) “node-direct” distribution with the intra-node bus and a local I/O bus, (2) use of dedicated I/O nodes which are placed in the hexagonal mesh as regular applications nodes but which provide I/O services rather than computing services, and (3) use of a separate I/O network which has led to the proposal of an “interlaced” I/O network. The interlaced I/O network is intended to provide both high performance without burdening node processors with I/O overhead as well as a high degree of reliability. Both static and dynamic multi-ownership protocols are developed for managing I/O device access in this I/O network. The relative merits of the two protocols are explored and the performance and accessibility which each provide are simulated.

The structure of ammonia overlayers physisorbed onto the surface of single crystal graphite, determined by means of atomic beam diffraction

The structure of NH3 monolayers and submonolayers physisorbed on graphite C(0001) has been determined by means of low energy helium atom beam diffraction experiments. The measured diffraction pattern is found to consist of diffraction ‘‘rings,’’ indicating a large degree of orientational disorder among the adsorbed domains. We observe up to fourth order diffraction and periodicities which can be generated from a rectangular 3.53×6.11 Å unit cell or by a 7.06×7.06 Å hexagonal mesh. Both of these possibilities are characteristic of a 3.53 Å nearest neighbor separation. These findings suggest that, because of the relatively strong molecule–molecule interactions, the degree of order within a given domain is relatively high, while the domain’s orientational disorder may be due to the insensitivity of the adlayer to the corrugation and anisotropy of the graphite substrate. This behavior is atypical, since HCl, CH3F, CH3Cl, and CH3Br all form well organized monolayers which have a single well defined orientation with respect to the graphite substrate.

Addressing, routing, and broadcasting in hexagonal mesh multiprocessors

A family of six-regular graphs, called hexagonal meshes or H-meshes, is considered as a multiprocessor interconnection network. Processing nodes on the periphery of an H-mesh are first wrapped around to achieve regularity and homogeneity. The diameter of a wrapped H-mesh is shown to be of O(p/sup 1/2/), where p is the number of nodes in the H-mesh. An elegant, distributed routing scheme is developed for wrapped H-meshes so that each node in an H-mesh can compute shortest paths from itself to any other node with a straightforward algorithm of O(1) using the addresses of the source-destination pair only, i.e. independent of the network's size. This is in sharp contrast with those previously known algorithms that rely on using routing tables. Furthermore, the authors also develop an efficient point-to-point broadcasting algorithm for the H-meshes which is proved to be optimal in the number of required communication steps. The wrapped H-meshes are compared against some other existing multiprocessor interconnection networks, such as hypercubes, trees, and square meshes. The comparison reinforces the attractiveness of the H-mesh architecture.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A hexagonal array machine for multilayer wire routing

A novel hardware accelerator comprised of several fast processors interconnected in the form of a hexagonal mesh with wraparound connections is proposed. The novelty of the proposed architecture stems from the fact that it is suitable not only for single-layer routing, but also for routing in parallel on multiple layers. A hexagonal machine of dimension square root kG, with about 3kG processors, can handle a k-layer grid consisting of kG/sup 2/ grid points at about the same speed as a full-grid machine with kG/sup 2/ processors. A technique for measuring the performance of a hardware accelerator in terms of the average delay incurred over a full-grid machine is suggested. This has been formalized in the case of the hexagonal architecture, and is presented for various nets and mesh dimensions. The results have been accurately verified by extensive simulation done in C++ language. It is demonstrated that the hexagonal mesh, by virtue of its additional links for expansion, is resilient to about 10% of failure in the links and processing elements. A detailed design for a chip implementation of the hexagonal machine is discussed. >

Hex–square moire patterns in imagers using microchannel plates

In electronic imaging detectors using microchannel plates, the mismatch between the pixels on a square mesh and the microchannels on a hexagonal mesh produces moire image defects. Theoretical statistical estimates of the sizes of the microposition offsets and the flat field intensity errors are calculated, showing the trade-off between resolution and position accuracy. A distinction is made between moments of spot images and moments of the single pixel response functions. As the resolution between the hex and square meshes is improved, the detector resolution is improved but at the expense of an ~10% moire pattern. These moire patterns will not be properly corrected by dividing by the flat field image.

High-coverage surface phases of tellurium on Ni(111)

The complex surface phases formed when tellurium is adsorbed to high coverage (&amp;gt;0.4 monolayer) on Ni(111) have been studied using a mirror electron microscope–low-energy electron diffraction apparatus and Auger electron spectroscopy. The unit meshes of the complex overlayer structures all have one side along the [1,−1] surface direction with length equal to the Te–Te nearest-neighbor spacing in the (√3×√3)R30 structure and one side along the [11] direction with lengths of 10, 11, 13, 14, and 16 Ni–Ni nearest-neighbor spacings. These one-dimensional coincidence meshes can be described in terms of ordered dislocation structures in a compressed hexagonal Te unit mesh. Two intermediate phases with unequal diffraction beam spacings are also observed and transform with a small hysteresis into phases with equal spot spacings.

Films formed on well-defined stainless steel single-crystal surfaces in oxygen and water: studies of the (111) plane by LEED, Auger and XPS

Reported here are studies by LEED, Auger and X-ray photo-electron spectroscopy of the (111) plane of a face-centered cubic Fe-Cr-Ni alloy single-crystal of composition (70 at% Fe, 18 at% Cr, 12 at% Ni) resembling type 304 stainless steel. Surface films resulting from treatment with O 2, water vapor or liquid water at ambient temperature or with annealing were characterized. A disordered oxygen-containing layer was formed at ambient temperature. When formed from water, the layer contained oxide and undissociated water. Some of the water was co-ordinated and the remainder hydrogen bonded within the film. Annealing, or formation of the film at temperatures above 1000 K, produced an ordered oxide film consisting primarily of chromium oxides in the form of hexagonal meshes of Cr 2O 3(001), square meshes of CrO and an antiphase-domain adlattice of chemisorbed oxygen.

Approximation order from bivariate 𝐶¹-cubics: a counterexample

It is shown that the space of bivariate C 1 {C^1} piecewise cubic functions on a hexagonal mesh of size h h approximates to certain smooth functions only to within O ( h 3 ) O({h^3}) even though it contains a local partition of every cubic polynomial.

The hexagon theorem

We wish to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\int_{S}|Z-f(Z)|^{2},S</tex> the unit square, over all choices of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(Z)</tex> which take just n values. For large n it is shown that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(Z)</tex> approaches that function which on each face of a "hexagonal mesh" has the value of the centroid of that face. This problem in the design of quantizers for a pulse-code modulation (PCM) system arose in which pairs of adjacent samples are quantized in an effort to capitalize on the correlation between samples and on the geometry of the plane.

Data Compression of the Kanji Character Patterns Digitized on the Hexagonal Mesh

This correspondence describes new two-stage data compression algorithms of Kanji character patterns digitized on the hexagonal mesh. One third of the pattern elements are stored, and an additional small amount of data is used to correct effors in the recovered pattern. A data reduction of 60 percent has been achieved.

Bridal Veil Nylon

Commercially available bridal veil nylon (BVN) in 2.0-3,0-, and 4.0-mm hexagonal mesh is being used as a sterile dressing for burns and many surgical problems. BVN appears to promote more rapid reepithelialization of granulating burn wounds than other dressings. I suggest that the BVN mesh provides a "trellis effect", acting as a supporting structure across which, or over which, epithelium will grow more rapidly than it would without the dressing. Photographic studies illustrating this effect are included. BVN also allows us to secure recent skin grafts, and it appears to be an ideal dressing for recent hair plug transfers. It is possible to examine wounds directly and to clean them with whatever technique is indicated, including hydrotherapy and Hubbard tank regimen, and yet not to disrupt underlying structures such as skin grafts and hair plugs. A major advantage of this dressing is that it minimizes painful removal of Kling and Kurlex type dressings. Photographs demonstrate the use of BVN, which is quite inexpensive and can be gas-autoclaved in any hospital facility.