Nonexistence of Certain Skew-symmetric Amorphous Association Schemes

An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.Comment: 10 page

Amorphous procedure extraction

The procedure extraction problem is concerned with the meaning preserving formation of a procedure from a (not necessarily contiguous) selected set of statements. Previous approaches to the problem have used dependence analysis to identify the non-selected statements which must be 'promoted' (also selected) in order to preserve semantics. All previous approaches to the problem have been syntax preserving. This work shows that by allowing transformation of the program's syntax it is possible to extract both procedures and functions in an amorphous manner. That is, although the amorphous extraction process is meaning preserving it is not necessarily syntax preserving. The amorphous approach is advantageous in a variety of situations. These include when it is desirable to avoid promotion, when a value-returning function is to be extracted from a scattered set of assignments to a variable, and when side effects are present in the program from which the procedure is to be extracted

Theory of amorphous ices

We derive a phase diagram for amorphous solids and liquid supercooled water and explain why the amorphous solids of water exist in several different forms. Application of large-deviation theory allows us to prepare such phases in computer simulations. Along with nonequilibrium transitions between the ergodic liquid and two distinct amorphous solids, we establish coexistence between these two amorphous solids. The phase diagram we predict includes a nonequilibrium triple point where two amorphous phases and the liquid coexist. While the amorphous solids are long-lived and slowly-aging glasses, their melting can lead quickly to the formation of crystalline ice. Further, melting of the higher density amorphous solid at low pressures takes place in steps, transitioning to the lower density glass before accessing a nonequilibrium liquid from which ice coarsens.Comment: revision following review comment

Amorphous-silicon module hot-spot testing

Hot spot heating occurs when cell short-circuit current is lower than string operating current. Amorphous cell hot spot are tested to develop the techniques required for performing reverse bias testing of amorphous cells. Also, to quantify the response of amorphous cells to reverse biasing. Guidelines are developed from testing for reducing hot spot susceptibility of amorphous modules and to develop a qualification test for hot spot testing of amorphous modules. It is concluded that amorphous cells undergo hot spot heating similarly to crystalline cells. Comparison of results obtained with submodules versus actual modules indicate heating levels lower in actual modules. Module design must address hot spot testing and hot spot qualification test conducted on modules showed no instabilities and minor cell erosion

Low-Temperature Crystallization of Amorphous Silicate in Astrophysical Environments

We construct a theoretical model for low-temperature crystallization of amorphous silicate grains induced by exothermic chemical reactions. As a first step, the model is applied to the annealing experiments, in which the samples are (1) amorphous silicate grains and (2) amorphous silicate grains covered with an amorphous carbon layer. We derive the activation energies of crystallization for amorphous silicate and amorphous carbon from the analysis of the experiments. Furthermore, we apply the model to the experiment of low-temperature crystallization of amorphous silicate core covered with an amorphous carbon layer containing reactive molecules. We clarify the conditions of low-temperature crystallization due to exothermic chemical reactions. Next, we formulate the crystallization conditions so as to be applicable to astrophysical environments. We show that the present crystallization mechanism is characterized by two quantities: the stored energy density Q in a grain and the duration of the chemical reactions \tau . The crystallization conditions are given by Q > Q_{min} and \tau < \tau _{cool} regardless of details of the reactions and grain structure, where \tau _{cool} is the cooling timescale of the grains heated by exothermic reactions, and Q_{min} is minimum stored energy density determined by the activation energy of crystallization. Our results suggest that silicate crystallization occurs in wider astrophysical conditions than hitherto considered.Comment: 9 figures, accepted for publication in Astrophysical

Structure, stability and stress properties of amorphous and nanostructured carbon films

Structural and mechanical properties of amorphous and nanocomposite carbon are investigated using tight-binding molecular dynamics and Monte Carlo simulations. In the case of amorphous carbon, we show that the variation of sp^3 fraction as a function of density is linear over the whole range of possible densities, and that the bulk moduli follow closely the power-law variation suggested by Thorpe. We also review earlier work pertained to the intrinsic stress state of tetrahedral amorphous carbon. In the case of nanocomposites, we show that the diamond inclusions are stable only in dense amorphous tetrahedral matrices. Their hardness is considerably higher than that of pure amorphous carbon films. Fully relaxed diamond nanocomposites possess zero average intrinsic stress.Comment: 10 pages, 6 figure