Random Network Theory Research Articles

Structure and mechanical properties of thin films deposited from 1,3,5-trimethyl-1,3,5-trivinylcyclotrisiloxane and water

Pulsed-plasma chemical vapor deposition of 1,3,5-trimethyl-1,3,5-trivinylcyclotrisiloxane (V3D3) and water produced thin films with significant Si–OH content. Subsequent annealing of the films resulted in condensation of proximal Si–OH groups, further generating a Si–O–Si network and strengthening the film. Fourier-transform infrared spectroscopy analysis showed increasing OH content with increasing plasma duty cycle, and nanoindentation results confirmed increasing hardness with duty cycle, with the 10–40 duty cycle annealed sample having a hardness value of 0.527 GPa. These results were explained within the context of the continuous random network theory and percolation of rigidity arguments. Thermal stability was excellent, with a best-case thickness retention of 99.25% after a 2 h anneal at 400 °C under N2. Dielectric constants for the annealed films ranged between 2.55 and 2.9. The moderate power involved (200 W peak) is amenable to inclusion of a porogen species, opening the possibility of using this methodology to generate a porous thin film with adequate mechanical properties via chemical vapor deposition.

Large deviations and mean-field theory for asymmetric random recurrent neural networks

In this article, we study the asymptotic dynamics of a noisy discrete time neural network, with random asymmetric couplings and thresholds. More precisely, we focus our interest on the limit behaviour of the network when its size grows to infinity with bounded time. In the case of gaussian connection weights, we use the same techniques as Ben Arous and Guionnet (see [3]) to prove that the image law of the distribution of the neurons' activation states by the empirical measure satisfies a temperature free large deviation principle. Moreover, we prove that if the connection weights satisfy a general condition of domination by gaussian tails, then the distribution of the activation potential of each neuron converges weakly towards an explicit gaussian law, the characteristics of which are contained in the mean-field equations stated by Cessac-Doyon-Quoy-Samuelides (see [4–6]). Furthermore, under this hypothesis, we obtain a law of large numbers and a propagation of chaos result. Finally, we show that many classical distributions on the couplings fulfill our general condition. Thus, this paper provides rigorous mean-field results for a large class of neural networks which is currently investigated in neural network literature.

Statistical self-similarity of width function maxima with implications to floods

Recently a new theory of random self-similar river networks, called the RSN model, was introduced to explain empirical observations regarding the scaling properties of distributions of various topologic and geometric variables in natural basins. The RSN model predicts that such variables exhibit statistical simple scaling, when indexed by Horton–Strahler order. The average side tributary structure of RSN networks also exhibits Tokunaga-type self-similarity which is widely observed in nature. We examine the scaling structure of distributions of the maximum of the width function for RSNs for nested, complete Strahler basins by performing ensemble simulations. The maximum of the width function exhibits distributional simple scaling, when indexed by Horton–Strahler order, for both RSNs and natural river networks extracted from digital elevation models (DEMs). We also test a powerlaw relationship between Horton ratios for the maximum of the width function and drainage areas. These results represent first steps in formulating a comprehensive physical statistical theory of floods at multiple space-time scales for RSNs as discrete hierarchical branching structures.

Phase transition and elasticity of protein-based hydrogels

Reported are specific materials characterizations of three protein-based polymers comprised of repeating pentapeptide sequences, namely (GVGVP)251, (GVGIP)260 and (GVGVP GVGVP GEGVP GVGVP GVGVP GVGVP)n](GVGVP) where G = glycine, V = valine, P = proline, I = isoleucine, and E = glutamic acid, which had been previously prepared and γ-irradiation cross-linked into elastic matrices. These polymers exhibit a hydrophobic folding and assembling transition on raising the temperature above a critical temperature, designated by Tt. Their equilibrium swelling ratio, uniaxial tensile and dynamic shear behavior were studied. The effect of the transition on swelling and mechanical properties was demonstrated. Equilibrium swelling ratio below the transition temperature decreased with the increase of γ-irradiation dose. Above the transition temperature, hysteresis and frequency dependence were found in tensile loading-unloading tests and dynamic shear measurements, respectively. The rubber elasticity theory of random chain networks was applied to the data only below the transition temperature, where they may properly be considered random network hydrogels, to estimate molecular weight between cross-links and the Flory-Huggins interaction parameter.

Power-Law Distribution of the World Wide Web

Barabasi and Albert ([1][1]) propose an improved version of the Erdos-Renyi (ER) theory of random networks to account for the scaling properties of a number of systems, including the link structure of the World Wide Web (WWW). The theory they present, however, is inconsistent with empirically

Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.

Effective medium approximation for the conductivity of sensible heat in dry snow

We developed an inductive model for thermal conductivity of sensible heat of deposited snow using random resistance network theory and parametric statistics. The model identifies the geometric quantities that determine this physical property. It allows us to quantitatively link conductivity to natural transformations that are known to change conductivity and increases our ability to test such theories experimentally. We are now able to show how microstructural quantities such as grain size distribution and average coordination number interact with each other to govern conductivity. These results may easily be extended to other porous geological and industrial materials.

A network problem: Modelling alkali-silicate glasses with RMC

Structural models of four potassium-silicate glasses, (K2O)x(SiO2)1-x with x=0, 0.15, 0.25 and 0.45, have been created using the reverse Monte Carlo (RMC) method. The current use of RMC for creating topologically constrained models of amorphous materials is described in detail. The models are based on the simultaneous combination of neutron diffraction and 29Si magic angle spinning NMR data, the latter for the first time. We show that the predictions of Modified Random Network theory are consistent with the data. It is found that models whose topology is determined by short-range chemical bonding constraints and the macroscopic density are able to reproduce all details of the structure factor, including its complex form at low momentum transfer. It is not necessary to ‘build in’ specific ring structures or other complex units beforehand; these arise naturally as a consequence of the constraints of density and chemical bonding.

Simulation of Infrared Spectra of Carbonaceous Grains

Random covalent network (RCN) theory is applied to describe the infrared spectroscopic properties of carbonaceous solids with compositions containing a mixture of aromatic, aliphatic, and diamond-like hydrocarbons. Application of this technique to carbonaceous dust is equivalent to the synthesis of solids whose structure and bonding satisfy stoicheometry while minimizing strain energy. The result involves a range of compositions compatible with carbon bonding and the hydrogen concentration incorporated in the network. In general, only a limited range of compositions is available rather than the infinite number of possible compositions expected without the inclusion of these constraints. When compositions have been defined in this way, infrared spectra may be synthesized for comparison with astronomical spectra of interstellar carbonaceous solids. Such spectra contain components corresponding to absorption by CHn groups in which n = 1-3. We find, however, that additional spectral features, not included in our simple chemical model, must be present also in dust. We give plots of such spectra in the 3100-2800 cm-1 (3.2-3.6 μm) region for comparison with infrared spectra of interstellar dust. We have also developed an RCN formalism that incorporates oxygen into the carbon network as OH groups, and we show that this inclusion introduces a strong additional absorption band in the 3300 cm-1 (3.0 μm) region.

An electrical model for two-dimensional layers of conductive polymers

Conducting polymers are a topic of great interest in the field of molecular electronics as well as for sensor applications. In this paper, we present a model for the evaluation of the d.c. conductance of a layer of conductive polymers, whose thickness is negligible if compared with the lateral extension. In our model all the monomers constituting a chain are represented by resistors with a fixed value of conductance and are disposed in a square network. The nodes of the network are structured in such a way that each monomer converging to the node under consideration can be connected to all the other three through resistors of different values, whose alternated occurrence is ruled by a probabilistic law. The global conductance of such a network is studied while the values of the probabilities referred to the above-said occurrences are varied. Finally, the treatment of this network according to the traditional theory of random networks is considered.

A thermodynamic, molecular dynamics and neutron diffraction investigation of the distribution of tetrahedral {;Si(n)} species and the network modifying cation environment in alkali silicate glasses

Previous molecular dynamics (MD) simulations of alkali silicate glasses are extended to keep a separate record of the bridging and non-bridging oxygen atoms and the SiO and NaO first neighbour distance distributions are compared with those extracted from neutron diffraction data. The model of ideal associated solutions is used to predict the distributions of Si(n) tetrahedral species for the glasses studied and these are in good agreement with nuclear magnetic resonance data. However, the corresponding distributions for the MD simulations indicate a much higher fictive temperature than for the real glasses. The spatial distribution of the Si(4) species for the MD simulations is more uniform than would pertain if the various Si(n) species were interconnected randomly, which has implications for the modified random network theory.

Vitreous borate networks containing superstructural units: a challenge to the random network theory?

Borate glasses are an enigma in that there is now increasing evidence that their structures are dominated by superstructural units. Crystallographic data for a wide range of crystalline borates are used as a basis to propose a set of criteria for the formation of vitreous borate networks, taking into account the topological degrees of freedom necessary for conventional glass formation and using the PbOB2O3 system as an example. It is concluded that random network models of vitreous B2O3 containing large numbers of boroxol groups can be built with the correct density if they contain locally independent interpenetrating networks.

Diamond, aromatic, aliphatic components of interstellar dust grains: Random covalent networks in carbonaceous grains

view Abstract Citations (15) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Diamond, Aromatic, and Aliphatic Components of Interstellar Dust Grains: Random Covalent Networks in Carbonaceous Grains Duley, W. W. Abstract A formalism based on the theory of random covalent networks (RCNs) in amorphous solids is developed for carbonaceous dust grains. RCN solutions provide optimized structures and relative compositions for amorphous materials. By inclusion of aliphatic, aromatic, and diamond clusters, solutions specific to interstellar materials can be obtained and compared with infrared spectral data. It is found that distinct RCN solutions corresponding to diffuse cloud and molecular cloud materials are possible. Specific solutions are derived for three representative objects: VI Cyg No. 12, NGC 7538 (IRS 9), and GC IRS 7. While diffuse cloud conditions with a preponderance of sp2 and sp3 bonded aliphatic CH species can be reproduced under a variety of RCN conditions, the presence of an abundant tertiary CH or diamond component is highly constrained. These solutions are related quantitatively to carbon depletions and can be used to provide a quantitative estimate of carbon in these various dust components. Despite the abundance of C6 aromatic rings in many RCN solutions, the infrared absorption due to the aromatic stretch at approximately 3.3 micrometers is weak under all conditions. The RCN formalism is shown to provide a useful method for tracing the evolutionary properties of interstellar carbonaceous grains. Publication: The Astrophysical Journal Pub Date: May 1995 DOI: 10.1086/175691 Bibcode: 1995ApJ...445..240D Keywords: Aliphatic Hydrocarbons; Carbonaceous Materials; Cosmic Dust; Covalence; Diamonds; Infrared Absorption; Interstellar Matter; Absorptivity; Chemical Analysis; Covalent Bonds; Hydrogen Bonds; Astrophysics; ISM: DUST; EXTINCTION; INFRARED: ISM: LINES AND BANDS; ISM: CLOUDS full text sources ADS | data products SIMBAD (5)

Stereochemical random networks. A contribution to a structurally aware hopping theory in oxide glasses

A rewriting of the continuous random network theory is presented. It is based upon the hypothesis that ill-condensed matter may be described assuming that structural units are preserved when moving from crystals to glasses, although spatial correlations among them are lost. Following these guidelines, a detailed structural picture is built of a class of oxide glasses, characterized by finite or infinite chains. Hopping theory is used to predict the dependence of the electronic mobility on the hopping center density. Further, the trend of the mass density versus the composition is foreseen. The theory is corroborated with experimental data collected on phosphate glasses.

Molecular dynamics simulation of lead metaphosphate Pb(PO3)2 glass

A molecular dynamics study of lead metaphosphate glass, of composition Pb(PO3)2, has been performed in order to evaluate structural details of this system. This simulation reproduces well experimentally determined bulk structural features and short-range order has been verified by the presence of corner-linked phosphate tetrahedra. A connectivity study of the phosphate backbone shows the presence of phosphate chains and ring structures. Further, a secondary network, made up of the modifier lead cations linked by non-bridging oxygens, is observed, as postulated by the modified random network theory.

Atomic constraint in hydrogenated ‘‘diamond-like’’ carbon

Carbon bonding environments (measured by nuclear magnetic resonance spectroscopy) and compressive stress in plasma-deposited hydrogenated diamond-like carbon (DLC) films have been examined systematically as a function of substrate bias voltage. These results are related in terms of random network theory to show that hard DLC formed in an intermediate voltage range (100–400 V) consists of small graphitic clusters linked in a random network which is stiffened by a high density of quaternary carbon.

Liquid Chromatography and Raman Scattering Spectroscopy Measurements of Lead-Iron Phosphate Glasses

Due to the limited amount of structural information that can be obtained using traditional techniques of solid state physics (e.g., x-ray or neutron diffraction), the structure of oxide glasses has remained a controversial topic since the introduction of the “random network theory” in 1932. While there are several experimental methods that can provide detailed information about the local structural properties of glasses (e.g., NMR, EXAFS, optical absorption, Mössbauer absorption, and EPR spectroscopy), very little information is available regarding the distribution of intermediate size (∼10–500 Å) structural units.

Percolation theory and resistance of random electrical networks

Percolation theory and resistance of random electrical networks

On the effective medium theory of random linear networks

The author studies the effective medium approximation for uncorrelated random linear networks. For various probability distributions of conductance compares the effective medium average value to the direct numerical average and study the magnitude of the correction terms by a mixture of analytical and numerical arguments. He argues that for all 'non-critical' conductance distributions-for systems not dominated by very low values of conductance and not near the conduction threshold-the effective medium approximation is quite accurate, with errors of order 1%. For any conduction distribution, effective medium theory is shown to be exact in the two limits of coordination number sigma =2 and sigma to infinity . Some remarks on the critical path approximation are presented.

The structure of vitreous silica: Validity of the random network theory

Abstract It is shown that the random network theory of glass structure accounts satisfactorily for the observed x-ray and neutron radial distribution functions of vitreous silica, out to interatomic distances of at least 0·8 nm (8 Å). This result is based on the study of a molecular model containing sample atomic arrangements consistent with the general precepts of the random network theory. Analysis of a range of molecular models, discussed briefly, suggests that the distribution of bond angles may not be the only factor determining the overall agreement between theoretical and experimental radial distribution functions. The distribution of molecular loops in the network seems to be of importance in this context. Details of the satisfactory model are given in the Appendix, in the form of a list of atomic coordinates and nearest neighbour connections.