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We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erdőos-Rényi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems.

In this document I report my research outcome during my stay at the Yukawa Institute of Theoretical Physics from March 1st and March 31st, 2016, which is supported by the International Research Unit of Advanced Future Studies. The report mainly contains a nontechnical summary of my recent study on effects of triangles in several network.

The results of researches on the electric conductivity in the percolation transition region of the oligoglycol/nanotubes systems are reported. It is shown that the conductivity can be described in the framework of the critical percolation theory. The critical parameters of percolation transition are found to change, by depending on various factors, and to differ from the predictions of the statistical percolation theory. A relationship between the critical conductivity indices and the fractal dimensionality of a conducting cluster is found. It is demonstrated that the application of a scaling function allows the concentration dependences of conductivity to be described with the help of a unique universal function., Представлено результати дослiджень електропровiдностi в системах типу олiгоглiколь/нанотрубки в областi перколяцiйного переходу. Показано, що електропровiднiсть може бути описана в рамках теорiї критичної перколяцiї. Встановлено, що критичнi параметри перколяцiйного переходу можуть змiнюватись в залежностi вiд рiзних факторiв i вiдрiзняються вiд передбачень статистичної теорiї перколяцiї. Знайдено зв’язок мiж критичними iндексами провiдностi та фрактальною розмiрнiстю провiдного кластера. Показано, що використання масштабної функцiї дозволяє описати концентрацiйнi залежностi провiдностi за допомогою єдиної унiверсальної залежностi.

Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T &gt, Tc) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/d) T, and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states, a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = Tc. For T &gt, Tc, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension.

High-temperature and pressure boundaries of the liquid and gas states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure(p) ratios ( ) for the percolation transitions are = 1.495 ± 0.015 and = 1.100 ± 0.015. Further MD computations of percolation loci, for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B), show the connection between the ideal gas percolation transitions and the 1st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception and opens a debate on the definitions of gaseous and liquid states. info:eu-repo/semantics/publishedVersion

The transition from a semiconductor to a fast-ion conductor with increasing silver content along the Ag x (Ge 0.25 Se 0.75 ) (100− x ) tie line (0≤ x ≤25) was investigated on multiple length scales by employing a combination of electric force microscopy, X-ray diffraction, and neutron diffraction. The microscopy results show separation into silver-rich and silver-poor phases, where the Ag-rich phase percolates at the onset of fast-ion conductivity. The method of neutron diffraction with Ag isotope substitution was applied to the x =5 and x =25 compositions, and the results indicate an evolution in structure of the Ag-rich phase with change of composition. The Ag–Se nearest-neighbours are distributed about a distance of 2.64(1) Å, and the Ag–Se coordination number increases from 2.6(3) at x =5 to 3.3(2) at x =25. For x =25, the measured Ag–Ag partial pair-distribution function gives 1.9(2) Ag–Ag nearest-neighbours at a distance of 3.02(2) Å. The results show breakage of Se–Se homopolar bonds as silver is added to the Ge 0.25 Se 0.75 base glass, and the limit of glass-formation at x ≃28 coincides with an elimination of these bonds. A model is proposed for tracking the breakage of Se–Se homopolar bonds as silver is added to the base glass.

The use of non-traditional ways for energy accumulation (absorption) is a reserve to increase efficiency of accumulating and damping devices. The work is aimed at experimental and theoretical verification of possibility to create the accumulating and energy damping devices based on the heterogeneous systems (HS). The HS includes a couple i.e. a porous body (silochromes) with pore diameter from 20 nm to 360 nm) and a lyophobic (non-wetting) liquid (Wood's alloy). The paper briefly presents provisions of the theory of processes in HS based on the kinetics of percolation transition that allows us to calculate power, power and temporary characteristics of devices and prove the methods for choosing the couples for HS with the specified characteristics. It explains effect of hysteresis function of changing liquid volume that fills a porous body and outflows from it under the differential pressure, as well as conditions to realize effect of non-outflowing liquid after removal of the differential pressure thanks to which energy accumulation in HS is possible. The stand diagram, device parameters to study static and dynamic processes in HS, and measurement system characteristics are provided. Research results of static processes to fill (outflow) pores of various silochromes with Wood's alloy are presented. It is shown that among considered HS the most efficient one is the HS possessing S-120 silochrome, hexamethyldisilazane-modified. The certain filling pores specific energy of HS made 71 J/g, while the outflow specific energy was 28 J/g. The paper presents a scheme of device model damping a force impact on the support. Test results of spring and hydraulic dampers and the model, as well, with HS based on silochromes with various lyophobic liquids are given. High HS efficiency that allows the 4 times less impact value is shown. Further researches concern a development of engineering techniques to design and optimize the HS parameters and a choice of the most effective couples in HS. Results of work can find application in space engineering to create damping and synchronization systems of design components movement, in fuel-feed systems of MEMS engines, and in solving the problems of power systems miniaturization when creating nano- and pico-satellites.

High-temperature and pressure boundaries of the liquid and gaseous states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure (p) ratios (T* = kBT/pσ3) for the percolation transitions are TPE ∗ = 1.495 ± 0.01 and TPA ∗ = 1.100 ± 0.01. Further MD computations of percolation loci for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B) show the connection between the ideal gas percolation transitions and the 1st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception, and reopens a debate of “what is liquid”. We append this contribution to the science of liquid-gas criticality and liquid-state bounds with further open debate. info:eu-repo/semantics/publishedVersion

The morphology and the microscopic internal dynamics of a bidimensional gel formed by spontaneous aggregation of gold nanoparticles confined at the water surface are investigated by a suite of techniques, including grazing-incidence x-ray photon correlation spectroscopy (GI-XPCS). The range of concentrations studied spans across the percolation transition for the formation of the gel. The dynamical features observed by GI-XPCS are interpreted in view of the results of microscopical imaging; an intrinsic link between the mechanical modulus and internal dynamics is demonstrated for all the concentrations. Our work presents, to the best of our knowledge, the first example of a transition from stretched to compressed correlation function actively controlled by quasistatically varying the relevant thermodynamic variable. Moreover, by applying a model proposed time ago by Duri and Cipelletti [A. Duri and L. Cipelletti, Europhys. Lett. 76, 972 (2006)] we are able to build a novel master curve for the shape parameter, whose scaling factor allows us to quantify a 'long time displacement length'. This characteristic length is shown to converge, as the concentration is increased, to the 'short time localization length' determined by pseudo Debye-Waller analysis of the initial contrast. Finally, the intrinsic dynamics of the system are then compared with that induced by means of a delicate mechanical perturbation applied to the interface.

Percolation and critical phenomena show common features such as scaling and universality. Colloidal particles, immersed in a solvent close to criticality, experience long-range effective forces, named critical Casimir forces. %These originate from the confinement of the solvent critical fluctuations between the colloids. Building on the analogy between critical phenomena and percolation, we explore the possibility of observing long-range forces near a percolation threshold. To this aim we numerically evaluate the effective potential between two colloidal particles dispersed in a chemical sol and we show that it becomes attractive and long-ranged on approaching the sol percolation transition. We develop a theoretical description based on a polydisperse Asakura-Oosawa model which captures the divergence of the interaction range, allowing us to interpret such effect in terms of depletion interactions in a structured solvent. Our results provide the geometric analogue of the critical Casimir force, suggesting a novel way for tuning colloidal interactions by controlling the clustering properties of the solvent., Comment: final version of the manuscript

Critical properties for Lennard-Jones fluids are seen to be consistent with an alternative description of liquid-gas criticality to the van der Waals hypothesis. At the critical temperature (T-c) there is a critical dividing line on the Gibbs density surface rather than a critical point singularity. We report high-precision thermodynamic pressures from MD simulations for more than 2000 state points along 7 near-critical isotherms, for system sizes N=4096 and 10,976 for a Lennard-Jones fluid. We obtain k(B)T(c)/epsilon = 1.3365 +/- 0.0005 and critical pressure p(c)sigma(3)/epsilon = 0.1405 +/- 0.0002 which remains constant between two coexisting densities rho(c)(gas) sigma(3) = 0.266 +/- 0.01 and rho(c)(liquid) sigma(3) = 0.376 +/- 0.01 determined by supercritical percolation transition loci. A revised plot of the liquid-vapor surface tension shows that it goes to zero at this density difference, which, along with a direct evaluation of Gibbs chemical potential along the critical isotherm, reaffirms a coexisting dividing line of critical states. Analysis of the distribution of clusters from MD simulations along a supercritical isotherm (T*=1.5) gives new insight into the supercritical boundaries of gas and liquid phases, and the nature of the supercritical mesophase. (C) 2013 Elsevier B.V. All rights reserved. info:eu-repo/semantics/publishedVersion

Mittels MD-Simulation wurden Konformationseigenschaften des ungekürzten Insel-Amyloid-Polypeptids 1–37 (humanes amyloidogenes hIAPP und nicht amyloidogenes rIAPP der Ratte) bei physiologischen Temperaturen untersucht, beide sowohl mit Cystein- (reduziertes IAPP) als auch mit Cystinresten (oxidiertes IAPP). Bei der Durchführung von Messungen bei Temperaturen von 250K bis 450K in Intervallen von 20K zeigte sich, dass der Perkolationsübergang des Wassers zwischen 310K und 330K stattfindet. Somit wurden diese Temperaturen ausgewählt, um die Konformationseigenschaften des IAPP bei seiner höchsten biologischen Aktivität zu studieren. Tatsächlich zeigen die meisten lebenden Organismen ihre höchste biologische Aktivität in einem Temperaturbereich, der dem eines Perkolationsübergangs entspricht. Für hIAPP ergab die Berechnung einen Wert von ˜320 K. DieserWert scheint unabhängig von der chemischen Zusammensetzung der IAPP-Variante zu sein. Bei allen untersuchten Temperaturen nimmt IAPP keine definierte Konformation ein, sondern liegt in Lösung im Wesentlichen als zufälliges Knäuel vor, obwohl sich vor allem in der reduzierten Form kurzlebige Helices zwischen den Aminosäureresten 8 und 12 zu bilden scheinen. Oberhalb des Perkolationsübergangs von Wasser zeigt das reduzierte und immer noch strukturlose hIAPP einen deutlich verminderten helikalen Anteil. Währenddessen erreicht der natürliche Cystinrest einen recht kompakten Zustand mit einem, gegen¨ber den Messergebnissen der anderen Varianten, um nahezu 10% verminderten Trägheitsradius. Dies wird durch die intrapeptidischen Wasserstoffbrückenbindungen, welche viele ß-Brücken in der Region des C-Terminus bilden, hevorgerufen. Die kompakte Konformation weist einen geringen Abstand beider Termini auf und scheint sich durch die Ausbildung von ß-Faltblattkonformationen in der C-terminalen Gegend mit einer Minimierung der Y/F-Abstände in einem zweischrittigen Mechanismus zu bilden. Der erste Schritt findet bei einem Y37/F23 Abstand von ˜1:1 nm statt, woraufhin Y37/F15 ihre minimale Distanz von ˜0:86 nm erreichen. Das nicht aggregierende rIAPP zeigt ebenfalls kurzlebige helikale Konformationen. Eine besonders stabile Helix befindet sich in der Nähe der C-terminalen Region, beginnend mit den Aminosäureresten L27 und P28. Diese MD-Simulationen zeigen, dass P28 in rIAPP die Sekundärstruktur von IAPP durch die Stabilisierung des Peptids in helikalen Konformationen beeinflusst. Wenn diese Helix nicht vorhanden ist, zeigt das Peptid Krümmungen oder Hverbrückte Schleifen bei P28, die die Bildung von ß-Brücken, wie sie in hIAPP gefunden wurden, unterdrücken. Im Gegensatz dazu ist hIAPP in der C-terminalen Region deutlich ungeordneter und zeigt, besonders bei höheren Temperaturen und wenn die natürliche Disulfidbrücke vorhanden ist, kurzlebige isolierte ß-Strand-Konformationen. Derartige konformationelle Unterschiede, wie sie in diesen Simulationen gefunden wurden, könnten für die unterschiedlichen Aggregationsneigungen der beiden Homologe verantwortlich sein. Tatsächlich ist bekannt, dass der bei beiden Homologen identische Abschnitt 30–37 in vitro aggregiert, daher muss die gesamte Sequenz für die Amyloidogenität des hIAPP ursächlich sein. Es erscheint plausibel, dass der durch den Ersatz von Serin durch Prolin an Aminosäurerest 28 hervorgerufene höhere Anteil helikaler Konformationen im rIAPP dessen Aggregation inhibiert. Die spezifische Position des P28 könnte hierbei wichtiger für die Inhibierung sein als die intrinsischen Eigenschaften des Prolins allein. Tatsächlich wurde im IAPP von Katzen, die einen Diabetes Mellitus Typ II entwickelt haben und Insel-Amyloid-Ablagerungen zeigen, ein Prolinrest an Position 29 gefunden. Weiterhin ist für den oben genannten kompakten Zustand des monomeren, oxidierten hIAPP charakteristisch, dass eine besonders reaktive Konformation, die während der Faltung gefunden wurde, durch Disulfidbrücken stabilisiert ist. Eine solche Konformation besitzt einen geringen Abstand beider Termini, was dazu führt, dass die amyloidogene Sequenz N22FGAIL27 gegenüber benachbarten Peptiden exponiert ist. Im reduzierten hIAPP-Rest scheint sich dieser Zustand nicht für einen signifikanten Zeitraum zu bilden, was durch die fluktuierende Distanz der Endgruppen nachgewiesen wurde. Der mittlere Abstand zwischen den Termini ist kleiner als der aus dem Irrflugmodell bestimmte Wert. Dies zeigt die hohe Flexibilität des hIAPP und dass Interaktionen, die das Peptid in eine kompakte Form überführen, vorhanden sind. Im Gegensatz dazu scheinen beide Formen des rIAPP auf Grund der dem Prolin eigenen Starrheit zu unflexibel zu sein, um sich so zu falten, dass ein geringer Abstand zwischen den Termini, wie bei der oxidierten Form des hIAPP, zustande kommt. Allerdings sind auch Fälle beobachtet wurden, in denen oxidiertes rIAPP kurze Termini-Abstände erreicht. Dies stimmt mit der Abwesenheit von Helices in der P28-Region überein. Diese Konformationen treten möglicherweise dank der bei hIAPP beobachteten Interaktionen zwischen Disulfidbrücken und C-Terminus auf. Kurze Abstände zwischen Y37 und L23 werden im selben Zeitrahmen wie die geringen Abstände zwischen Y37 und F23 in hIAPP beobachtet. Allerdings ist es durch die Tatsache, dass Leucin nicht aromatisch ist, möglich, dass der erste Schritt des beim hIAPP beobachteten Faltungsprozesses im Wildtyp des rIAPP nicht stattfinden kann. Auf den gefalteten Zustand, der durch Simulation des oxidierten hIAPP bei 330K erhalten wurde, wurden in silico Mutationen eingebaut, um zu beobachten, welchen Einfluss Prolin auf die Konformation ausübt. Insbesondere der S28P-Austausch scheit die Bildung einer Helix in dieser Region zu induzieren und die besonders stabile, kompakte Struktur durch Trennung der Termini zu zerstören: Tatsächlich bleibt der Wildtyp des oxidierten Homologen kompakt bis zu einer Temperatur von 390 K. Somit scheinen, in Anbetracht der Ergebnisse dieser Arbeit, drei Charakteristika notwendig zu sein, damit die monomere Form des Polypeptids in einen kollabierten Zustand übergeht: 1. Anwesenheit einer Disulfidbrücke, die, wie beobachtet, flexibler als die reduzierte Entsprechung ist und den kurzen Abstand zwischen den Termini in IAPP stabilisiert. 2. Abwesenheit helikaler Anteile in der C-terminalen Region, um dieser Flexibilität für die Faltung des Peptids zu verleihen. P28 scheint den hochbeweglichen und unstrukturierten Abschnitt von IAPP zu stabilisieren. Ferner scheint derartige Helikalität kurze Abstände der Termini zu unterdrücken. 3. Anwesenheit aromatischer Reste, im Besonderen F23, welches einen der ersten Schritte im Faltungsprozess zu stabilisieren scheint. Da diese Ergebnisse zur monomeren Form erhalten wurden, sind weitere Studien notwendig, um zu bestimmen, ob diese drei strukturellen Charakteristika auch für die Aggregationsneigungen des IAPP relevant sind.

A new class of percolation model in complex networks, in which nodes are characterized by hidden variables reflecting the properties of nodes and the occupied probability of each link is determined by the hidden variables of the end nodes, is studied in this paper. By the mean field theory, the analytical expressions for the phase of percolation transition is deduced. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on., {"references":["R. Albert and A. L. Barab'asi, Rev. Mod. Phys. 74, 47 (2002).","S. Yoon, S. H. Yook, and Y. Kim, Phys. Rev. E 76, 056104 (2007).","D. J. Watts, and S. H. Strogatz, Nature (London) 393, 440 (1998).","A. L. Barab'asi, and R. Albert, Science 286, 509(1999)","M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 64,\n026118 (2001).","S. N. Dorogovtsev, and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).","D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys.\nRev. Lett. 85, 5468 (2000).","A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 78,\n051105 (2008).","M. A' . Serrano and P. D. L. Rios, Phys. Rev. E 76, 056121 (2007).\n[10] A. Zen, A. Kabakc┬©─▒o╦çglu, and A. L. Stella, Phys. Rev. E 76, 016110\n(2007).\n[11] E. L'oez, R. Parshani, R. Cohen, S. Carmi, and S. Havlin, Phys. Rev.\nLett. 99, 188701 (2007).\n[12] J. D. Noh, Phys. Rev. E 76, 026116 (2007).\n[13] M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001).\n[14] R. P. Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).\n[15] C. Moore and M. E. J. Newman, Phys. Rev. E 61, 5678 (2000).\n[16] M. Bogu╦£n'a and R. P. Satorras, Phys. Rev. E 66, 047104 (2002).\n[17] J. D. Noh, Phys. Rev. E 76, 026116 (2007).\n[18] A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 78,\n051105 (2008).\n[19] A. Zen, A. Kabakc─▒o╦çglu, and A. L. Stella, Phys. Rev. E 76, 026110\n(2007).\n[20] M. A. Serrano and P. D. L. Rios, Phys. Rev. E 76, 056121(2007).\n[21] E. L'opez, R. Parshani, R. Cohen, S. Carmi, and S. Havlin, Phys. Rev.\nE 99, 188701 (2007).\n[22] L. Apolo, O. Melchert, and A. K. Hartmann, Phys. Rev. E 79, 031103\n(2009).\n[23] D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd\nedition, Taylor and Francis, London (1992).\n[24] G. Caldarelli, A. Capocci, P. D. L. Rios, and M. A. Mun╦£noz5, Phys.\nRev. Lett. 89, 258702 (2002).\n[25] B. S┬¿oderberg, Phys. Rev. E 66, 066126 (2002).\n[26] M. Bogu╦£n'a and R. P. Satorras, Phys. Rev. E 68, 036112 (2003)."]}

Stochastic and deterministic approaches for modeling complex networks are presented. The methodology combines analysis of the structure formed by the interconnections among the elements of a network with an assessment of the vulnerability towards the propagation of cascading failures. The goal is to understand the mutual interplay between the structure of the network connections and the propagation of cascading failures. Two fundamental issues related to the optimal design and operation of complex networks are addressed. The first concerns the impact that cascading failures have on networks due to the connectivity pattern linking their components. If the state of load on the network components is high, the risk of cascade spreadings becomes significant. In this case, the needed reduction of the connectivity efficiency to prevent the propagation of failures affecting the entire system is quantified. The second issue concerns the realization of the most efficient connectivity in a network that minimizes the propagations of cascading failures. It is found that a system that routinely approaches the critical load for the onset of cascading failures during its operation should have a larger efficiency value. This allows for a smoother transition to the cascade region and for a reasonable reaction time to counteract the onset of significant cascading failures. The interplay between the structure of the network connections and the propagation of cascading failures is assessed also in interdependent networks. In these systems, the linking among several network infrastructures is necessary for their optimal and economical operation. Yet, the interdependencies introduce weaknesses due to the fact that failures may cascade from one system to other interdependent systems, possibly affecting their overall functioning. Inspired by the global efficiency, a measure of the communication capabilities among interdependent systems, i.e. the interdependency efficiency, is defined. The relations between the structural parameters, i.e. the system links and the interdependency links, and the interdependency efficiency, are also quantified, as well as the relations between the structural parameters and the vulnerability towards the propagation of cascading failures. Resorting to this knowledge, the optimal interdependency connectivity is identified. Similar to the spreading of failures, the formation of a giant component is a critical phenomenon emerging as a result of the connectivity pattern in a network. This structural transition is exploited to identify the formation of macrometastases in the developed model for metastatic colonization in tumor growth. The methods of network theory proves particularly suitable to reproduce the local interactions among tumor cells that lead to the emergent global behavior of the metastasis as a community. This model for intercellular sensing reproduces the stepwise behavior characteristic of metastatic colonization. Moreover, it prompts the consideration of a curative intervention that hinders intercellular communication, even in the presence of a significant tumor cell population. Ph. D.

Surfaces of polyacrylamide hydrogels synthesized in the presence of surfactants were imaged by atomic force microscopy (AFM), and the surface morphology was studied by numerical scaling analysis. The gels were formed by polymerizing acrylamide plus a cross-linker in the presence of surfactants, which were then removed by soaking in distilled water. Gels formed in the presence of over 20% surfactant (by weight) formed clear, but became opaque upon removal of the surfactants. Other gels formed and remained clear. The surface morphology of the gels was studied by several one- and two-dimensional numerical scaling methods. The surfaces were found to be self-affine on short length scales, with a roughness (Hurst) exponent in the range from 0.85 to 1, crossing over to a constant root-mean-square surface width at long scales. Both the crossover length between these two regimes and the saturation value of the surface width increased significantly with increasing surfactant concentration, coincident with the increase in opacity. We propose that the changes in the surface morphology are due to a percolation transition in the system of voids formed upon removal of the surfactants from the bulk.

We review the scientific history of random close packing (RCP) of equal spheres, advocated by J D Bernal as a more plausible alternative to the non-ideal gas or imperfect crystal as a structural model of simple liquids. After decades of neglect, computer experiments are revealing a central role for RCP in the theory of liquids. These demonstrate that the RCP amorphous state of hard spheres can be well defined, is reproducible, and has the thermodynamic status of a metastable ground state. Further evidence from simulations of square-well model liquids indicates an extended role of RCP as an amorphous ground state that terminates a supercooled liquid coexistence line, suggesting likewise for real liquids. A phase diagram involving percolation boundaries has been proposed in which there is no merging of liquid and gas phases, and no critical singularity as assumed by van der Waals. Rather, the liquid phase continuously spans all temperatures, but above a critical dividing line on the Gibbs density surface, it is bounded by a percolation transition and separated from the gas phase by a colloidal supercritical mesophase. The colloidal-like inversion in the mesophase as it changes from gas-in-liquid to liquid-in-gas can be identified with the hypercritical line of Bernal. We therefore argue that the statistical theory of simple liquids should start from the RCP reference state rather than the ideal gas. Future experimental priorities are to (i) find evidence for an amorphous ground state in real supercooled liquids, (ii) explore the microscopic structures of the supercritical mesophase, and (iii) determine how these change from gas to liquid, especially across Bernal's hypercritical line. The theoretical priority is a statistical geometrical theory of RCP. Only then might we explain the coincident values of the RCP packing fraction with Buffon's constant, and the RCP residual entropy with Boltzmann's ideal gas constant. info:eu-repo/semantics/publishedVersion

The Invaded Cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics which exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation-dissipation theorem is no more valid. The relaxation time is found very short and does not present critical size dependence., Comment: notes and refernences added, some minor changes in text and fig.3,5,7 16 pages, Latex, 8 EPS figures, submitted to Phys. Rev. E