DSpace Collection:
http://hdl.handle.net/2117/395
Sun, 20 Apr 2014 09:27:23 GMT2014-04-20T09:27:23Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoSpin-polarized hydrogen adsorbed on the surface of superfluid He-4
http://hdl.handle.net/2117/22078
Title: Spin-polarized hydrogen adsorbed on the surface of superfluid He-4
Authors: Marín, J. M.; Vranješ Markic, Leandra; Boronat Medico, Jordi
Abstract: The experimental realization of a thin layer of spin-polarized hydrogen H double down arrow adsorbed on top of the surface of superfluid He-4 provides one of the best examples of a stable, nearly two-dimensional(2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid He-4 slab and the adsorbed H double down arrow layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied. (c) 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4843375]Fri, 14 Mar 2014 15:12:24 GMThttp://hdl.handle.net/2117/220782014-03-14T15:12:24ZMarín, J. M.; Vranješ Markic, Leandra; Boronat Medico, JordinoBOSE-EINSTEIN CONDENSATION, ATOMIC-HYDROGEN, LIQUID-HELIUM, ALIGNED HYDROGEN, QUANTUM SYSTEMS, GAS, ADSORPTION, SCATTERING, HEThe experimental realization of a thin layer of spin-polarized hydrogen H double down arrow adsorbed on top of the surface of superfluid He-4 provides one of the best examples of a stable, nearly two-dimensional(2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid He-4 slab and the adsorbed H double down arrow layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied. (c) 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4843375]Diffusion and spectroscopy of water and lipids in fully hydrated dimyristoylphosphatidylcholine bilayer membranes
http://hdl.handle.net/2117/21998
Title: Diffusion and spectroscopy of water and lipids in fully hydrated dimyristoylphosphatidylcholine bilayer membranes
Authors: Yang, Jing; Calero Borrallo, Carles; Martí Rabassa, Jordi
Abstract: Microscopic structure and dynamics of water and lipids in a fully hydrated dimyristoylphosphatidylcholine phospholipid lipid bilayer membrane in the liquid-crystalline phase have been analyzed with all-atom molecular dynamics simulations based on the recently parameterized CHARMM36 force field. The diffusive dynamics of the membrane lipids and of its hydration water, their reorientational motions as well as their corresponding spectral densities, related to the absorption of radiation, have been considered for the first time using the present force field. In addition, structural properties such as density and pressure profiles, a deuterium-order parameter, surface tension, and the extent of water penetration in the membrane have been analyzed. Molecular self-diffusion, reorientational motions, and spectral densities of atomic species reveal a variety of time scales playing a role in membrane dynamics. The mechanisms of lipid motion strongly depend on the time scale considered, from fast ballistic translation at the scale of picoseconds (effective diffusion coefficients of the order of 10-5 cm2/s) to diffusive flow of a few lipids forming nanodomains at the scale of hundreds of nanoseconds (diffusion coefficients of the order of 10-8 cm2/s). In the intermediate regime of sub-diffusion, collisions with nearest neighbors prevent the lipids to achieve full diffusion. Lipid reorientations along selected directions agree well with reported nuclear magnetic resonance data and indicate two different time scales, one about 1 ns and a second one in the range of 2–8 ns. We associated the two time scales of reorientational motions with angular distributions of selected vectors. Calculated spectral densities corresponding to lipid and water reveal an overall good qualitative agreement with Fourier transform infrared spectroscopy experiments. Our simulations indicate a blue-shift of the low frequency spectral bands of hydration water as a result of its interaction with lipids. We have thoroughly analyzed the physical meaning of all spectral features from lipid atomic sites and correlated them with experimental data. Our findings include a “wagging of the tails” frequency around 30 cm-1, which essentially corresponds to motions of the tail-group along the instantaneous plane formed by the two lipid tails, i.e., in-plane oscillations are clearly of bigger importance than those along the normal-to-the plane direction.Tue, 11 Mar 2014 15:30:00 GMThttp://hdl.handle.net/2117/219982014-03-11T15:30:00ZYang, Jing; Calero Borrallo, Carles; Martí Rabassa, Jordinolipid bilayer membrane, molecular dynamics, dynamics (diffusion, spectroscopy)Microscopic structure and dynamics of water and lipids in a fully hydrated dimyristoylphosphatidylcholine phospholipid lipid bilayer membrane in the liquid-crystalline phase have been analyzed with all-atom molecular dynamics simulations based on the recently parameterized CHARMM36 force field. The diffusive dynamics of the membrane lipids and of its hydration water, their reorientational motions as well as their corresponding spectral densities, related to the absorption of radiation, have been considered for the first time using the present force field. In addition, structural properties such as density and pressure profiles, a deuterium-order parameter, surface tension, and the extent of water penetration in the membrane have been analyzed. Molecular self-diffusion, reorientational motions, and spectral densities of atomic species reveal a variety of time scales playing a role in membrane dynamics. The mechanisms of lipid motion strongly depend on the time scale considered, from fast ballistic translation at the scale of picoseconds (effective diffusion coefficients of the order of 10-5 cm2/s) to diffusive flow of a few lipids forming nanodomains at the scale of hundreds of nanoseconds (diffusion coefficients of the order of 10-8 cm2/s). In the intermediate regime of sub-diffusion, collisions with nearest neighbors prevent the lipids to achieve full diffusion. Lipid reorientations along selected directions agree well with reported nuclear magnetic resonance data and indicate two different time scales, one about 1 ns and a second one in the range of 2–8 ns. We associated the two time scales of reorientational motions with angular distributions of selected vectors. Calculated spectral densities corresponding to lipid and water reveal an overall good qualitative agreement with Fourier transform infrared spectroscopy experiments. Our simulations indicate a blue-shift of the low frequency spectral bands of hydration water as a result of its interaction with lipids. We have thoroughly analyzed the physical meaning of all spectral features from lipid atomic sites and correlated them with experimental data. Our findings include a “wagging of the tails” frequency around 30 cm-1, which essentially corresponds to motions of the tail-group along the instantaneous plane formed by the two lipid tails, i.e., in-plane oscillations are clearly of bigger importance than those along the normal-to-the plane direction.Pattern recognition and data mining software based on artificial neural networks applied to proton transfer in aqueous environments
http://hdl.handle.net/2117/21794
Title: Pattern recognition and data mining software based on artificial neural networks applied to proton transfer in aqueous environments
Authors: Tahat, Amani; Martí Rabassa, Jordi; Khwaldeh, Ali; Tahat, Kaher
Abstract: In computational physics proton transfer phenomena could be viewed as pattern classification problems based on a set of input features allowing to classify the proton motion into two categories: transfer‘occurred’and transfer‘not occurred’. The goal of this paper is to evaluate the use of artificial neural networks in the classification of proton transfer events, based on the feed-forward back propagation neural network, used as a classifier to distinguish between the two transfer cases. In this paper, we use a new developed data mining and pattern recognition tool for automating, controlling, and drawing charts of the output data of an Empirical Valence Bond existing code. The study analyzes the need of pattern recognition in aqueous proton transfer processes and how the learning approach in error back propagation (multilayer perceptron algorithms) could be satisfactorily employed in the present case. We present a tool for pattern recognition and validate the code including a real physical case study. The results of applying the artificial neural networks methodology to crowd patterns based upon selected physical properties (e.g., temperature, density) show the abilities of the network to learn proton transfer patterns corresponding to properties of the aqueous environments, which is in turn proved to be fully compatible with previous proton transfer studies.Thu, 27 Feb 2014 14:47:41 GMThttp://hdl.handle.net/2117/217942014-02-27T14:47:41ZTahat, Amani; Martí Rabassa, Jordi; Khwaldeh, Ali; Tahat, Kahernoproton transfer, pattern recognition, neural networks, water environments, chart pattern, data mining, artificial neural network, empirical valence bondIn computational physics proton transfer phenomena could be viewed as pattern classification problems based on a set of input features allowing to classify the proton motion into two categories: transfer‘occurred’and transfer‘not occurred’. The goal of this paper is to evaluate the use of artificial neural networks in the classification of proton transfer events, based on the feed-forward back propagation neural network, used as a classifier to distinguish between the two transfer cases. In this paper, we use a new developed data mining and pattern recognition tool for automating, controlling, and drawing charts of the output data of an Empirical Valence Bond existing code. The study analyzes the need of pattern recognition in aqueous proton transfer processes and how the learning approach in error back propagation (multilayer perceptron algorithms) could be satisfactorily employed in the present case. We present a tool for pattern recognition and validate the code including a real physical case study. The results of applying the artificial neural networks methodology to crowd patterns based upon selected physical properties (e.g., temperature, density) show the abilities of the network to learn proton transfer patterns corresponding to properties of the aqueous environments, which is in turn proved to be fully compatible with previous proton transfer studies.Possible superfluidity of molecular hydrogen in a two-dimensional crystal phase of sodium
http://hdl.handle.net/2117/21500
Title: Possible superfluidity of molecular hydrogen in a two-dimensional crystal phase of sodium
Authors: Cazorla Silva, Claudio; Boronat Medico, Jordi
Abstract: We theoretically investigate the ground-state properties of a molecular para-hydrogen (p-H 2 ) film in which crystallization is energetically frustrated by embedding sodium (Na) atoms periodically distributed in a triangular lattice. In order to fully deal with the quantum nature of p-H 2 molecules, we employ the diffusion Monte Carlo method and realistic semiempirical pairwise potentials describing the interactions between H 2 -H 2 and Na-H 2 species. In particular, we calculate the energetic, structural, and superfluid properties of two-dimensional Na-H 2 systems within a narrow density interval around equilibrium at zero temperature. In contrast to previous computational studies considering other alkali metal species such as rubidium and potassium, we find that the p-H 2 ground state is a liquid with a significantly large superfluid fraction of ρ s /ρ=0.29(2) . The appearance of p-H 2 superfluid response is due to the fact that the interactions between Na atoms and H 2 molecules are less attractive than between H 2 molecules. This induces a considerable reduction of the hydrogen density which favors the stabilization of the liquid phase.Mon, 10 Feb 2014 16:17:42 GMThttp://hdl.handle.net/2117/215002014-02-10T16:17:42ZCazorla Silva, Claudio; Boronat Medico, JordinoMolecular hydrogen, two-dimensional, crystal phase of sodiumWe theoretically investigate the ground-state properties of a molecular para-hydrogen (p-H 2 ) film in which crystallization is energetically frustrated by embedding sodium (Na) atoms periodically distributed in a triangular lattice. In order to fully deal with the quantum nature of p-H 2 molecules, we employ the diffusion Monte Carlo method and realistic semiempirical pairwise potentials describing the interactions between H 2 -H 2 and Na-H 2 species. In particular, we calculate the energetic, structural, and superfluid properties of two-dimensional Na-H 2 systems within a narrow density interval around equilibrium at zero temperature. In contrast to previous computational studies considering other alkali metal species such as rubidium and potassium, we find that the p-H 2 ground state is a liquid with a significantly large superfluid fraction of ρ s /ρ=0.29(2) . The appearance of p-H 2 superfluid response is due to the fact that the interactions between Na atoms and H 2 molecules are less attractive than between H 2 molecules. This induces a considerable reduction of the hydrogen density which favors the stabilization of the liquid phase.Shortcomings of the standard Lennard-Jones dispersion term in water models, studied with force matching
http://hdl.handle.net/2117/21290
Title: Shortcomings of the standard Lennard-Jones dispersion term in water models, studied with force matching
Authors: Nicolini, Paolo; Guàrdia Manuel, Elvira; Masia, Marco
Abstract: In this work, ab initio parametrization of water force field is used to get insights into the functional form of empirical potentials to properly model the physics underlying dispersion interactions. We exploited the force matching algorithm to fit the interaction forces obtained with dispersion corrected density functional theory based molecular dynamics simulations. We found that the standard Lennard-Jones interaction potentials poorly reproduce the attractive character of dispersion forces. This drawback can be resolved by accounting for the distinctive short range behavior of dispersion interactions, multiplying the r −6 term by a damping function. We propose two novel parametrizations of the force field using different damping functions. Structural and dynamical properties of the new models are computed and compared with the ones obtained from the non-damped force field, showing an improved agreement with reference first principle calculations.Mon, 20 Jan 2014 17:45:49 GMThttp://hdl.handle.net/2117/212902014-01-20T17:45:49ZNicolini, Paolo; Guàrdia Manuel, Elvira; Masia, MarconoDispersion interaction, Dispersion-corrected density functional, Dynamical properties, Empirical potentials, First principle calculations, Force-matching algorithm, Lennard-Jones interaction potential, Molecular dynamics simulationsIn this work, ab initio parametrization of water force field is used to get insights into the functional form of empirical potentials to properly model the physics underlying dispersion interactions. We exploited the force matching algorithm to fit the interaction forces obtained with dispersion corrected density functional theory based molecular dynamics simulations. We found that the standard Lennard-Jones interaction potentials poorly reproduce the attractive character of dispersion forces. This drawback can be resolved by accounting for the distinctive short range behavior of dispersion interactions, multiplying the r −6 term by a damping function. We propose two novel parametrizations of the force field using different damping functions. Structural and dynamical properties of the new models are computed and compared with the ones obtained from the non-damped force field, showing an improved agreement with reference first principle calculations.Zero-temperature phase diagram of D2 physisorbed on graphane
http://hdl.handle.net/2117/20842
Title: Zero-temperature phase diagram of D2 physisorbed on graphane
Authors: Carbonell Coronado, Carmen; De Soto Borrera, Feliciano Carlos; Cazorla Silva, Claudio; Boronat Medico, Jordi; Gordillo Bargueño, Maria Carmen
Abstract: We determined the zero-temperature phase diagram of D2 physisorbed on graphane using the diffusion Monte Carlo method. The substrate used was C-graphane, an allotropic form of the compound that has been experimentally obtained through hydrogenation of graphene. We found that the ground state is the δ phase, a commensurate structure observed experimentally when D2 is adsorbed on graphite, and not the registered structure characteristic of H2 on the same substrate.Thu, 28 Nov 2013 17:56:18 GMThttp://hdl.handle.net/2117/208422013-11-28T17:56:18ZCarbonell Coronado, Carmen; De Soto Borrera, Feliciano Carlos; Cazorla Silva, Claudio; Boronat Medico, Jordi; Gordillo Bargueño, Maria CarmennoAllotropic forms, Commensurate structure, Diffusion Monte Carlo method, Graphane, Physisorbed, Structure characteristic, Zero temperaturesWe determined the zero-temperature phase diagram of D2 physisorbed on graphane using the diffusion Monte Carlo method. The substrate used was C-graphane, an allotropic form of the compound that has been experimentally obtained through hydrogenation of graphene. We found that the ground state is the δ phase, a commensurate structure observed experimentally when D2 is adsorbed on graphite, and not the registered structure characteristic of H2 on the same substrate.Characterization of the methane–graphene hydrophobic interaction in aqueous solution from ab initio simulations
http://hdl.handle.net/2117/20817
Title: Characterization of the methane–graphene hydrophobic interaction in aqueous solution from ab initio simulations
Authors: Calero Borrallo, Carles; Martí Rabassa, Jordi; Guàrdia Manuel, Elvira; Masia, Marco
Abstract: In this article, the interaction between a methane molecule and a graphene plane in liquid water has been characterized employing DFT-based free energy Molecular Dynamics calculations. This system represents a good model to understand the generic interaction between a small hydrophobic solute (methane molecule) and an extense hydrophobic surface (graphene plane). The structural and dynamical properties of graphene and methane hydration water are analyzed and found to be closely related to the main features of the potential of mean force. The results could be used in coarse-grained models to take into account the effect of the hydrophobic interaction in realistic systems relevant to experiment.Wed, 27 Nov 2013 14:39:00 GMThttp://hdl.handle.net/2117/208172013-11-27T14:39:00ZCalero Borrallo, Carles; Martí Rabassa, Jordi; Guàrdia Manuel, Elvira; Masia, Marconomethane-graphene interactions, hydrophobic forces, ab-initio simulationIn this article, the interaction between a methane molecule and a graphene plane in liquid water has been characterized employing DFT-based free energy Molecular Dynamics calculations. This system represents a good model to understand the generic interaction between a small hydrophobic solute (methane molecule) and an extense hydrophobic surface (graphene plane). The structural and dynamical properties of graphene and methane hydration water are analyzed and found to be closely related to the main features of the potential of mean force. The results could be used in coarse-grained models to take into account the effect of the hydrophobic interaction in realistic systems relevant to experiment.Non-mean-field behavior of the contact process on scale-free networks
http://hdl.handle.net/2117/20765
Title: Non-mean-field behavior of the contact process on scale-free networks
Authors: Castellano, Claudio; Pastor Satorras, Romualdo
Abstract: We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a nontrivial critical behavior that cannot be quantitatively accounted for by mean-field theory.Mon, 25 Nov 2013 20:00:12 GMThttp://hdl.handle.net/2117/207652013-11-25T20:00:12ZCastellano, Claudio; Pastor Satorras, Romualdonoscale-free networks
complex networks and dynamic systemsWe present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a nontrivial critical behavior that cannot be quantitatively accounted for by mean-field theory.Zero temperature Glauber dynamics on complex networks
http://hdl.handle.net/2117/20762
Title: Zero temperature Glauber dynamics on complex networks
Authors: Castellano, Claudio; Pastor Satorras, Romualdo
Abstract: We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.Mon, 25 Nov 2013 19:08:44 GMThttp://hdl.handle.net/2117/207622013-11-25T19:08:44ZCastellano, Claudio; Pastor Satorras, Romualdonorandom graphs, networks
coarsening processes (theory)
disordered systems (theory)
stochastic particle dynamics (theory)We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.Percolation analysis of force networks in anisotropic granular matter
http://hdl.handle.net/2117/20597
Title: Percolation analysis of force networks in anisotropic granular matter
Authors: Pastor Satorras, Romualdo; Miguel Lopez, Maria del Carmen
Abstract: We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al (2006 Nature 439 828), we consider a percolation process in which forces smaller than a given threshold f are deleted in the
network. For a critical threshold fc, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation
laws in the model under scrutiny.Tue, 12 Nov 2013 19:25:24 GMThttp://hdl.handle.net/2117/205972013-11-12T19:25:24ZPastor Satorras, Romualdo; Miguel Lopez, Maria del Carmennofinite-size scaling, percolation problems (theory), granular matter, jamming and packingWe study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al (2006 Nature 439 828), we consider a percolation process in which forces smaller than a given threshold f are deleted in the
network. For a critical threshold fc, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation
laws in the model under scrutiny.Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks
http://hdl.handle.net/2117/20595
Title: Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks
Authors: de Souza Mata, Angelica; Ferreira, Silvio C.; Pastor Satorras, Romualdo
Abstract: We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean-field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allows us to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.Tue, 12 Nov 2013 17:35:18 GMThttp://hdl.handle.net/2117/205952013-11-12T17:35:18Zde Souza Mata, Angelica; Ferreira, Silvio C.; Pastor Satorras, Romualdonoreaction-diffusion model, metapopulation networksWe investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean-field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allows us to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
http://hdl.handle.net/2117/20592
Title: Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
Authors: Boguñá, Marian; Castellano, Claudio; Pastor Satorras, Romualdo
Abstract: We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.Tue, 12 Nov 2013 15:37:13 GMThttp://hdl.handle.net/2117/205922013-11-12T15:37:13ZBoguñá, Marian; Castellano, Claudio; Pastor Satorras, Romualdonosusceptible-infected-susceptible epidemic model, Epidemic ThresholdWe develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.Features in chemical kinetics. II. A self-emerging definition of slow manifolds
http://hdl.handle.net/2117/20345
Title: Features in chemical kinetics. II. A self-emerging definition of slow manifolds
Authors: Nicolini, Paolo; Frezzato, Diego
Abstract: In the preceding paper of this series (Part I, P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101(2013)) we have unveiled some ubiquitous features encoded in the systems of polynomial differential equations normally applied in the description of homogeneous and isothermal chemical kinetics
(mass-action law). Here we proceed by investigating a deeply related feature: the appearance of so-called slow manifolds (SMs) which are low-dimensional hyper-surfaces in the neighborhood of which the slow evolution of the reacting system occurs after an initial fast transient. Indeed a geometrical definition of SM, devoid of subjectivity, “naturally” follows in terms of a specific subdimensional domain embedded in the peculiar region of the concentrations phase-space that in Part I we termed as “attractiveness region.” Numerical inspections on simple low-dimensional model cases are presented, including the benchmark case of Davis and Skodje [J. Chem. Phys. 111, 859 (1999)] and the preliminary analysis of a simplified model mechanism of hydrogen combustion.Wed, 09 Oct 2013 10:12:45 GMThttp://hdl.handle.net/2117/203452013-10-09T10:12:45ZNicolini, Paolo; Frezzato, DiegonoIn the preceding paper of this series (Part I, P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101(2013)) we have unveiled some ubiquitous features encoded in the systems of polynomial differential equations normally applied in the description of homogeneous and isothermal chemical kinetics
(mass-action law). Here we proceed by investigating a deeply related feature: the appearance of so-called slow manifolds (SMs) which are low-dimensional hyper-surfaces in the neighborhood of which the slow evolution of the reacting system occurs after an initial fast transient. Indeed a geometrical definition of SM, devoid of subjectivity, “naturally” follows in terms of a specific subdimensional domain embedded in the peculiar region of the concentrations phase-space that in Part I we termed as “attractiveness region.” Numerical inspections on simple low-dimensional model cases are presented, including the benchmark case of Davis and Skodje [J. Chem. Phys. 111, 859 (1999)] and the preliminary analysis of a simplified model mechanism of hydrogen combustion.Features in chemical kinetics. I. Signatures of self-emerging dimensional reduction from a general format of the evolution law
http://hdl.handle.net/2117/20344
Title: Features in chemical kinetics. I. Signatures of self-emerging dimensional reduction from a general format of the evolution law
Authors: Nicolini, Paolo; Frezzato, Diego
Abstract: Simplification of chemical kinetics description through dimensional reduction is particularly important to achieve an accurate numerical treatment of complex reacting systems, especially when stiff kinetics are considered and a comprehensive picture of the evolving system is required. To this aim several tools have been proposed in the past decades, such as sensitivity analysis, lumping approaches, and exploitation of time scales separation. In addition, there are methods based on the existence of the so-called slow manifolds, which are hyper-surfaces of lower dimension than the one of the whole phase-space and in whose neighborhood the slow evolution occurs after an initial fast transient. On the other hand, all tools contain to some extent a degree of subjectivity which seems to be irremovable. With reference to macroscopic and spatially homogeneous reacting systems under isothermal conditions, in this work we shall adopt a phenomenological approach to let self-emerge the dimensional reduction from the mathematical structure of the evolution law. By transforming the original system of polynomial differential equations, which describes the chemical evolution, into a universal quadratic format, and making a direct inspection of the high-order time-derivatives of the new dynamic variables, we then formulate a conjecture which leads to the concept of an “attractiveness” region in the phase-space where a well-defined state-dependent rate function ω has the simple evolution math = −ω2 along any trajectory up to the stationary state. This constitutes, by itself, a drastic dimensional reduction from a system of N-dimensional equations (being N the number of chemical species) to a one-dimensional and universal evolution law for such a characteristic rate. Step-by-step numerical inspections on model kinetic schemes are presented. In the companion paper [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)]10.1063/1.4809593 this outcome will be naturally related to the appearance (and hence, to the definition) of the slow manifolds.Wed, 09 Oct 2013 09:59:47 GMThttp://hdl.handle.net/2117/203442013-10-09T09:59:47ZNicolini, Paolo; Frezzato, DiegonoSimplification of chemical kinetics description through dimensional reduction is particularly important to achieve an accurate numerical treatment of complex reacting systems, especially when stiff kinetics are considered and a comprehensive picture of the evolving system is required. To this aim several tools have been proposed in the past decades, such as sensitivity analysis, lumping approaches, and exploitation of time scales separation. In addition, there are methods based on the existence of the so-called slow manifolds, which are hyper-surfaces of lower dimension than the one of the whole phase-space and in whose neighborhood the slow evolution occurs after an initial fast transient. On the other hand, all tools contain to some extent a degree of subjectivity which seems to be irremovable. With reference to macroscopic and spatially homogeneous reacting systems under isothermal conditions, in this work we shall adopt a phenomenological approach to let self-emerge the dimensional reduction from the mathematical structure of the evolution law. By transforming the original system of polynomial differential equations, which describes the chemical evolution, into a universal quadratic format, and making a direct inspection of the high-order time-derivatives of the new dynamic variables, we then formulate a conjecture which leads to the concept of an “attractiveness” region in the phase-space where a well-defined state-dependent rate function ω has the simple evolution math = −ω2 along any trajectory up to the stationary state. This constitutes, by itself, a drastic dimensional reduction from a system of N-dimensional equations (being N the number of chemical species) to a one-dimensional and universal evolution law for such a characteristic rate. Step-by-step numerical inspections on model kinetic schemes are presented. In the companion paper [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)]10.1063/1.4809593 this outcome will be naturally related to the appearance (and hence, to the definition) of the slow manifolds.Ultrafast librational relaxation of H2O in liquid water
http://hdl.handle.net/2117/20138
Title: Ultrafast librational relaxation of H2O in liquid water
Authors: Petersen, Jakob; Möller, Klaus Braagaard; Rey Oriol, Rosendo; Hynes, James T.
Abstract: The ultrafast librational (hindered rotational) relaxation of a rotationally excited H2O molecule in pure liquid water is investigated by means of classical nonequilibrium molecular dynamics simulations and a power and work analysis. This analysis allows the mechanism of the energy transfer from the excited H2O to its water neighbors, which occurs on a sub-100 fs time scale, to be followed in molecular detail, i.e., to determine which water molecules receive the energy and in which degrees of freedom. It is found that the dominant energy flow is to the four hydrogen-bonded water partners in the first hydration shell, dominated by those partners’ rotational motion, in a fairly symmetric fashion over the hydration shell. The minority component of the energy transfer, to these neighboring waters’ translational motion, exhibits an asymmetry in energy reception between hydrogen-bond-donating and -accepting water molecules. The variation of the energy flow characteristics with rotational axis, initial rotational energy excitation magnitude, method of excitation, and temperature is discussed. Finally, the relation of the nonequilibrium results to equilibrium time correlations is investigated.Fri, 13 Sep 2013 15:18:36 GMThttp://hdl.handle.net/2117/201382013-09-13T15:18:36ZPetersen, Jakob; Möller, Klaus Braagaard; Rey Oriol, Rosendo; Hynes, James T.noEquilibrium time, First hydration shell, Non equilibrium, Nonequilibrium molecular dynamics simulation, Rotational axis, Rotational energy, Rotational motion, Translational motionsThe ultrafast librational (hindered rotational) relaxation of a rotationally excited H2O molecule in pure liquid water is investigated by means of classical nonequilibrium molecular dynamics simulations and a power and work analysis. This analysis allows the mechanism of the energy transfer from the excited H2O to its water neighbors, which occurs on a sub-100 fs time scale, to be followed in molecular detail, i.e., to determine which water molecules receive the energy and in which degrees of freedom. It is found that the dominant energy flow is to the four hydrogen-bonded water partners in the first hydration shell, dominated by those partners’ rotational motion, in a fairly symmetric fashion over the hydration shell. The minority component of the energy transfer, to these neighboring waters’ translational motion, exhibits an asymmetry in energy reception between hydrogen-bond-donating and -accepting water molecules. The variation of the energy flow characteristics with rotational axis, initial rotational energy excitation magnitude, method of excitation, and temperature is discussed. Finally, the relation of the nonequilibrium results to equilibrium time correlations is investigated.