On the transition from localized to delocalized electronic states in divalent-metal clusters

The transition from van der Waals to covalent bonding, which is expected to occur in divalent-metal clusters with increasing cluster size, is discussed. We propose a model which takes into account, within the same electronic theory, the three main competing contributions, namely the kinetic energy of the electrons, the Coulomb interactions between electrons, and the s \gdw p intraatomic transitions responsible for van der Waals like bonding. The model is solved by taking into account electron correlations using a generalized Gutzwiller approximation (slave boson method). The occurrence of electron localization is studied as a function of the interaction parameters and cluster size.

Femtosecond dynamics of molecules and clusters

The real-time dynamics of multiphoton ionization and fragmentation of molecules - Na_2 , Na_3 - and clusters - Na_n, Hg_n - has been studied in molecular beam experiments employing ion and electron spectroscopy together with femtosecond pump-probe techniques. Experiments with Na_2 and Na_3 reveal unexpected features of the dynamics of the absorption of several photons as seen in the one- and three dimensional vibrational wave packet motion in different potential surfaces and in high laser fields. Cluster size dependent studies of physical properties such as absorption resonances, lifetimes and decay channels have been performed using tunable femtosecond light pulses in resonance enhanced multiphoton ionization (REMPI) of the cluster size under investigation. This method failed in ns-laser experiments due to the ultrafast decay of the studied cluster. For Na_n, cluster we find that for cluster sizes n \le 21 molecular excitations and properties prevail over collective excitations of plasmon-like resonances. In the case of Hg_n cluster prompt formation of singly and doubly charged cluster are observed up to n \approx 60. The transient multiphoton ionization spectra show a 'short' time wave packet dynamics, which is identical for singly and doubly charged mercury clusters while the 'long' time fragmentation dynamics is different.

Mechanisms and dynamics of protein clustering on a solid surface

A methodology for discovering the mechanisms and dynamics of protein clustering on solid surfaces is presented. In situ atomic force microscopy images are quantitatively compared to Monte Carlo simulations using cluster statistics to differentiate various models. We study lysozyme adsorption on mica as a model system and find that all surface-supported clusters are mobile, not just the monomers, with diffusion constant inversely related to cluster size. The surface monomer diffusion constant is measured to be D1∼9×10-16  cm2 s-1, such a low value being difficult to measure using other techniques.

Theory of enhanced magnetic anisotropy induced by Pt adatoms on two-dimensional Co clusters supported on a Pt(111) substrate

Calculations are reported of the magnetic anisotropy energy of two-dimensional (2D) Co nanostructures on a Pt(111) substrate. The perpendicular magnetic anisotropy (PMA) of the 2D Co clusters strongly depends on their size and shape, and rapidly decreases with increasing cluster size. The PMA calculated is in reasonable agreement with experimental results. The sensitivity of the results to the Co-Pt spacing at the interface is also investigated and, in particular, for a complete Co monolayer we note that the value of the spacing at the interface determines whether PMA or in-plane anisotropy occurs. We find that the PMA can be greatly enhanced by the addition of Pt adatoms to the top surface of the 2D Co clusters. A single Pt atom can induce in excess of 5 meV to the anisotropy energy of a cluster. In the absence of the Pt adatoms the PMA of the Co clusters falls below 1 meV/Co atom for clusters of about 10 atoms whereas, with Pt atoms added to the surface of the clusters, a PMA of 1 meV/Co atom can be maintained for clusters as large as about 40 atoms. The effect of placing Os atoms on the top of the Co clusters is also considered. The addition of 5d atoms and clusters on the top of ferromagnetic nanoparticles may provide an approach to tune the magnetic anisotropy and moment separately.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Start-up rheometry of highly polydisperse magnetorheological fluids: experiments and simulations

An extensive experimental and simulation study is carried out in conventional magnetorheological fluids formulated by dispersion of mixtures of carbonyl iron particles having different sizes in Newtonian carriers. Apparent yield stress data are reported for a wide range of polydispersity indexes (PDI) from PDI = 1.63 to PDI = 3.31, which for a log-normal distribution corresponds to the standard deviation ranging from to . These results demonstrate that the effect of polydispersity is negligible in this range in spite of exhibiting very different microstructures. Experimental data in the magnetic saturation regime are in quantitative good agreement with particle-level simulations under the assumption of dipolar magnetostatic forces. The insensitivity of the yield stresses to the polydispersity can be understood from the interplay between the particle cluster size distribution and the packing density of particles inside the clusters.

Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

Observation of long-range, near-side angular correlations in proton-proton collisions at the LHC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Layered Clustering Communication Protocol for Wireless Sensor Networks

In this paper, we propose a Layered Clustering Hierarchy (LCH) communication protocol for Wireless Sensor Networks (WSNs). The design of LCH has two goals: scalability and energy-efficiency. In LCH, the sensor nodes are organized as a layered clustering structure. Each layer runs a distributed clustering protocol. By randomizing the rotation of cluster heads in each layer, the energy load is distributed evenly across sensors in the network. Our simulations show that LCH is effective in densely deployed sensor networks. On average, 70% of live sensor nodes are involved directly in the clustering communication hierarchy. Moreover, the simulations also show that the energy load and dead nodes are distributed evenly over the network. As studies prove that the performance of LCH depends mainly on the distributed clustering protocol, the location of cluster heads and cluster size are two critical factors in the design of LCH.

Effect of hydrogen bond formation on the elastic molecular scattering: a case study with methanol

Rayleigh optical activities of small hydrogen-bonded methanol clusters containing two to five molecules are reported. For the methanol trimer, tetramer, and pentamer both cyclic and linear structures are considered. After the geometry optimizations, the dipole moments and the dipole polarizabilities (mean, interaction, and anisotropic components) are calculated using HF, MP2 and DFT (B3LYP, B3P86 and BH&HLYP) with aug-cc-pVDZ extended basis set. The polarizabilities are used to analyse the depolarization ratios and the Rayleigh scattering activities. The variations in the activity and in the depolarization for Rayleigh scattered radiation with the increase in the cluster size for both cyclic and linear structures are analysed.

Encapsulation of small magnetic clusters in fullerene cages: A density functional theory investigation within van der Waals corrections

The encapsulation of magnetic transition-metal (TM) clusters inside carbon cages (fullerenes, nanotubes) has been of great interest due to the wide range of applications, which spread from medical sensors in magnetic resonance imaging to photonic crystals. Several theoretical studies have been reported; however, our atomistic understanding of the physical properties of encapsulated magnetic TM 3d clusters is far from satisfactory. In this work, we will report general trends, derived from density functional theory within the generalized gradient approximation proposed by Perdew, Burke, and Ernzerhof (PBE), for the encapsulation properties of the TMm@C-n (TM = Fe, Co, Ni; m = 2-6, n = 60,70,80,90) systems. Furthermore, to understand the role of the van der Waals corrections to the physical properties, we employed the empirical Grimme's correction (PBE + D2). We found that both PBE and PBE + D2 functionals yield almost the same geometric parameters, magnetic and electronic properties, however, PBE + D2 strongly enhances the encapsulation energy. We found that the center of mass of the TMm clusters is displaced towards the inside C-n surfaces, except for large TMm clusters (m = 5 and 6). For few cases, e. g., Co-4 and Fe-4, the encapsulation changes the putative lowest-energy structure compared to the isolated TMm clusters. We identified few physical parameters that play an important role in the sign and magnitude of the encapsulation energy, namely, cluster size, fullerene equatorial diameter, shape, curvature of the inside C-n surface, number of TM atoms that bind directly to the inside C-n surface, and the van der Waals correction. The total magnetic moment of encapsulated TMm clusters decreases compared with the isolated TMm clusters, which is expected due to the hybridization of the d-p states, and strongly depends on the size and shape of the fullerene cages.

Constraining mass and shape of galaxy clusters through large scale structures

The mass estimation of galaxy clusters is a crucial point for modern cosmology, and can be obtained by several different techniques. In this work we discuss a new method to measure the mass of galaxy clusters connecting the gravitational potential of the cluster with the kinematical properties of its surroundings. We explore the dynamics of the structures located in the region outside virialized cluster, We identify groups of galaxies, as sheets or filaments, in the cluster outer region, and model how the cluster gravitational potential perturbs the motion of these structures from the Hubble fow. This identification is done in the redshift space where we look for overdensities with a filamentary shape. Then we use a radial mean velocity profile that has been found as a quite universal trend in simulations, and we fit the radial infall velocity profile of the overdensities found. The method has been tested on several cluster-size haloes from cosmological N-body simulations giving results in very good agreement with the true values of virial masses of the haloes and orientation of the sheets. We then applied the method to the Coma cluster and even in this case we found a good correspondence with previous. It is possible to notice a mass discrepancy between sheets with different alignments respect to the center of the cluster. This difference can be used to reproduce the shape of the cluster, and to demonstrate that the spherical symmetry is not always a valid assumption. In fact, if the cluster is not spherical, sheets oriented along different axes should feel a slightly different gravitational potential, and so give different masses as result of the analysis described before. Even this estimation has been tested on cosmological simulations and then applied to Coma, showing the actual non-sphericity of this cluster.

Quantum-Mechanical Investigation of Large Water Clusters

The PM3 quantum-mechanical method has been used to study large water clusters ranging from 8 to 42 water molecules. These large clusters are built from smaller building blocks. The building blocks include cyclic tetramers, pentamers, octamers, and a pentagonal dodecahedron cage. The correlations between the strain energy resulting from bending of the hydrogen bonds formed by different cluster motifs and the number of waters involved in the cluster are discussed. The PM3 results are compared with TIP4P potential and ab initio results. The number of net hydrogen bonds per water increases with the cluster size. This places a limit on the size of clusters that would fit the Benson model of liquid water. Many of the 20-mer clusters fit the Benson model well. Calculations of the ion cluster (H20)4o(H30+)2 reveal that the m/e ratio obtainable by mass spectrometry experiments can uniquely indicate the conformation of the 20 water pentagonal dodecahedron cage present in the larger clusters.