Blocking effects in irreversible adsorption of linear macromolecules

A new variant of random sequential adsorption (RSA), namely random sequential ballistic adsorption (RSBA), is proposed to explore the possible role of blocking effects in the adsorption dynamics of ballistically arriving objects. These objects upon adsorption can protrude outside the substrate and in turn can obstruct and hence reject the adsorption of newly arriving objects. Adsorption of linear macromolecules (modeled as infinitesimally thin needles), on a two-dimensional continuum substrate is studied using RSBA model. It is shown analytically that in late time regime, the number n(t) of adsorbed objects at time t follows a power law n(t) ∼ t^α, as in RSA, but with a different exponent, α = 2/3. Computer simulations are also carried out. The simulation results are found to be in close agreement with the analytical results. The exponent behavior for real experimental conditions is also analyzed.     

Effects of mass media on opinion spreading in the Sznajd sociophysics model

In this work we consider the influence of mass media in the dynamics of the two-dimensional Sznajd model. This influence acts as an external field, and it is introduced in the model by means of a probability p of the agents to follow the media opinion. We performed Monte Carlo simulations on square lattices with different sizes, and our numerical results suggest a change on the critical behavior of the model, with the absence of the usual phase transition for p>∼0.18. Another effect of the probability p is to decrease the average relaxation times τ, that are log-normally distributed, as in the standard model. In addition, the τ values depend on the lattice size L in a power-law form, τ∼L^α, where the power-law exponent depends on the probability p.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

On the characterization of periodic signals using third-order statistical functions

In this paper the theoretical errors involved in the determination of a parameter by measuring g(³)(T,τ,τ') and n⁽³⁾(T) are pointed out. The values of this errors are calculated and compared with those obtained by measuring g(²)(T,τ) for a particular case.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

Impact of orientational distribution of adsorbing objects on dynamics of Random Sequential Ballistic Adsorption (RSBA) dynamics

Recently, by proposing a new variant of Random Sequential Adsorption (RSA) namely Random Sequential Ballistic Adsorption (RSBA) model [Pradip B. Shelke, A.G. Banpurkar, S.B. Ogale, A.V. Limaye, Surf. Sci. 601 (2007) 274], we addressed the issue of adsorption dynamics of extended objects where the objects, upon adsorption, protrude outside the substrate. This study brought out the role of the arriving trajectory in the adsorption dynamics. In the present work the possible role of the orientational distribution of the arriving objects in the RSBA dynamics is investigated. The dynamics of RSBA of needles (line segments) is studied analytically and by computer simulation for different types of θ distributions of arriving needles, θ being the angle made by the arriving needle with normal to the substrate. Three types of θ distributions, namely a uniform distribution over the range (0, π/2), a Gaussian distribution and a distribution uniform over the solid angle, are considered. Analytical treatment establishes that in all the three cases, the number n(t) of adsorbed objects at a late time t follows a power law n(t) ∼ t^α, and the exponent α depends on the specifics of the θ distribution. In general, for distribution f(θ) ∝ θ^β, for θ → 0, α is found to be 2/(β + 3). The simulation results are in excellent agreement with the analytical findings and together they reveal that the orientational distribution of arriving objects has significant consequences for the Random Sequential Ballistic Adsorption (RSBA) process.     

Coloring of a one-dimensional lattice by two independent random walkers

A new type of question in random walk theory is formulated and solved for the particular case of a periodic one-dimensional lattice. A “red” and a “blue” random walker perform simultaneous independent simple random walk. Each site is initially uncolored and takes irreversibly the color, red or blue, of the first walker by which it is visited. We study the resulting coloring of the final state, in which each site is either red or blue, on a ring of L sites. We calculate the probability P(n, L) that site n is red, in the scaling limit L → ∞ with n/L fixed, for walkers initially on diametrically opposite sites. We determine by simulation the number of interfaces (that is, pairs of neighboring red and blue sites), for initial separation a between the walkers. This number is ≈ 2.5 for initially diametrically opposite walkers, and appears to increase logarithmically with L/a.     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

Generalized Voigt functions and their derivatives

This paper deals with a special class of functions called generalized Voigt functions H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a) and their partial derivatives, which are useful in the theory of polarized spectral line formation in stochastic media. For n=0 they reduce to the usual Voigt and Faraday-Voigt functions H(x,a) and G(x,a). A detailed study is made of these new functions. Simple recurrence relations are established and employed for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are given for large values of x and a. They are used to examine the range of applicability of the recurrence relations and to construct a numerical algorithm for the calculation of the generalized Voigt functions and of their derivatives valid in a large (x,a) domain. It is also shown that the partial derivatives of the usual H(x,a) and G(x,a) can be expressed in terms of H⁽ⁿ⁾(x,a) and G⁽ⁿ⁾(x,a).     

Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equations

By using a characterization of the concept of analytic representation and a variational approach to self-adjointness introduced in a preceding paper, we prove a theorem, according to which a necessary and sufficient condition for a class $\text{C}$², regular, tensorial, quasi-linear system of field equations to admit an ordered direct analytic representation in terms of the Lagrange equations in a region R of its variables is that the system is self-adjoint in R. We point out as a first corollary that if the ordering requirement is removed from the definition of analytic representation, then the condition of self-adjointness of the field equations is only sufficient for the existence of a Lagrangian density. We then provide as a second corollary a methodology for the computation of the Lagrangian density for the representation of self-adjoint quasi-linear tensorial field equations. This methodology is also particularized for ordinary semilinear systems of tensorial field equations through a third corollary. The above results are interpreted from the viewpoint of interactions. We first recover, through a fourth corollary, the conventional structure of the total Lagrangian density L_Tot = Σ_{1 a}ⁿL_Free^(a) + L_Int for the semilinear form of the field equations, and then introduce through a fifth corollary a generalized structure of the type L_Tot = Σ_{1 a}ⁿL_{Int, I}^(a)L_Free^(a) + L_Int.II for t representations of the field equations in the quasi-linear form. Therefore, our analysis seems to indicate that a general form of representing interacting fields is characterized by (n+1)-interaction terms in the Lagrangian: n multiplicative terms and one additive term to the Lagrangian for the free fields.     

Fluctuation pressure of membrane between walls

We prove that a tensionless membrane, fluctuating harmonically with free ends between two parallel plates of spacing 2d. generates a pressure of the functional form p = (T/Ad)τa(τ), where τ is the dimensionless variable τ ≠ (T/κ)A/d², κ is th curvature elastic constant, and A the area of the plates. For large A, a(τ) becomes a constant which we determine by Monte Carlo simulation to be a_∞ = 0.060±0.003.     

Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Lifetimes of Rydberg states in ions of the group II elements

Total probabilities A _nl of spontaneous radiative transitions, which determine lifetimes τ _nl = 1/A _nl of nS-, nP-, nD- and nF-states in singly charged ions of the group IIa (Be⁺, Mg⁺, Ca⁺, Sr⁺, Ba⁺) and IIb (Zn⁺, Cd⁺, Hg⁺) elements, were calculated in the single-electron Fues’ model potential (FMP) method. An asymptotic dependence is determined for highly excited states with small angular momentums and presented in the form τ _nl = τ _l ⁽⁰⁾ n ³ Q _l (1/n) and numerical values of the factors τ _l ⁽⁰⁾ and coefficients of the cubic polynomial Q _l (x) are calculated, which approximate results of numerical computations with relative error below 2% in the range of states with principal quantum numbers from n = 7 to n ≈ 2000. The comparison of the numerical results with data in literature is presented, and applicability and reliability of single-electron model calculations are discussed in detail for positive singly charged ions of the group II elements.     

Temperature dependence of dispersive hopping transport and diffusion in disordered solids

The time- and temperature-dependent drift mobility μ_d for dispersive transients in disordered solids is $\text{μ}{}_{\mathrm{d}}\text{(T,t) =}\text{L}\text{Et}{}_{\mathrm{T}}$ in terms of distance L, field E and transit time t_T. Since current I ∝ tsu?(1?α) for t <_Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that $\text{μ}{}_{\mathrm{d}}\text{(T) = α[μ}{}_{\mathrm{d}}\text{(T,t)]}{}^{\mathrm{\alpha }}\text{(}\text{L}\text{Eτ}\text{)}{}^{\mathrm{1?\alpha }}$ where τ≈ 10^?13s is estimated. Further $\text{μ}{}_{\mathrm{d}}\text{(T) ∝ exp (}\text{?Δ}{}_0\text{KT}\text{)}$ and the activation energy Δ₀ is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As₂Se₃ is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μ_d(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As₂Se₃ as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ t^α?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ₀+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10^?13?10^?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν₀(t/τ)^α?1 exp(frsol|?Δ₀/KT) which applies also to bimolecular recombination.     

Relaxation dynamics in small clusters: A modified Monte Carlo approach

Relaxation dynamics in two-dimensional atomic clusters consisting of mono-atomic particles interacting through Lennard-Jones (L-J) potential has been investigated using Monte Carlo simulation. A modification of the conventional Metropolis algorithm is proposed to introduce realistic thermal motion of the particles moving in the interacting L-J potential field. The proposed algorithm leads to a quick equilibration from the nonequilibrium cluster configuration in a certain temperature regime, where the relaxation time (τ), measured in terms of Monte Carlo Steps (MCS) per particle, vary inversely with the square root of system temperature (√T) and pressure (P); τ ∝ (P√T)^?1. From this a realistic correlation between MCS and time has been predicted.     

Virasoro type Lie algebras and deformations

The first and second cohomologies of Cartan Type Lie algebras with coefficients in irreducible tensor modules are calculated. The spaceH ¹(L, U) is interpreted as a space of deformations of (L, U)-modules.H ²(L, L)≠0 ifL=S ₂,S ₂ ⁺ orL=H _n ,H _n ⁺ . Lie algebra of divergenceless vector fieldsS ₂ ⁺ has only one nontrivial local deformation. The two-sided simple hamiltonian algebraH _n has 2n ²+n new local deformations in addition to Moyal cocycle. The Lie algebrasL=W _n (n>3),S _n?1(n>2),H _n (n>1),K _n+1(n>1) have 3, 1, 1, 3 nonisomorphic tensor modules with irreducible bases and nonzero 1-cohomologies; respectively, the corresponding numbers for 2-cohomologies are 9, 6, 7 and 9.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Sonochemical syntheses and characterization of nano-sized lead(II) coordination polymer with ligand 1H-1,2,4-triazole-3-carboxylate

Nanoparticles of a two-dimensional coordination polymer, {[Pb(L)(μ_1,1-NCS)(H₂O)]}_n (1), (L⁻ = 1H-1,2,4-triazole-3-carboxylate), have been synthesized by a sonochemical process and characterized by scanning electron microscopy, X-ray powder diffraction, IR spectroscopy and elemental analyses. The thermal stability of compound 1 both its bulk and nano-size has been studied by thermal gravimetric (TG) and differential thermal (DTA) analyses and compared each other. Concentration of initial reagents effects and the role of power ultrasound irradiation on size and morphology of nano-structured compound 1, have been studied. Calcination of the single crystals and nano-sized compound 1 at 400 °C under air atmosphere yields mixture of PbS and Pb₂(SO₄)O nanoparticles. Results show that the size and morphology of the PbS and Pb₂(SO₄)O nanoparticles are dependent upon the particles size of compound 1. A decrease in the particles size of compound 1 leads to a decrease in the particles size of the PbS and Pb₂(SO₄)O.     

Moderate Deviations for Random Field Curie-Weiss Models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization S _n , which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number m, a positive real number ??, and a positive integer k such that (S _n ?nm)/n ^?? satisfies a moderate deviations principle with speed n ^1?2k(1???) and rate function ??x ^2k /(2k)!, where 1?1/(2(2k?1))<??<1.     

Topological cross sections in hadron-nucleon and hadron-nucleus collisions at very high energies

We apply our microscopic model for the topological cross section σ_n to produce n charged particles in hadron-proton interactions to hadron-nucleus scattering. The model is based on a stochastic branching process for hadronization. We calculate multiplicity distributions of hadron-nucleus collisions for 50 GeV ? E_L ? 400 GeV based on a multiple collision model. The production of “grey” $\text{(0.3 <}\text{ν}\text{c}\text{< 0.7)}$ particles is considered together with the shower $\text{(}\text{ν}\text{c}\text{> 0.7)}$ particles in order to test the model for higher number of collisions. The joint probability distribution of numbers of shower and grey particles F(n_s, n_g) is calculated. Finally, we critically compare the results to experimental data.