Critical behavior of the aqueous electrolytic system 3-methylpyridine+D2O+NaBr

The system 3-methylpyridine(3MP)+water(H2O)+NaBr has been the subject of an intense scientific debate since the work of Jacob [Phys. Rev. E. 58, 2188 (1988)] and Anisimov [Phys. Rev. Lett. 85, 2336 (2000)]. The crossover critical behavior of this system seemed to show remarkable sensitivity to the weight fraction (X) of the ionic impurity NaBr. In the range X <= 0.10 the system displayed Ising behavior and a pronounced crossover to mean-field behavior in the range 0.10 <= X <= 0.16. A complete mean-field behavior was observed at X=0.17, a result that was later attributed to the existence of long-living nonequilibrium states in this system [Kostko , Phys. Rev. E. 70, 026118 (2004)]. In this paper, we report the near-critical behavior of osmotic susceptibility in the isotopically related ternary system, 3MP+heavy water(D2O)+NaBr. Detailed light-scattering experiments performed at exactly the same NaBr concentrations as investigated by Jacob reveal that the system 3MP+D2O+NaBr shows a simple Ising-type critical behavior with gamma similar or equal to 1.24 and nu similar or equal to 0.63 over the entire NaBr concentration range 0 <= X <= 0.1900. The crossover behavior is predominantly nonmonotonic and is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (gamma(eff)) reveals that the crossover behavior is nonmonotonic for 0 <= X <= 0.1793 and tends to become monotonic for X > 0.1793. The correlation length amplitude xi(o), has a value of similar or equal to 2 A for 0.0250 <= X <= 0.1900, whereas for X=0, xi(o)similar or equal to 3.179 A. Since isotopic H -> D substitution is not expected to change the critical behavior of the system, our results support the recent results obtained by Kostko [Phys. Rev. E. 70, 026118 (2004)] that 3MP+H2O+NaBr exhibits universal Ising-type critical behavior typical for other aqueous solutions.

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

Investigations on the melting and bending modulus of polymer grafted bilayers using dissipative particle dynamics

Understanding the influence of polymer grafted bilayers on the physicomechanical properties of lipid membranes is important while developing liposomal based drug delivery systems. The melting characteristics and bending moduli of polymer grafted bilayers are investigated using dissipative particle dynamics simulations as a function of the amount of grafted polymer and lipid tail length. Simulations are carried out using a modified Andersen barostat, whereby the membrane is maintained in a tensionless state. For lipids made up of four to six tail beads, the transition from the low temperature L-beta phase to the L-alpha phase is lowered only above a grafting fraction of G(f)=0.12 for polymers made up of 20 beads. Below G(f)=0.12 small changes are observed only for the HT4 bilayer. The bending modulus of the bilayers is obtained as a function of G(f) from a Fourier analysis of the height fluctuations. Using the theory developed by Marsh Biochim. Biophys. Acta 1615, 33 (2003)] for polymer grafted membranes, the contributions to the bending modulus due to changes arising from the grafted polymer and bilayer thinning are partitioned. The contributions to the changes in kappa from bilayer thinning were found to lie within 11% for the lipids with four to six tail beads, increasing to 15% for the lipids containing nine tail beads. The changes in the area stretch modulus were also assessed and were found to have a small influence on the overall contribution from membrane thinning. The increase in the area per head group of the lipids was found to be consistent with the scalings predicted by self-consistent mean field results. (C) 2010 American Institute of Physics.

Effect of interface friction on the mechanics of indentation of a finite layer resting on a rigid substrate

Copper strips of 2.5 mm thickness resting on stainless steel anvils were normally indented by wedges under nominal plane strain conditions. Inflections in the hardness-penetration characteristics were identified. Inflections separate stages where each stage has typical mechanics of deformation. These are arrived at by studying the distortion of 0.125 mm spaced grids inscribed on the deformation plane of the strip. The sensitivity of hardness and deformation mechanics to wedge angle and the interfacial friction between strip and anvil were investigated within the framework of existing slip line field models of indentation of semi-infinite and finite blocks.

Metal-Insulator Transition in the Hubbard Model on a Triangular Lattice

We discuss the results of an extensive mean-field investigation of the half-filled Hubbard model on a triangular lattice at zero temperature. At intermediate U we find a first-order metal-insulator transition from an incommensurate spiral magnetic metal to a semiconducting state with a commensurate linear spin density wave ordering stabilized by the competition between the kinetic energy and the frustrated nature of the magnetic interaction. At large U the ground state is that of a classical triangular antiferromagnet within our approximation. In the incommensurate spiral metallic phase the Fermi surface has parts in which the wave function renormalization Z is extremely small. The evolution of the Fermi surface and the broadening of the quasi-particle band along with the variation of the plasma frequency and a charge stiffness constant with U/t are discussed.

Spiral states in the square-lattice Hubbard model

We present a variety of physical implications of a mean-field theory for spiral spin-density-wave states in the square-lattice Hubbard model for small deviations from half filling. The phase diagram with the paramagnetic metal, two spiral (semimetallic) states, and ferromagnet is calculated. The momentum distribution function and the (quasiparticle) density of states are discussed. There is a significant broadening of the quasiparticle bands when the antiferromagnetic insulator is doped. The evolution of the Fermi surface and the variation of the plasma frequency and a charge-stiffness constant with U/t and δ are calculated. The connection to results based on the Schwinger-boson-slave-fermion formalism is made.

The shear dynamo problem for small magnetic Reynolds numbers

We study large-scale kinematic dynamo action due to turbulence in the presence of a linear shear flow in the low-conductivity limit. Our treatment is non-perturbative in the shear strength and makes systematic use of both the shearing coordinate transformation and the Galilean invariance of the linear shear flow. The velocity fluctuations are assumed to have low magnetic Reynolds number (Re-m), but could have arbitrary fluid Reynolds number. The equation for the magnetic fluctuations is expanded perturbatively in the small quantity, Re-m. Our principal results are as follows: (i) the magnetic fluctuations are determined to the lowest order in Rem by explicit calculation of the resistive Green's function for the linear shear flow; (ii) the mean electromotive force is then calculated and an integro-differential equation is derived for the time evolution of the mean magnetic field. In this equation, velocity fluctuations contribute to two different kinds of terms, the 'C' and 'D' terms, respectively, in which first and second spatial derivatives of the mean magnetic field, respectively, appear inside the space-time integrals; (iii) the contribution of the D term is such that its contribution to the time evolution of the cross-shear components of the mean field does not depend on any other components except itself. Therefore, to the lowest order in Re-m, but to all orders in the shear strength, the D term cannot give rise to a shear-current-assisted dynamo effect; (iv) casting the integro-differential equation in Fourier space, we show that the normal modes of the theory are a set of shearing waves, labelled by their sheared wavevectors; (v) the integral kernels are expressed in terms of the velocity-spectrum tensor, which is the fundamental dynamical quantity that needs to be specified to complete the integro-differential equation description of the time evolution of the mean magnetic field; (vi) the C term couples different components of the mean magnetic field, so they can, in principle, give rise to a shear-current-type effect. We discuss the application to a slowly varying magnetic field, where it can be shown that forced non-helical velocity dynamics at low fluid Reynolds number does not result in a shear-current-assisted dynamo effect.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Glass Transition in the Density Functional Theory of Freezing

A mean-field description of the glass transition in the hard-sphere system is obtained by numerically locating "glassy" minima of a model free-energy functional. These minima, characterized by inhomogeneous but aperiodic density distributions, appear as the average density is increased above the value at which equilibrium crystallization takes place. Investigations of the density distribution and local bond-orientational order at these minima yield results similar to those obtained from simulations.

Origin of the insulating state in NaCuO2

We study the electronic structure of NaCuO2 by analysing experimental core level photoemission and X-ray absorption spectra using a cluster as well as an Anderson impurity Hamiltonian including the band structure of the oxygen sublattice. We show that the X-ray absorption results unambiguously establish a negative value of the charge transfer energy, A. Further, mean-field calculations for the edge-shared one-dimensional CuO2 lattice of NaCuO2 within the multiband Hubbard Hamiltonian show that the origin of the insulating nature lies in the band structure rather than in the correlation effects. LMTO-ASA band structure calculations suggest that NaCuO2 is an insulator with a gap of around 1 eV.

An Efficient Simulated Annealing With a Valid Solution Mechanism For TDMA Brodcast Scheduling problem

This paper presents an efficient Simulated Annealing with valid solution mechanism for finding an optimum conflict-free transmission schedule for a broadcast radio network. This is known as a Broadcast Scheduling Problem (BSP) and shown as an NP-complete problem, in earlier studies. Because of this NP-complete nature, earlier studies used genetic algorithms, mean field annealing, neural networks, factor graph and sum product algorithm, and sequential vertex coloring algorithm to obtain the solution. In our study, a valid solution mechanism is included in simulated annealing. Because of this inclusion, we are able to achieve better results even for networks with 100 nodes and 300 links. The results obtained using our methodology is compared with all the other earlier solution methods.

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Effect of fluctuations on the freezing of a colloidal suspension in an external periodic potential

We incorporate the effects of fluctuations in a density functional analysis of the freezing of a colloidal liquid in the presence of an external potential generated by interfering laser beams. A mean-field treatment, using a density functional theory, predicts that with the increase in the strength of the modulating potential, the freezing transition changes from a first order to a continuous one via a tricritical point for a suitable choice of the modulating wavevectors. We demonstrate here that the continuous nature of the freezing transition at large values of the external potential V-e survives the presence of fluctuations. We also show that fluctuations tend to stabilize the liquid phase in the large V-e regime.

Magnetism, charge ordering, and metal-insulator transition in the lanthanum manganites

We examine the magnetic and structural properties of the lanthanum manganite-based double-exchange magnets exhibiting colossal magnetoresistance. A model Hamiltonian containing the double-exchange, superexchange, and the Hubbard terms, with parameters obtained from density–functional calculations (Ref. 1), is studied within a mean-field approximation both at temperature T=0 and T>0 and with the effects of the magnetic field included. The phase diagrams we obtain with magnetic and charge-ordered phases enable us to examine the competition between the double- and superexchange terms as functions of doping and temperature. Our theoretical study provides a qualitative understanding of the phase diagram observed in the experiments. © 1997 American Institute of Physics.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.