Non-Linear Poisson-Boltzmann Theory of a Wigner-Seitz Model for Swollen Clays

Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of microscopic co and counterions, within a primitive model description. The non-linear Poisson-Boltzmann (PB) equation for the electrostatic potential profile is solved numerically within a highly efficient Green's function formulation. Previous predictions of linearised Poisson-Boltzmann (LPB) theory are confirmed at a qualitative level, but large quantitative differences between PB and LPB theories are found at physically relevant values of the charge carried by the platelets. A hybrid theory treating edge effect at the linearised level yields good potential profiles. The force between two coaxial platelets, calculated within PB theory, is an order of magnitude smaller than predicted by LPB theoryComment: 22 pages, 12 figures, accepted in Physical Review

Weighted Estimates for the Berezin Transform and Bergman Projection on the Unit Ball in Cn\mathbb{C}^{n}

Using modern techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Bergman spaces on the unit ball in $\mathbb{C}^n$. The estimates are in terms of the Bekolle-Bonami constant of the weight.Comment: v1 19 page

Dynamic Compression of in situ Grown Living Polymer Brush: Simulation and Experiment

A comparative dynamic Monte Carlo simulation study of polydisperse living polymer brushes, created by surface initiated living polymerization, and conventional polymer monodisperse brush, comprising linear polymer chains, grafted to a planar substrate under good solvent conditions, is presented. The living brush is created by end-monomer (de)polymerization reaction after placing an array of initiators on a grafting plane in contact with a solution of initially non-bonded segments (monomers). At equilibrium, the monomer density profile \phi(z) of the LPB is found to decline as \phi(z) ~ z^{-\alpha} with the distance from the grafting plane z, while the distribution of chain lengths in the brush scales as c(N) ~ N^{-\tau}. The measured values \alpha = 0.64 and \tau = 1.70 are very close to those, predicted within the framework of the Diffusion-Limited Aggregation theory, \alpha = 2/3 and \tau = 7/4. At varying mean degree of polymerization (from L = 28 to L = 170) and effective grafting density (from \sigma_g = 0.0625 to \sigma_g = 1.0), we observe a nearly perfect agreement in the force-distance behavior of the simulated LPB with own experimental data obtained from colloidal probe AFM analysis on PNIPAAm brush and with data obtained by Plunkett et. al., [Langmuir 2006, 22, 4259] from SFA measurements on same polymer

Perceptual bias, more than age, impacts on eye movements during face processing

Consistent with the right hemispheric dominance for face processing, a left perceptual bias (LPB) is typically demonstrated by younger adults viewing faces and a left eye movement bias has also been revealed. Hemispheric asymmetry is predicted to reduce with age and older adults have demonstrated a weaker LPB, particularly when viewing time is restricted. What is currently unclear is whether age also weakens the left eye movement bias. Additionally, a right perceptual bias (RPB) for facial judgments has less frequently been demonstrated, but whether this is accompanied by a right eye movement bias has not been investigated. To address these issues older and younger adults’ eye movements and gender judgments of chimeric faces were recorded in two time conditions. Age did not significantly weaken the LPB or eye movement bias; both groups looked initially to the left side of the face and made more fixations when the gender judgment was based on the left side. A positive association was found between LPB and initial saccades in the freeview condition and with all eye movements (initial saccades, number and duration of fixations) when time was restricted. The accompanying eye movement bias revealed by LPB participants contrasted with RPB participants who demonstrated no eye movement bias in either time condition. Consequently, increased age is not clearly associated with weakened perceptual and eye movement biases. Instead an eye movement bias accompanies an LPB (particularly under restricted viewing time conditions) but not an RPB

LO-phonon assisted polariton lasing in a ZnO based microcavity

Polariton relaxation mechanisms are analysed experimentally and theoretically in a ZnO-based polariton laser. A minimum lasing threshold is obtained when the energy difference between the exciton reservoir and the bottom of the lower polariton branch is resonant with the LO phonon energy. Tuning off this resonance increases the threshold, and exciton-exciton scattering processes become involved in the polariton relaxation. These observations are qualitatively reproduced by simulations based on the numerical solution of the semi-classical Boltzmann equations

The organisation of spinoparabrachial neurons in the mouse

The anterolateral tract (ALT), which originates from neurons in lamina I and the deep dorsal horn, represents a major ascending output through which nociceptive information is transmitted to brain areas involved in pain perception. Although there is detailed quantitative information concerning the ALT in the rat, much less is known about this system in the mouse, which is increasingly being used for studies of spinal pain mechanisms because of the availability of genetically modified lines. The aim of this study was therefore to determine the extent to which information about the ALT in the rat can be extrapolated to the mouse. Our results suggest that as in the rat, most lamina I ALT projection neurons in the lumbar enlargement can be retrogradely labelled from the lateral parabrachial area, that the great majority of these cells (~90%) express the neurokinin 1 receptor (NK1r), and that these are larger than other NK1r-expressing neurons in this lamina. This means that many lamina I spinoparabrachial cells can be identified in NK1r-immunostained sections from animals that have not received retrograde tracer injections. However, we also observed certain species differences, in particular we found that many spinoparabrachial cells in lamina III-IV lack the NK1r, meaning that they cannot be identified based solely on expression of this receptor. We also provide evidence that the vast majority of spinoparabrachial cells are glutamatergic, and that some express substance P. These findings will be important for studies designed to unravel the complex neuronal circuitry that underlies spinal pain processing

Poisson-Boltzmann Theory of Charged Colloids: Limits of the Cell Model for Salty Suspensions

Thermodynamic properties of charge-stabilised colloidal suspensions are commonly modeled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing solution of the nonlinear PB equation, the cell model neglects microion-induced correlations between macroions, precluding modeling of macroion ordering phenomena. An alternative approach, avoiding artificial constraints of cell geometry, maps a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interactions. In practice, effective-interaction models are usually based on linear screening approximations, which can accurately describe nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions of nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modeling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate in predicting osmotic pressures of deionized suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions grows, leading predictions of the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to soft materials.Comment: 27 pages, 5 figures, special issue of Journal of Physics: Condensed Matter on "Classical density functional theory methods in soft and hard matter

Strong Uniform Attractors for Non-Autonomous Dissipative PDEs with non translation-compact external forces

We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces which are not translation compact, but nevertheless allow to verify the attraction in a strong topology of the phase space and discuss in a more detailed way the class of so-called normal external forces introduced before. We also develop a unified approach to verify the asymptotic compactness for such systems based on the energy method and apply it to a number of equations of mathematical physics including the Navier-Stokes equations, damped wave equations and reaction-diffusing equations in unbounded domains

Looking for Light Pseudoscalar Bosons in the Binary Pulsar System J0737-3039

We present numerical calculations of the photon-light-pseudoscalar-boson conversion in the recently discovered binary pulsar system J0737-3039. Light pseudoscalar bosons (LPBs) oscillate into photons in the presence of strong magnetic fields. In the context of this binary pulsar system, this phenomenon attenuates the light beam emitted by one of the pulsars, when the light ray goes through the magnetosphere of the companion pulsar. We show that such an effect is observable in the gamma-ray band since the binary pulsar is seen almost edge-on, depending on the value of the LPB mass and on the strenght of its two-photon coupling. Our results are surprising in that they show a very sharp and significant (up to 50%) transition probability in the gamma-ray ($>$ tens of MeV) domain. The observations can be performed by the upcoming NASA GLAST mission.Comment: to appear in Phys. Rev. Let