Compression of polymer brushes: quantitative comparison of self-consistent field theory with experiment

The self-consistent field theory (SCFT) prediction for the compression force between two semi-dilute polymer brushes is compared to the benchmark experiments of Taunton et al. [Nature, 1988, 332, 712]. The comparison is done with previously established parameters, and without any fitting parameters whatsoever. The SCFT provides a significant quantitative improvement over the classical strong-stretching theory (SST), yielding excellent quantitative agreement with the experiment. Contrary to earlier suggestions, chain fluctuations cannot be ignored for normal experimental conditions. Although the analytical expressions of SST provide invaluable aids to understanding the qualitative behavior of polymeric brushes, the numerical SCFT is necessary in order to provide quantitatively accurate predictions.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Electrorhythmogenesis and anaesthesia in a physiological mean field theory

We solve eight partial-differential, two-dimensional, nonlinear mean field equations, which describe the dynamics of large populations of cortical neurons. Linearized versions of these equations have been used to generate the strong resonances observed in the human EEG, in particular the α-rhythm (8–), with physiologically plausible parameters. We extend these results here by numerically solving the full equations on a cortex of realistic size, which receives appropriately “colored” noise as extra-cortical input. A brief summary of the numerical methods is provided. As an outlook to future applications, we explain how the effects of GABA-enhancing general anaesthetics can be simulated and present first results.

Understanding the effects of anesthetic agents on the EEG through neural field theory

Anesthetic and analgesic agents act through a diverse range of pharmacological mechanisms. Existing empirical data clearly shows that such "microscopic" pharmacological diversity is reflected in their "macroscopic" effects on the human electroencephalogram (EEG). Based on a detailed mesoscopic neural field model we theoretically posit that anesthetic induced EEG activity is due to selective parametric changes in synaptic efficacy and dynamics. Specifically, on the basis of physiologically constrained modeling, it is speculated that the selective modification of inhibitory or excitatory synaptic activity may differentially effect the EEG spectrum. Such results emphasize the importance of neural field theories of brain electrical activity for elucidating the principles whereby pharmacological agents effect the EEG. Such insights will contribute to improved methods for monitoring depth of anesthesia using the EEG.

Neural population models and cortical field theory: overview

The term neural population models (NPMs) is used here as catchall for a wide range of approaches that have been variously called neural mass models, mean field models, neural field models, bulk models, and so forth. All NPMs attempt to describe the collective action of neural assemblies directly. Some NPMs treat the densely populated tissue of cortex as an excitable medium, leading to spatially continuous cortical field theories (CFTs). An indirect approach would start by modelling individual cells and then would explain the collective action of a group of cells by coupling many individual models together. In contrast, NPMs employ collective state variables, typically defined as averages over the group of cells, in order to describe the population activity directly in a single model. The strength and the weakness of his approach are hence one and the same: simplification by bulk. Is this justified and indeed useful, or does it lead to oversimplification which fails to capture the pheno ...

Comments on regularization of identity based solutions in string field theory

We analyze the consistency of the recently proposed regularization of an identity based solution in open bosonic string field theory. We show that the equation of motion is satisfied when it is contracted with the regularized solution itself. Additionally, we propose a similar regularization of an identity based solution in the modified cubic superstring field theory.

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E(N+1) - E(n))t). The gap E(N+1) - E(n) can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m(b) in HQET.

Ice and pulsed electromagnetic field to reduce pain and swelling after distal radius fractures

Objective: To examine the relative effectiveness of ice therapy and/or pulsed electromagnetic field in reducing pain and swelling after the immobilization period following a distal radius fracture.Methods: A total of 83 subjects were randomly allocated to receive 30 minutes of either ice plus pulsed electromagnetic field (group A); ice plus sham pulsed electromagnetic field (group B); pulsed electromagnetic field alone (group C), or sham pulsed electromagnetic field treatment for 5 consecutive days (group D). All subjects received a standard home exercise programme. A visual analogue scale was used for recording pain; volumetric displacement for measuring the swelling of the forearm; and a hand-held goniometer for measuring the range of wrist motions before treatment on days 1, 3 and 5.Results: At day 5, a significantly greater cumulative reduction in the visual analogue scores as well as ulnar deviation range of motion was found in group A than the other 3 groups. For volumetric measurement and pronation, participants in group A performed better than subjects in group D but not those in group B.Conclusion: The addition of pulsed electromagnetic field to ice therapy produces better overall treatment outcomes than ice alone, or pulsed electromagnetic field alone in pain reduction and range of joint motion in ulnar deviation and flexion for a distal radius fracture after an immobilization period of 6 weeks.

A study of the effects of flux density and frequency on Pulsed electromagnetic field on Neurite outgrowth in PC12 cells.

The aim of this study was to investigate the influence of pulsed electromagnetic fields with various flux densities and frequencies on neurite outgrowth in PC12 rat pheochromocytoma cells. We have studied the percentage of neurite-bearing cells, average length of neurites and directivity of neurite outgrowth in PC12 cells cultured for 96 hours in the presence of nerve growth factor (NGF). PC12 cells were exposed to 50 Hz pulsed electromagnetic fields with a flux density of 1.37 mT, 0.19 mT and 0.016 mT respectively. The field was generated through a Helmholtz coil pair housed in one incubator and the control samples were placed in another identical incubator. It was found that exposure to both a relatively high flux density (1.37 mT) and a medium flux density (0.19 mT) inhibited the percentage of neurite-bearing cells and promoted neurite length significantly. Exposure to high flux density (1.37 mT) also resulted in nearly 20% enhancement of neurite directivity along the field direction. However, exposure to low flux density field (0.016 mT) had no detectable effect on neurite outgrowth. We also studied the effect of frequency at the constant flux density of 1.37 mT. In the range from 1 ~ 100 Hz, only 50 and 70 Hz pulse frequencies had significant effects on neurite outgrowth. Our study has shown that neurite outgrowth in PC12 cells is sensitive to flux density and frequency of pulsed electromagnetic field.

Structuring in liquid alkanes between solid surfaces : force measurements and mean-field theory

Measurements have been made of the solvation forces between mica surfaces in the even-numbered n-alkanes from hexane to hexadecane. In all cases the force law is qualitatively very similar, characterized by a decaying oscillatory function of distance, as occurs for simple isotropic liquids. The spacing between successive minima in the force does not increase with carbon number, and is comparable to the width of a linear alkane molecule rather than its length or any average diameter. This suggests that the alkanes have some tendency towards a parallel orientation near the mica surfaces. The measurements give no indication of any strong repulsive component expected from mean-field theories of higher alkanes or polymers. The results of one such theory are presented, and the reasons for its failure to match the experimental data are discussed.