On the spectral properties of L_{+-} in three dimensions

This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators which arise in this setting, traditionally denoted by L_{+-}, satisfy the gap property, at least over the radial functions. This means that the interval (0,1] does not contain any eigenvalues of L_{+-} and that the threshold 1 is neither an eigenvalue nor a resonance. The gap property is required in order to prove scattering to the ground states for solutions starting on the center-stable manifold associated with these states. This paper therefore provides the final installment in the proof of this scattering property for the cubic Klein-Gordon and Schrodinger equations in the radial case, see the recent theory of Nakanishi and the third author, as well as the earlier work of the third author and Beceanu on NLS. The method developed here is quite general, and applicable to other spectral problems which arise in the theory of nonlinear equations

The Curious Question of Exercise-Induced Pulmonary Edema

The question of whether pulmonary edema develops during exercise on land is controversial. Yet, the development of pulmonary edema during swimming and diving is well established. This paper addresses the current controversies that exist in the field of exercise-induced pulmonary edema on land and with water immersion. It also discusses the mechanisms by which pulmonary edema can develop during land exercise, swimming, and diving and the current gaps in knowledge that exist. Finally, this paper discusses how these fields can continue to advance and the areas where clinical knowledge is lacking

Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers

We compute phase diagrams for $A_nB_m$ starblock copolymers in the strong-segregation regime as a function of volume fraction $\phi$, including bicontinuous phases related to minimal surfaces (G, D, and P surfaces) as candidate structures. We present the details of a general method to compute free energies in the strong segregation limit, and demonstrate that the gyroid G phase is the most nearly stable among the bicontinuous phases considered. We explore some effects of conformational asymmetry on the topology of the phase diagram.Comment: 14 pages, latex, 21 figures, to appear in Macromolecule

Domains in Melts of Comb-Coil Diblock Copolymers: Superstrong Segregation Regime

Conditions for the crossover from the strong to the superstrong segregation regime are analyzed for the case of comb-coil diblock copolymers. It is shown that the critical interaction energy between the components required to induce the crossover to the superstrong segregation regime is inversely proportional to mb = 1 + n/m, where n is the degree of polymerization of the side chain and m is the distance between successive grafting points. As a result, the superstrong segregation regime, being rather rare in the case of ordinary block copolymers, has a much better chance to be realized in the case of diblock copolymers with combs grafted to one of the blocks.

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Inversion of the Diffraction Pattern from an Inhomogeneously Strained Crystal using an Iterative Algorithm

The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign and derivatives of the different components of the displacement field. This algorithm is applied to an experimental reciprocal space map measured using high resolution X-ray diffraction from an array of silicon lines and the obtained component of the displacement field is in very good agreement with the one calculated using a finite element model.Comment: 5 pages, 4 figure

A unified evaluation of iterative projection algorithms for phase retrieval

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational ``instruments'' developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte

Primordial helium recombination III: Thomson scattering, isotope shifts, and cumulative results

Upcoming precision measurements of the temperature anisotropy of the cosmic microwave background (CMB) at high multipoles will need to be complemented by a more complete understanding of recombination, which determines the damping of anisotropies on these scales. This is the third in a series of papers describing an accurate theory of HeI and HeII recombination. Here we describe the effect of Thomson scattering, the $^3$He isotope shift, the contribution of rare decays, collisional processes, and peculiar motion. These effects are found to be negligible: Thomson and $^3$He scattering modify the free electron fraction $x_e$ at the level of several $\times 10^{-4}$. The uncertainty in the $2^3P^o-1^1S$ rate is significant, and for conservative estimates gives uncertainties in $x_e$ of order $10^{-3}$. We describe several convergence tests for the atomic level code and its inputs, derive an overall $C_\ell$ error budget, and relate shifts in $x_e(z)$ to the changes in $C_\ell$, which are at the level of 0.5% at $\ell =3000$. Finally, we summarize the main corrections developed thus far. The remaining uncertainty from known effects is $\sim 0.3$ in $x_e$.Comment: 19 pages, 15 figures, to be submitted to PR

Movement Variability Increases With Shoulder Pain When Compensatory Strategies of the Upper Body Are Constrained

[DE] This cross-sectional study analyzed the influence of chronic shoulder pain (CSP) on movement variability/kinematics during humeral elevation, with the trunk and elbow motions constrained to avoid compensatory strategies. For this purpose, 37 volunteers with CSP as the injured group (IG) and 58 participants with asymptomatic shoulders as the control group (CG) participated in the study. Maximum humeral elevation (Emax), maximum angular velocity (Velmax), variability of the maximum angle (CVEmax), functional variability (Func_var), and approximate entropy (ApEn) were calculated from the kinematic data. Patients' pain was measured on the visual analogue scale (VAS). Compared with the CG, the IG presented lower Emax and Velmax and higher variability (i.e., CVEmax, Func_var, and ApEn). Moderate correlations were achieved for the VAS score and the kinematic variables Emax, Velmax and variability of curve analysis, Func_varm, and ApEn. No significant correlation was found for CVEmax. In conclusion, CSP results in a decrease of angle and velocity and an increased shoulder movement variability when the neuromuscular system cannot use compensatory strategies to avoid painful positions.This work was funded by the Spanish Government and cofinanced by EU FEDER funds (Grant DPI2013-44227-R)Lopez Pascual, J.; Page Del Pozo, AF.; Serra Añó, P. (2017). Movement Variability Increases With Shoulder Pain When Compensatory Strategies of the Upper Body Are Constrained. Journal of Motor Behavior. 1-8. https://doi.org/10.1080/00222895.2017.1371109S1