Through inhalation of, e.g., hyperpolarized ^3He, it is possible to acquire gas diffusion magnetic resonance measurements that depend on the local geometry in the vast network of microscopic airways that form the respiratory zone of the human lung. Here, we demonstrate that this can be used to determine the dimensions (length and radius) of these airways noninvasively. Specifically, the above technique allows measurement of the weighted time-dependent diffusion coefficient (also called the apparent diffusion coefficient), which we here derive in analytic form using symmetries in the airway network. Agreement with experiment is found for the full span of published hyperpolarized ^3He diffusion magnetic resonance measurements (diffusion times from milliseconds to seconds) and published invasive airway dimension measurements.We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale ξ_E, so that the central limit theorem dictates the emergence of continuum linear isotropic elasticity on increasing the specimen size. The stiffness matrix of systems of finite size L>ξ_E is obtained, adding to that predicted by linear isotropic elasticity a random one of spectral norm (L/ξ_E)^-3/2 in three spatial dimensions. We further demonstrate that the elastic length scale corresponds to that of structural correlations, which in polycrystals reflect the typical size of the grain boundaries and length scales characterizing correlations in the stress field. We finally demonstrate that the elastic length scale affects the decay of the anisotropic long-range correlations of locally defined shear modulus and shear stress.We report on recent results that show that the pair correlation function of systems with exponentially decaying interactions can fail to exhibit Ornstein-Zernike asymptotics at all sufficiently high temperatures and all sufficiently small densities. This turns out to be related to a lack of analyticity of the correlation length as a function of temperature and/or density and even occurs for one-dimensional systems.The global linear stability of a water drop on hot nonwetting surfaces is studied. The droplet is assumed to have a static shape and the surface tension gradient is neglected. First, the nonlinear steady Boussinesq equation is solved to obtain the axisymmetric toroidal base flow. Then, the linear stability analysis is conducted for different contact angles β=110^∘ (hydrophobic) and β=160^∘ (superhydrophobic) which correspond to the experimental study of Dash et al. [Phys. Rev. E 90, 062407 (2014)PLEEE81539-375510.1103/PhysRevE.90.062407]. The droplet with β=110^∘ is stable while the one with β=160^∘ is unstable to the azimuthal wave number m=1 mode. This suggests that the experimental observation for a droplet with β=110^∘ corresponds to the steady toroidal base flow, while for β=160^∘, the m=1 instability promotes the rigid body rotation motion. A marginal stability analysis for different β shows that a 3-μL water droplet is unstable to the m=1 mode when the contact angle β is larger than 130^∘. A marginal stability analysis for different volumes is also conducted for the two contact angles β=110^∘ and 160^∘. The droplet with β=110^∘ becomes unstable when the volume is larger than 3.5μL while the one with β=160^∘ is always unstable to m=1 mode for the considered volume range (2-5μL). In contrast to classical buoyancy driven (Rayleigh-Bénard) problems whose instability is controlled independently by the geometrical aspect ratio and the Rayleigh number, in this problem, these parameters are all linked together with the volume and contact angles.Using the FitzHugh-Nagumo equations to represent the oscillatory electrical behavior of β-cells, we develop a coupled oscillator network model with cubic lattice topology, showing that the emergence of pacemakers or hubs in the system can be viewed as a natural consequence of oscillator population diversity. The optimal hub to nonhub ratio is determined by the position of the diversity-induced resonance maximum for a given set of FitzHugh-Nagumo equation parameters and is predicted by the model to be in a range that is fully consistent with experimental observations. The model also suggests that hubs in a β-cell network should have the ability to “switch on” and “off” their pacemaker function. RS 33295-198 3HCl As a consequence, their relative amount in the population can vary in order to ensure an optimal oscillatory performance of the network in response to environmental changes, such as variations of an external stimulus.We report on the increase in the accelerated electron number and energy using compound parabolic concentrator (CPC) targets from a short-pulse (∼150 fs), high-intensity (>10^18 W/cm^2), and high-contrast (∼10^8) laser-solid interaction. We report on experimental measurements using CPC targets where the hot-electron temperature is enhanced up to ∼9 times when compared to planar targets. The temperature measured from the CPC target is 〈T_e〉=4.4±1.3 MeV. Using hydrodynamic and particle in cell simulations, we identify the primary source of this temperature enhancement is the intensity increase caused by the CPC geometry that focuses the laser, reducing the focal spot and therefore increasing the intensity of the laser-solid interaction, which is also consistent with analytic expectations for the geometrical focusing.We study a quantum-dots (QDs) dispersed bent-core nematic liquid crystalline system in planar geometry and present experimental measurements of the birefringence (Δn), order parameter (S), dielectric dispersion, absorption spectra, and optical textures with attention to variations with temperature. A bent-core liquid crystal (LC) 14-2M-CH_3 is used as the host material and CdSe/ZnS core-shell type QDs are used as the dopant. The nematic (N) phase of the pristine (undoped) LC 14-2M-CH_3 contains cybotactic clusters, which are retained by its QDs incorporated LC nanocomposite. Our experimental findings support (i) reduced orientational order parameter of the QDs dispersed LC system compared to its pristine counterpart at fixed temperatures, (ii) reduced cybotactic cluster sizes due to the incorporation of QDs, and (iii) increased activation energies related to reduced cluster sizes. We complement the experiments with a novel Landau-de Gennes-type free energy for a doped bent-core LC system that qualitatively captures the doping-induced reduced order parameter and its dependence on the properties of the QDs and its variation with temperature.