Nonlinear Frechet derivative and its De Wolf approximation

We introduce and derive the nonlinear Frechet derivative for the acoustic wave equation. It turns out that the high order Frechet derivatives can be realized by consecutive applications of the scattering operator and a zero-order propagator to the source. We prove that the higher order Frechet derivatives are not negligible and the linear Frechet derivative may not be appropriate in many cases, especially when forward scattering is involved for large scale perturbations. Then we derive the De Wolf approximation (multiple forescattering and single backscattering approximation) for the nonlinear Frechet derivative. We split the linear derivative operator (i.e. the scattering operator) onto forward and backward derivatives, and then reorder and renormalize the nonlinear derivative series before making the approximation by dropping the multiple backscattering terms. Numerical simulations for a Gaussian ball model show significant difference between the linear and nonlinear Frechet derivatives.University of California, Santa Cruz (Wavelet Transform on Propagation and Imaging for seismic exploration Research Consortium); Massachusetts Institute of Technology. Earth Resources Laborator

Homotopy analysis of the Lippmann-Schwinger equation for seismic wavefield modeling in strongly scattering media

We present an application of the homotopy analysis method for solving the integral equations of the Lippmann-Schwinger type, which occurs frequently in acoustic and seismic scattering theory. In this method, a series solution is created which is guaranteed to converge independent of the scattering potential. This series solution differs from the conventional Born series because it contains two auxiliary parameters ε and h and an operator H that can be selected freely in order to control the convergence properties of the scattering series. The ε-parameter which controls the degree of dissipation in the reference medium (that makes the wavefield updates localized in space) is known from the so-called convergent Born series theory; but its use in conjunction with the homotopy analysis method represents a novel feature of this work. By using H = I (where I is the identity operator) and varying the convergence control parameters h and ε, we obtain a family of scattering series which reduces to the conventional Born series when h = −1 and ε = 0. By using H = γ where γ is a particular preconditioner and varying the convergence control parameters h and ε, we obtain another family of scattering series which reduces to the so-called convergent Born series when h = −1 and ε ≥ εc where εc is a critical dissipation parameter depending on the largest value of the scattering potential. This means that we have developed a kind of unified scattering series theory that includes the conventional and convergent Born series as special cases. By performing a series of 12 numerical experiments with a strongly scattering medium, we illustrate the effects of varying the (ε, h, H)-parameters on the convergence properties of the new homotopy scattering series. By using (ε, h, H) = (0.5, −0.8, I) we obtain a new scattering series that converges significantly faster than the convergent Born series. The use of a non-zero dissipation parameter ε seems to improve on the convergence properties of any scattering series, but one can now relax on the requirement ε ≥ εc from the convergent Born series theory, provided that a suitable value of the convergence control parameter h and operator H is used.publishedVersio

How many supermassive black hole binaries are detectable through tracking relative motions by sub/millimeter VLBI

The sub/millimeter wavelengths (86-690 GHz) very long baseline interferometry (VLBI) will provide $\sim5-40\ \mu$as angular resolution, $\sim10$ mJy baseline sensitivity, and $\sim 1\ \mu$as/yr proper motion precision, which can directly detect supermassive black hole binary (SMBHB) systems by imaging the two visible sources and tracking their relative motions. Such a way exhibits an advantage compared to indirect detect methods of observing periodic signals in motion and light curves, which are difficult to confirm from competing models. Moreover, tracking relative motion at sub/millimeter wavelengths is more reliable, as there is a negligible offset between the emission region and the black hole center. In this way, it is unnecessary to correct the black hole location by a prior of jet morphology as it would be required at longer wavelengths. We extend the formalism developed in D'Orazio & Loeb (2018) to link the observations with the orbital evolution of SMBHBs from the $\lesssim$10 kpc dynamical friction stages to the $\lesssim 0.01$ pc gravitational radiation stages, and estimate the detectable numbers of SMBHBs. By assuming 5\% of AGNs holding SMBHBs, we find that the number of detectable SMBHBs with redshift $z\le 0.5$ and mass $M\leq 10^{11}M_\odot$ is about 20. Such detection relies heavily on proper motion precision and sensitivity. Furthermore, we propose that the simultaneous multi-frequency technique plays a key role in meeting the observational requirements

Liquid-Crystal-Based Phase Gratings and Beam Steerers for Terahertz Waves

We review our theoretical and experimental studies on a class of liquid crystal (LC) photonic devices, i.e., terahertz (THz) phase gratings and beam steerers by using LCs. Such gratings can function as a THz polarizer and tunable THz beam splitters. The beam splitting ratio of the zeroth-order diffraction to the first-order diffraction by the grating can be tuned from 10:1 to 3:5. Gratings with two different base dimensions were prepared. The insertion loss is lower by approximately 2.5 dB for the one with the smaller base. The response times of the gratings were also studied and were long (tens of seconds) as expected because of the thick LC layer used. Accordingly, the devices are not suitable for applications that require fast modulation. However, they are suitable for instrumentation or apparatuses that require precise control, e.g., an apparatus requiring a fixed beam splitting ratio with occasional fine tuning. Schemes for speeding up the device responses were proposed. Based on the grating structure, we also achieved an electrically tunable THz beam steerer. Broadband THz radiation can be steered by 8.5° with respect to the incident beam by varying the driving voltages to yield the designed phase gradient

4-{[1-(4-Ethoxy­phen­yl)-5-methyl-1H-1,2,3-triazol-4-yl]diphenyl­meth­yl}morpholine

The title compound, C28H30N4O2, synthesized from 4-[1-(4-ethoxy­phen­yl)-5-methyl-1H-1,2,3-triazol-4-yl]diphenyl­meth­an­ol and morpholine, consists of a subsituted triazolyl group and a morpholinyl group that crowd the aliphatic C atom of a diphenyl­methyl unit [Ctriaz—C—Nmorph = 110.1 (1)° and Cphen­yl—C—Cphen­yl = 103.9 (1)°]. The morpholine ring adopts a chair conformation

Fixel-Based Analysis Effectively Identifies White Matter Tract Degeneration in Huntington’s Disease

Microstructure damage in white matter might be linked to regional and global atrophy in Huntington’s Disease (HD). We hypothesize that degeneration of subcortical regions, including the basal ganglia, is associated with damage of white matter tracts linking these affected regions. We aim to use fixel-based analysis to identify microstructural changes in the white matter tracts. To further assess the associated gray matter damage, diffusion tensor-derived indices were measured from regions of interest located in the basal ganglia. Diffusion weighted images were acquired from 12 patients with HD and 12 healthy unrelated controls using a 3 Tesla scanner. Reductions in fixel-derived metrics occurs in major white matter tracts, noticeably in corpus callosum, internal capsule, and the corticospinal tract, which were closely co-localized with the regions of increased diffusivity in basal ganglia. These changes in diffusion can be attributed to potential axonal degeneration. Fixel-based analysis is effective in studying white matter tractography and fiber changes in HD

A Novel Nanobody Specific for Respiratory Surfactant Protein A has Potential for Lung Targeting

Lung-targeting drugs are thought to be potential therapies of refractory lung diseases by maximizing local drug concentrations in the lung to avoid systemic circulation. However, a major limitation in developing lung-targeted drugs is the acquirement of lung-specific ligands. Pulmonary surfactant protein A (SPA) is predominantly synthesized by type II alveolar epithelial cells, and may serve as a potential lung-targeting ligand. Here, we generated recombinant rat pulmonary SPA (rSPA) as an antigen and immunized an alpaca to produce two nanobodies (the smallest naturally occurring antibodies) specific for rSPA, designated Nb6 and Nb17. To assess these nanobodies\u27 potential for lung targeting, we evaluated their specificity to lung tissue and toxicity in mice. Using immunohistochemistry, we demonstrated that these anti-rSPA nanobodies selectively bound to rat lungs with high affinity. Furthermore, we intravenously injected fluorescein isothiocyanate-Nb17 in nude mice and observed its preferential accumulation in the lung to other tissues, suggesting high affinity of the nanobody for the lung. Studying acute and chronic toxicity of Nb17 revealed its safety in rats without causing apparent histological alterations. Collectively, we have generated and characterized lung-specific nanobodies, which may be applicable for lung drug delivery

Was the first industrial revolution a conjuncture in the history of the world economy?

Quantitative analysis of flavonoids in flower petals of Nymphaea ‘King of Siam’. (DOCX 18 kb