Search

Drug discovery relies on efficient identification of small-molecule leads and their interactions with macromolecular targets. However, understanding how chemotypes impact mechanistically important conformational states often remains secondary among high-throughput discovery methods. Here, we present a conformational discovery pipeline integrating time-resolved, high-throughput small-angle X-ray scattering (TR-HT-SAXS) and classic fragment screening applied to allosteric states of the mitochondrial import oxidoreductase apoptosis-inducing factor (AIF). By monitoring oxidized and X-ray-reduced AIF states, TR-HT-SAXS leverages structure and kinetics to generate a multidimensional screening dataset that identifies fragment chemotypes allosterically stimulating AIF dimerization. Fragment-induced dimerization rates, quantified with time-resolved SAXS similarity analysis (kVR), capture structure-activity relationships (SAR) across the top-ranked 4-aminoquinoline chemotype. Crystallized AIF-aminoquinoline complexes validate TR-SAXS-guided SAR, supporting this conformational chemotype for optimization. AIF-aminoquinoline structures and mutational analysis reveal active site F482 as an underappreciated allosteric stabilizer of AIF dimerization. This conformational discovery pipeline illustrates TR-HT-SAXS as an effective technology for targeting chemical leads to important macromolecular states.

Highly concentrated aqueous electrolytes (termed water-in-salt electrolytes, WiSEs) at solid-liquid interfaces are ubiquitous in myriad applications including biological signaling, electrosynthesis, and energy storage. This interface, known as the electrical double layer (EDL), has a different structure in WiSEs than in dilute electrolytes. Here, we investigate how divalent salts [zinc bis(trifluoromethylsulfonyl)imide, Zn(TFSI)2], as well as mixtures of mono- and divalent salts [lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) mixed with Zn(TFSI)2], affect the short- and long-range structure of the EDL under confinement using a multimodal combination of scattering, spectroscopy, and surface forces measurements. Raman spectroscopy of bulk electrolytes suggests that the cation is closely associated with the anion regardless of valency. Wide-angle X-ray scattering reveals that all bulk electrolytes form ion clusters; however, the clusters are suppressed with increasing concentration of the divalent ion. To probe the EDL under confinement, we use a Surface Forces Apparatus and demonstrate that the thickness of the adsorbed layer of ions at the interface grows with increasing divalent ion concentration. Multiple interfacial layers form following this adlayer; their thicknesses appear dependent on anion size, rather than cation. Importantly, all electrolytes exhibit very long electrostatic decay lengths that are insensitive to valency. It is likely that in the WiSE regime, electrostatic screening is mediated by the formation of ion clusters rather than individual well-solvated ions. This work contributes to understanding the structure and charge-neutralization mechanism in this class of electrolytes and the interfacial behavior of mixed-electrolyte systems encountered in electrochemistry and biology.

The molecular foundations of epidermal cell wall mechanics are critical for understanding structure-function relationships of primary cell walls in plants and facilitating the design of bioinspired materials. To uncover the molecular mechanisms regulating the high extensibility and strength of the cell wall, the onion epidermal wall is stretched uniaxially to various strains and cell wall structures from mesoscale to atomic scale are characterized. Upon longitudinal stretching to high strain, epidermal walls contract in the transverse direction, resulting in a reduced area. Atomic force microscopy shows that cellulose microfibrils exhibit orientation-dependent rearrangements at high strains: longitudinal microfibrils are straightened out and become highly ordered, while transverse microfibrils curve and kink. Small-angle X-ray scattering detects a 7.4 nm spacing aligned along the stretch direction at high strain, which is attributed to distances between individual cellulose microfibrils. Furthermore, wide-angle X-ray scattering reveals a widening of (004) lattice spacing and contraction of (200) lattice spacing in longitudinally aligned cellulose microfibrils at high strain, which implies longitudinal stretching of the cellulose crystal. These findings provide molecular insights into the ability of the wall to bear additional load after yielding: the aggregation of longitudinal microfibrils impedes sliding and enables further stretching of the cellulose to bear increased loads.

In this article we investigate novel signatures of radiation reaction via the angular deflection of an electron beam colliding at 90 degrees with an intense laser pulse. Due to the radiation reaction effect, the electrons can be deflected towards the beam axis for plane wave backgrounds, which is not possible in the absence of radiation reaction effects. The magnitude and size of the deflection angle can be controlled by tailoring the laser pulse shapes. The effect is first derived analytically using the Landau-Lifshitz equation, which allows to determine the important scaling behavior with laser intensity and particle energy. We then move on to full scale 3D Monte Carlo simulations to verify the effect is observable with present day laser technology. We investigate the opportunities for an indirect observation of laser depletion in such side scattering scenarios.

The axon-initial-segment (AIS) of mature neurons contains microtubule (MT) fascicles (linear bundles) implicated as retrograde diffusion barriers in the retention of MT-associated protein (MAP) tau inside axons. Tau dysfunction and leakage outside of the axon is associated with neurodegeneration. We report on the structure of steady-state MT bundles in varying concentrations of Mg2+ or Ca2+ divalent cations in mixtures containing αβ-tubulin, full-length tau, and GTP at 37 °C in a physiological buffer. A concentration-time kinetic phase diagram generated by synchrotron SAXS reveals a wide-spacing MT bundle phase (Bws), a transient intermediate MT bundle phase (Bint), and a tubulin ring phase. SAXS with TEM of plastic-embedded samples provides evidence of a viscoelastic intervening network (IN) of complexes of tubulin oligomers and tau stabilizing MT bundles. In this model, αβ-tubulin oligomers in the IN are crosslinked by taus MT binding repeats, which also link αβ-tubulin oligomers to αβ-tubulin within the MT lattice. The model challenges whether the cross-bridging of MTs is attributed entirely to MAPs. Tubulin-tau complexes in the IN or bound to isolated MTs are potential sites for enzymatic modification of tau, promoting nucleation and growth of tau fibrils in tauopathies.

Electron bifurcation (BF) is an evolutionarily ancient energy coupling mechanism in anaerobes, whose associated enzymatic machinery remains enigmatic. In BF-flavoenzymes, a chemically high-potential electron forms in a thermodynamically favorable fashion by simultaneously dropping the potential of a second electron before its donation to physiological acceptors. The cryo-EM and spectroscopic analyses of the BF-enzyme Fix/EtfABCX from Thermotoga maritima suggest that the BF-site contains a special flavin-adenine dinucleotide and, upon its reduction with NADH, a low-potential electron transfers to ferredoxin and a high-potential electron reduces menaquinone. The transfer of energy from high-energy intermediates must be carefully orchestrated conformationally to avoid equilibration. Herein, anaerobic size exclusion-coupled small-angle X-ray scattering (SEC-SAXS) shows that the Fix/EtfAB heterodimer subcomplex, which houses BF- and electron transfer (ET)-flavins, exists in a conformational equilibrium of compacted and extended states between flavin-binding domains, the abundance of which is impacted by reduction and NAD(H) binding. The conformations identify dynamics associated with the T. maritima enzyme and also recapitulate states identified in static structures of homologous BF-flavoenzymes. Reduction of Fix/EtfABCX's flavins alone is insufficient to elicit domain movements conducive to ET but requires a structural "trigger" induced by NAD(H) binding. Models show that Fix/EtfABCX's superdimer exists in a combination of states with respect to its BF-subcomplexes, suggesting a cooperative mechanism between supermonomers for optimizing catalysis. The correlation of conformational states with pathway steps suggests a structural means with which Fix/EtfABCX may progress through its catalytic cycle. Collectively, these observations provide a structural framework for tracing Fix/EtfABCX's catalysis.

We consider a Schrödinger equation with a nonlinearity which is a general perturbation of a power nonlinearity. We construct a profile decomposition adapted to this nonlinearity. We also prove global existence and scattering in a general defocusing setting, assuming that the critical Sobolev norm is bounded in the energy-supercritical case. This generalizes several previous works on double-power nonlinearities. [ABSTRACT FROM AUTHOR]

Context. The connection between quasi-periodic oscillations (QPOs) and magnetic fields has been investigated in various celestial bodies. Magnetohydrodynamic (MHD) waves have been employed to explain the simultaneous upper and lower kilohertz (kHz) QPOs. Nevertheless, the intricate and undefined formation pathways of twin kHz QPOs present a compelling avenue for exploration. This study area holds great interest as it provides an opportunity for deriving crucial parameters related to compact stars. Aims. We strive to develop a self-consistent model elucidating the radiation mechanism of twin kHz QPOs, which we then compare it with observations. Methods. A sample of 28 twin kHz QPOs detected from the X-ray binary 4U 1636–53 was used for a comparison with the results of the Markov chain Monte Carlo calculations based on our model of the radiation mechanism of twin kHz QPOs, which is related to twin MHD waves. Results. We obtained 28 groups of parameters of 4U 1636–53 and a tight exponential fit between the flux and the temperature of seed photons to Compton up-scattering and find that the electron temperature in the corona around the neutron star decreases with increasing seed photon temperature. Conclusions. The origin of twin kHz QPOs are dual disturbances that arise from twin MHD waves that are generated at the innermost radius of an accretion disc. The seed photons can be transported through a high temperature corona and are Compton up-scattered. The photons that vary the frequencies of twin MHD waves lead to the observed twin kHz QPOs. [ABSTRACT FROM AUTHOR]

The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear combination of frequency coherent and fully incoherent scattering. The method of solution is based on an eigenfunction expansion of the radiation field, leading to two singular integral equations with Cauchy or Cauchy-type kernels, that have to be solved one after the other. We reconsider this problem, using as starting point the integral formulation of the radiative transfer equation, where the terms involving the coupling between the two scattering mechanisms are clearly displayed, as well as the primary source of photons. With an inverse Laplace transform, we recover the singular integral equations previously established and, with Hilbert transforms as in the previous work, recast them as boundary value problems in the complex plane. Their solutions are presented in detail for an infinite and a semi-infinite medium. The coupling terms are carefully analyzed and consistency with either the coherent or the incoherent limit is systematically checked. We recover the important result of the previous work that an exact solution exists for an infinite medium, whereas for a semi-infinite medium, which requires the introduction of half-space auxiliary functions, the solution is given by a Fredholm integral equation to be solved numerically. The solutions of the singular integral equations are used to construct explicit expressions providing the radiation field for an arbitrary primary source and for the Green's function. An explicit expression is given for the radiation field emerging from a semi-infinite medium. [ABSTRACT FROM AUTHOR]

We investigate the terahertz (THz) scattering and emission properties of lunar regolith by modeling it as a random medium with rough top and bottom boundaries and a host medium situated beneath. The total scattering and emission arise from three sources: the rough boundaries, the volume, and the interactions between the boundaries and the volume. To account for these sources, we model their respective phase matrices and apply the matrix doubling approach to couple these phase matrices to compute the total emission. The model is then used to explore insights into lunar regolith scattering and emission processes. The simulations reveal that surface roughness is the primary contributor to total scattering, while dielectric contrasts between the volume and the boundaries dominate total emission. The THz emissivity is highly sensitive to the regolith dielectric constant, particularly its imaginary part, making it a promising alternative for identifying previously undetected water ice in the lunar polar regions. The THz emissivity model developed in this study can be readily applied to invert the surface parameters of lunar regolith using THz observations. [ABSTRACT FROM AUTHOR]

The role of various light scattering phenomena in aesthetics and clinical practice is explored in this review. Four main types of light scattering, Tyndall, Rayleigh, Mie, and Raman, are discussed. Each type is explained in terms of its physical principles and its applications in aesthetic medicine. Tyndall scattering is relevant in understanding the blue appearance of certain dermal fillers. Rayleigh scattering contributes to skin tone perception and plays a role in certain laser treatments. Mie scattering is important in laser hair removal and the appearance of skin conditions like melasma. Raman scattering, while primarily used in research, shows promise for non‐invasive skin analysis, personalized skincare, treatment monitoring, and early skin cancer detection. It is important to understand these scattering phenomena for optimizing light‐based aesthetic procedures and developing effective treatments. Properly applying the appropriate scattering theory based on relative particle size is crucial in clinical aesthetic practice. [ABSTRACT FROM AUTHOR]

Irregular topographies are widely distributed in nature, particularly in mountainous areas. The cliff on the canyon top forming over long periods of geological evolution significantly influences the amplification or reduction of ground motion. In this study adopting the wave function expansion method, a comprehensive analytical solution is formulated to address the scattering issue under shear horizontal (SH) waves induced by a shallow asymmetrical V-shaped canyon with cliffs. In general, employing the appropriate Graf's addition formula, wave function expressions in different polar coordinate systems can be unified. According to continuity conditions of stress and displacement on the auxiliary boundary, the region-matching technique (RMT) has also been adopted to determine the unknown coefficients in the algebraic equation. Further, by comparing the results obtained in this study with those from previous studies, the correctness and applicability of the proposed theoretical model and analytical solution have been verified. A significant finding indicates that the maximum difference in peak displacement under a canyon with cliffs (d1/a = 0.4) can reach 1.81 times that without cliffs (d1/a = 0). Meanwhile, the asymmetric effect in this study is mainly concentrated on the ground motion of the canyon inner surface (−1 ≤ x/a ≤ 1), as opposed to a symmetrical V-shaped canyon with cliffs and an asymmetrical V-shaped canyon without cliffs. The proposed analytical solution not only enriches the category of well-known canyon problems related to SH-waves scattering, but also can serve as a reference for numerical verification and engineering practice. [ABSTRACT FROM AUTHOR]

Severe joint infections, such as septic arthritis, require rapid diagnostic testing of the synovial fluid aspirated from joints level so that a surgical team can be assembled quickly. We present a diffuse reflectance spectroscopy (DRS) system for noncontact determination of infection. Using a light‐tight syringe holder and fiber optic probe, diffusely reflected light from 475 to 655 nm was acquired from 18 patient samples through the wall of a syringe in a noncontact and sterile manner. We determined the reflectance ratios at two different wavelengths—R490/R600 and R580/R600 and found statistically significant differences (p < 0.05) in both ratios between the infected and noninfected groups. Critically, the R490/R600 and R580/R600 ratios were significantly correlated with clinical biomarkers—the white blood cell (WBC) and red blood cell (RBC) counts, respectively. This study demonstrates the potential of DRS as a rapid diagnostic tool for joint infections. [ABSTRACT FROM AUTHOR]

Conventional absorbing, reflective and scattering polarizers are facing various issues, such as severe optical loss, necessary oblique incidence, humidity sensitivity or aging‐caused failure. Subnanowires (SNWs) with polymer‐analogue properties, intrinsic order, and multi‐level interactions attract widespread attention as superior candidates for building blocks of polarizers. Herein, freestanding and flexible liquid crystal (LC)‐SNW films are prepared through a facile directional coating method, not only exhibiting good stability for water and repeated temperature fluctuations, but also showing good polarization performance for visible and near‐infrared (NIR) light, with the polarization degree (P) values of 93%, 84%, and 63% at the wavelengths of 580, 780 and 960 nm. And the average haze achieves 85%. The LC‐SNW films have great potential in applications for polarizers, holographic projection imaging and flexible optical devices. [ABSTRACT FROM AUTHOR]

This study presents an implementation of a new melting layer model in the ZJU‐AERO radar observation operator (Accurate and Efficient Radar Operator designed by ZheJiang University). The proposed model utilizes a coated spheroid to represent melting snow and graupel. It consists of three stages–coating, soaking, and melting–to account for the dielectric and density effects of melting particles. The scattering properties of the melting particles are computed with the Invariant‐Imbedding T‐Matrix (IITM) method, and the results are tabulated as look‐up tables for the radar operator. Regarding the parameterization of bulk optical properties, a flux‐conservation scheme is employed to estimate the size distribution of melting particles. To demonstrate its flexibility and superiority, the single and bulk scattering properties of our multi‐stage melting model are compared against the traditional homogeneous model, which uses the effective medium approximation (EMA). The effectiveness of the multi‐stage melting model has also been assessed by mapping model states in the regional mesoscale model of the China Meteorology Administration (CMA‐MESO) to radar observations. In the microphysics package of CMA‐MESO, the melting process is not explicitly represented, and we assume that melting hydrometeors occur where solid and liquid phases overlap. When compared with observations, the present multi‐stage melting model successfully reproduces melting layer signatures, highlighting its potential for microphysic validation, quantitative precipitation estimations, and data assimilation studies. Plain Language Summary: In this study, we present a new melting particle modeling scheme for a radar observation simulator. This scheme features the representation of the melting procedure of solid precipitation particles through three stages: an initial coating stage, an intermediate soaking stage, and a final melting stage. By incorporating these stages into the simulation, this new melting model surpasses the limitation of the commonly used model that treats melting particles as homogeneous mixtures of water, air, and ice. Additionally, we calculate the probability distributions of melting particle sizes using a rigorous falling‐flux‐conservation rule that considers the acceleration of particles during melting. The scattering properties of these coated‐spheroid melting particles are computed using the Invariant‐Imbedding T‐Matrix (IITM) method. Finally, the results are compared against those obtained using the traditional melting particle model. These comparisons demonstrate the potential of this newly proposed approach for improving the accuracy and reliability of radar simulations. Key Points: A three‐stage nonspherical particle model is proposed to account for the changes of dielectric constant and density of melting hydrometeorsA rigorous flux‐conservation bulk parameterization scheme is implemented to incorporate the terminal velocity variation as particles meltThe scattering properties of melting particles are rigorously computed using the state‐of‐the‐art invariant‐imbedding T‐matrix method [ABSTRACT FROM AUTHOR]

This study investigates terahertz (THz) wave scattering from a simulated lunar regolith surface, with a focus on the Brewster feature, backscattering, and bistatic scattering within the 325 to 500 GHz range. We employed a generalized power-law spectrum to characterize surface roughness and fabricated Gaussian correlated surfaces from Durable Resin V2 using 3D printing technology. The complex dielectric permittivity of these materials was determined through THz time-domain spectroscopy (THz-TDS). Our experimental setup comprised a vector network analyzer (VNA) equipped with dual waveguide frequency extenders for the WR-2.2 band, transmitter and receiver modules, polarizing components, and a scattering chamber. We systematically analyzed the effects of root-mean-square (RMS) height, correlation length, dielectric constant, frequency, polarization, and observation angle on THz scattering. The findings highlight the significant impact of surface roughness on the Brewster angle shift, backscattering, and bistatic scattering. These insights are crucial for refining theoretical models and developing algorithms to retrieve physical parameters for lunar and other celestial explorations. [ABSTRACT FROM AUTHOR]

Previous modeling studies have not properly explained the measured mass absorption cross section (MAC) at 550 nm, the linear backscattering depolarization ratio (LDR) at 355 and 532 nm, and the scattering matrix of soot at 532 nm. In this work, we attempt to use a black carbon (BC) model with an intrinsic organic carbon (OC) coating to explain the large MAC, large LDR, and measured scattering matrix. Our results show that the bare fractal BC model is not able to explain MAC, LDR, and scattering matrix simultaneously and that the modeling values do not cover the measurement range. This study shows that the modeled LDR and scattering matrix can cover the measurement range if we constrain the MAC of the BC in the measurement range by the intrinsic OC coating when we consider the effects of monomer radius, monomer number, and monomer overlap simultaneously. Therefore, intrinsic OC coating can be a significant source of uncertainty in the optical properties of fresh soot. Plain Language Summary: Since soot is the most important absorbing particle in the atmosphere, an accurate calculation of the optical properties of soot is of great importance for climate assessment and remote sensing. However, some of the observed optical properties of soot are difficult to explain with current models. In this study, a black carbon (BC) model with an intrinsic organic carbon (OC) coating is used to explain these difficult‐to‐explain optical properties. The results show that the simulated mass absorption cross section (MAC), linear backscattering depolarization ratio (LDR), and scattering matrix are difficult to explain when only the influence of BC is considered, although the effects of monomer size, monomer number, and monomer overlap are taken into account. Range of observation. However, after accounting for the intrinsic OC coating, the model is able to account for the range of realistic optical observations. Therefore, the intrinsic OC coating may be responsible for some optical properties that are difficult to explain with the current models. Key Points: The model of pure black carbon (BC) has difficulty explaining some optical observations of sootWe have proposed a soot model consisting of a BC core and an intrinsic organic carbon (OC) shellThe intrinsic OC coating may be a cause of some unexplained optical properties in current models [ABSTRACT FROM AUTHOR]

Attributed scattering problems have been found to be helpful in inverse synthetic aperture radar (ISAR) imaging and target recognition problems. In this model, the scattering centres are divided into two categories: localised and distributed. Localised scattering centres are those that are concentrated in a small area, while distributed scattering centres are spread out over a larger area. Several methods have been proposed to estimate the scattering centres which aim to accurately identify the location and characteristics of the scattering centres. However, detecting a distributed scattering centre remains a challenging task. A novel technique is proposed based on sparse signals to improve the detection of distributed scattering centres from localised ones. This technique takes advantage of the sparsity of the signals to accurately identify the location of the distributed scattering centres. Experimental results demonstrate the superiority of algorithm in detecting distributed scattering centres. This improved detection capability has significant implications for ISAR imaging and target recognition problems. [ABSTRACT FROM AUTHOR]

This study is devoted to analyze the scattering from spherical homogeneous rain droplet particles illuminated by structured light beam i.e., Gaussian vortex beam (GVB) with different orbital angular momentum (OAM). The promising applications of intricate optical beam fields regarding environmental monitoring and detection have mesmerized the consideration of optical community. The optical effects i.e., absorption and scattering of the atmospheric environment cause intensity distribution of GVB which lowers quality of beam signal. GVB carries OAM and when it propagates in the atmosphere then its interaction with the environment constituents (rain, fog, snow, clouds, water vapours, atmospheric gases, and other particles) makes the problem quite interesting. Rainy medium is considered as a uniformly spherical shaped sphere. So, the interaction between a linearly polarized GVB and a rainy atmosphere is investigated using the generalized Lorenz–Mie theory (GLMT). The expressions for electromagnetic fields (incident + scattered + inside) of GVB are expanded using spherical vector wave functions (SVWFs). By implementing continuous boundary conditions (BCs) at the spherical surface of rain droplets, the scattering coefficients in context of beam shape coefficients are obtained. The efficiencies (scattering, extinction, and absorption), forward scattering, backward scattering, GVB attenuation as well as transmittance are computed and discussed. In addition to that, the influence of OAM mode number, beam waist radius, and incident beam operating wavelengths of rainy medium on the efficiencies, electromagnetic scattering, attenuation, and transmittance is analyzed. This study establishes the groundwork for examining the tuning capability of GVBs for rainy atmosphere at various parameters. [ABSTRACT FROM AUTHOR]

The current study investigates the effects of strong potential porous materials to absorb the transmitted energy in a dissipative device containing a wave-bearing cavity. The expansion chamber consists of horizontal as well as vertical elastic boundaries that is filled with a compressible fluid and porous media. The porous media is dealt as an equivalent fluid with complex propagation speed and density, has effects on the eigenfunctions of cavity regions. The vibrational response of the vertical elastic components having different sets of edge conditions are incorporated by mode-matching tailored-Galerkin (MMTG) approach. This approach provides displacement of vertical elastic membrane which deals with various edge conditions. The MMTG approach has point-wise convergence that is conform through generalized orthogonal relations. The MMTG solutions are used to reconstruct matching conditions and to satisfy law of conservation of energy. It confirms the validity of retained solutions and accuracy of performed algebra. It is observed from the curves of TL and P abs that by varying edge conditions the absorbed power and TL are enhanced. [ABSTRACT FROM AUTHOR]

We characterize the subsurface thermal degradation of an inert analog of high-explosive molecular crystals (Eu:Y(acac)3(DPEPO)) (EYAD) embedded inside of a plastic bonded explosive simulant using feedback-assisted wavefront shaping-based fluorescence and Raman spectroscopies. This technique utilizes wavefront shaping to focus pump light inside a heterogeneous material onto a target particle, which significantly improves its spectroscopic signature. We find that embedding the EYAD crystals in the heterogeneous polymer results in improved thermal stability, relative to bare crystal measurements, with the crystal remaining fluorescent to >612 K inside of the heterogeneous material, while the bare crystal's fluorescence is fully quenched by 500 K. We hypothesize that this improvement is due to the polymer restricting the effects of EYAD melting, which occurs at 400 K and is the primary mechanism for spectroscopic changes in the temperature range explored. [ABSTRACT FROM AUTHOR]

The diverse Lyman-alpha (Ly  |$\alpha$|⁠) line profiles are essential probes of gas in and around galaxies. While isotropic models can successfully reproduce a range of  Ly  |$\alpha$| observables, the correspondence between the model and actual physical parameters remains uncertain. We investigate the effect of anisotropies on Ly  |$\alpha$| escape using a simplified setup: an empty hole (fractional size |$\tilde{s}$|⁠) within a semi-infinite slab with constant column density. Due to the slab's high line-centre optical depth (⁠|$\tau _0\gtrsim 10^{5-6}$|⁠), most photons should escape through the empty channel. However, our numerical findings indicate that only a fraction |${\sim} \tilde{s}$| of photons exit through this channel. To explain this puzzle, we developed an analytical model describing the scattering and transmission behaviour of  Ly  |$\alpha$| photons in an externally illuminated slab. Our findings show that the number of scatterings per reflection follows a Lévy distribution (⁠|${\propto} N^{-3/2}$|⁠). This means that the mean number of scatterings is orders of magnitude greater than expectations, facilitating a shift in frequency and the subsequent photon escape. Our results imply that  Ly  |$\alpha$| photons are more prone to traverse high-density gas and are surprisingly less biased to the 'path of least resistance'. Hence,  Ly  |$\alpha$| can trace an average hydrogen distribution rather than only low-column density channels. [ABSTRACT FROM AUTHOR]

In this paper, we mainly concern with the system of the coupled nonlinear Schrödinger equation with initial data in critical spaces in dimension 3. We first obtain the global well-posedness of the solution to the coupled nonlinear Schrödinger equation with initial data in a critical space $ W^{\frac {11}{7}, \frac 76}({\mathbb {R}}^3) $ W 11 7 , 7 6 ( R 3). The key is to derive a uniform bound of a modified energy $ \mathcal {E}(t) $ E (t) based on a decomposition for the solution as in Dodson [Global well-posedness for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. Rev Mat Iberoam. 2022;38:1087–1100]. In addition, inspired by Dodson [Scattering for the defocusing, cubic nonlinear Schrödinger equation with initial data in a critical space. International mathematics research notices; 2023], we make a new decomposition for the solution and show the scattering to the coupled nonlinear Schrödinger equation with radially symmetric initial data in a critical Besov space $ B_{1,1}^2({\mathbb {R}}^3) $ B 1 , 1 2 ( R 3). [ABSTRACT FROM AUTHOR]

This study presents the self-assembly of polyethylene oxide (PEO)-block-polypropylene oxide (PPO)-block-polyethylene oxide (PEO)-based block copolymer (BCP) commercially known as Pluronic® P123 in water and in the presence of different copolymeric surfactants (L61, L62, L64, and F68) with varying degree of hydrophilicity, i.e., %EO content. The clouding behavior demonstrates the varied phase transition ranging from solution, blue point (BP), and cloud point (CP). The characteristics of the micelles in the single and mix system are characterized utilizing dynamic light scattering (DLS) and small-angle neutron scattering (SANS) techniques at different temperatures. These scattering approaches provide an insightful information on the micelle size and shape. The size variations in self-assembled micelles designated the micelles to undergo growth/transition in shape from spherical to elongated ellipsoidal as function of temperature. Additionally, the application of these nanoscale micellar aggregates as carriers for delivering the anticancer drug Quercetin (QCT) was undertaken by a thorough quantitative and qualitative analysis to gain valuable insights into the effectiveness of the mix-micellar system as an ideal platform for drug delivery. A comprehensive investigation of drug release kinetics is presented using various kinetic models. The MTT (cytotoxicity assay) assay is used to gauge the effectiveness of the QCT-loaded copolymeric micelles. Micellar transition of 5% w/v P123 in water and in the presence of copolymeric surfactants as additives at 0.2% weight fraction (fix) at different temperatures [ABSTRACT FROM AUTHOR]

We conduct simulations of Spin Echo Small Angle Neutron Scattering (SESANS) by employing Monte Carlo methods to a setup using four magnetic Wollaston prisms. Our primary focus involves the validation of these models, encompassing monochromatic scenarios across various neutron wavelengths to ascertain the reliability of the simulations. Subsequently, we extend this validation to encompass simulations in time-of-flight mode. Our model consistently and precisely predicts the scattering patterns emanating from dilute spheres in both monochromatic and time-of-flight modes. Notably, it also accurately reproduces the intricate encoding associated with scattering occurring between the third and fourth magnetic Wollaston prism, which provides us with another approach to increase the solid angle coverage of a SESANS instrument. This validation process conclusively demonstrates the efficacy of our simulation methods. Importantly, it paves the way for simulating more intricate and realistic instrumental configurations, broadening the horizons for future research endeavours. [ABSTRACT FROM AUTHOR]

This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (Comm. Contemp. Math. , 19 (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method. [ABSTRACT FROM AUTHOR]

In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when $ E_{V}(u_{0})M(u_{0}) = E_{0}(Q)M(Q) $. Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold. [ABSTRACT FROM AUTHOR]

Since both top and bottom illuminations are widely used in infrared transmission measurements, in this paper, we study the effects of different illuminations on the signatures in infrared microspectroscopy. By simulating a series of dielectric samples, we show that their extinction efficiency, Qext, remains unchanged when the direction of the incident plane wave is reversed, even though the field distributions both inside and outside of the sample may be dramatically different. We find features in Qext that are correlated with whispering gallery modes for one beam direction and correspond to completely different field distributions for the opposite beam direction. In addition, by linking the optical theorem and the reciprocity relation of far‐field scattered field, we rigorously prove the invariance of Qext for arbitrary dielectric targets under opposite plane‐wave illuminations. Furthermore, we show the difference in the apparent absorbance spectrum for opposite beam directions when considering numerical apertures. [ABSTRACT FROM AUTHOR]

This research introduces an innovative application of physics-informed neural networks (PINNs) to tackle the intricate challenges of radiative transfer (RT) modelling in exoplanetary atmospheres, with a special focus on efficiently handling scattering phenomena. Traditional RT models often simplify scattering as absorption, leading to inaccuracies. Our approach utilizes PINNs, noted for their ability to incorporate the governing differential equations of RT directly into their loss function, thus offering a more precise yet potentially fast modelling technique. The core of our method involves the development of a parametrized PINN tailored for a modified RT equation, enhancing its adaptability to various atmospheric scenarios. We focus on RT in transiting exoplanet atmospheres using a simplified 1D isothermal model with pressure-dependent coefficients for absorption and Rayleigh scattering. In scenarios of pure absorption, the PINN demonstrates its effectiveness in predicting transmission spectra for diverse absorption profiles. For Rayleigh scattering, the network successfully computes the RT equation, addressing both direct and diffuse stellar light components. While our preliminary results with simplified models are promising, indicating the potential of PINNs in improving RT calculations, we acknowledge the errors stemming from our approximations as well as the challenges in applying this technique to more complex atmospheric conditions. Specifically, extending our approach to atmospheres with intricate temperature-pressure profiles and varying scattering properties, such as those introduced by clouds and hazes, remains a significant area for future development. [ABSTRACT FROM AUTHOR]

This study investigates the optical properties (light reflectance, absorptance, transmittance, and scattering) of black silicon (b‐Si) layers formed using reactive ion etching method. The corresponding spectra are determined across the visible, near‐infrared, and near‐ultraviolet wavelength ranges (250–1400 nm). It is demonstrated that b‐Si layers reduce the reflectance, and increase the absorptance and light scattering due to the disordered distribution of the nanoneedles. Increasing the etching duration strengthens this trend. It is shown that b‐Si layers etched for 10 min can be considered perfect light scatterers upon reflection at wavelengths less than 700 nm. Based on the obtained results, the possible profits of light scattering from the b‐Si interlayer for perovskite/Si tandem solar cells are analyzed. It is substantiated that the b‐Si interlayer can increase the useful absorptance not only within the bottom Si solar subcell but also in the top perovskite solar subcell. The prospects for future research directions and challenges are also provided. [ABSTRACT FROM AUTHOR]

Light from ground-based sources directed into the upper hemisphere can be partially controlled, for example, through suitable lamp shades or by reducing the number of luminaires and their lumen output. However, ground-reflected radiation is pervasive in artificially lit urban environments and cannot be entirely avoided. This component of upward-directed light is typically modelled using Lambertian diffuse reflection. Here, we demonstrate that the current analytical models for ground-reflected radiation can be improved by incorporating additional components, such as reflections from vertically oriented surfaces and vegetation. Our findings indicate that near edges of cities, the contribution of the reflected radiation to the overall skyglow is slightly higher than recent models predict. However, at medium-to-long distances the skyglow increases by 50–200 per cent compared to what these models suggest. This is because non-horizontal surfaces reflect more light towards small angles above the horizontal, contrasting with the outcomes predicted by the basic Lambertian framework. Consequently, light escaping from ground-based sources can propagate more effectively over longer distances, even when there is a complete cutoff of light emitted from luminaires in the upper half-space. These findings have significant implications for skyglow modelling. Furthermore, it also limits the available options for implementing measures to reduce skyglow levels at astronomical observatories located well beyond city boundaries. [ABSTRACT FROM AUTHOR]

In this study, we use the UK Molecular r-matrix (ukrmol) codes in the close-coupling approximation to examine the photoionization of hydrogen halides (hydrogen fluoride, hydrogen chloride, and hydrogen bromide). This article reports the total and partial photoionization cross-sections for the |$\mathrm{X}^2 \Pi$|⁠ , |$\mathrm{A}^2 \Sigma ^{+}$|⁠ , and |$\mathrm{B}^2 \Sigma ^{+}$| ionic states of these halides. The calculated cross-sections are compared with the available literature, which does not accurately represent the effective cross-sections near the threshold region, which is dominated by the Rydberg series autoionization resonances converging to the |$\mathrm{A}^2 \Sigma ^{+}$| ionic state. There seems to have been minimal effort to investigate the Rydberg-bound states of these halides. Meanwhile, the r-matrix approaches have traditionally excelled at characterizing such studies. This indicates the effectiveness of this method for molecular photoionization as well as for understanding the resonant contribution to the photoionization cross-sections. The detailed cross-sections calculated comprise the complex autoionizing resonance structures capable of significantly contributing to the computations of total photoionization rates, which are necessary to maintain a steady state of ionization in astrophysical plasmas. Comparisons with the experimental measurements and the theoretical data generally show reasonable agreement across the reported energy range. [ABSTRACT FROM AUTHOR]

The printing accuracy in ceramic stereolithography is deteriorated by shrinkage due to photopolymerization of monomers and broadening owing to scattering of light. To improve the accuracy of printed alumina parts, a series of experiments involving the reduce of shrinkage and broadening were conducted. Firstly, the dependence of conversion of monomers, shrinkage of suspensions and warpage of parts on energy doses was quantitively investigated and correlated, with which the shrinkage was well controlled through optimization. Besides, the warpage problem was effectively resolved when adding 30 wt% PEG-200 in the suspensions to release the accumulated internal stress. Next, the broadening under different energy doses was observed and reduced by addition of absorbers, after which a self-defined parameter C d / W e was applied to suggest strategies in the selection of appropriate processing parameters and absorber content. On this basis, the holes with a diameter ranging from 50–200 μm were successfully printed. [ABSTRACT FROM AUTHOR]

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems along with their significance and potential future applications in scattering and inverse scattering. [ABSTRACT FROM AUTHOR]

Doping is a key method employed in semiconductor technology for tuning the carrier‐density‐dependent electrical properties. In thermoelectric materials, which are typically heavily doped semiconductors, more impact factors are needed to be considered due to the heavy dose doping compared to normal semiconductors beyond carrier concentration optimization, such as band structure modification, carrier scattering mechanism and even thermal transport property. In this review, the doping effect determined by the intrinsic band features and vice versa the influence of dopants on band structure is first illustrated; and then introduce the approaches to overcoming the dilemma in effective doping caused by the temperature‐dependent optimal carrier concentration. Second, the strategies including rational vacancy design, proper selection of dopants and lattice purification toward high efficient doping and weakened carrier scattering strength are reviewed. Third, the recent discovery of the effect of dopant on thermal transport is highlighted covering the dopant‐induced local lattice distortion and exceptional strong electron‐phonon coupling. Finally, a perspective is given for the doping strategies to further boost the performance of thermoelectric materials. [ABSTRACT FROM AUTHOR]

Significance: Although spatial frequency domain imaging (SFDI) has been well characterized under diffuse optical conditions, tissue measurements made outside the diffuse regime can provide new diagnostic information. Before such measurements can become clinically relevant, however, the behavior of sub-diffuse SFDI and its effect on the accuracy of derived tissue parameters must be assessed. Aim: We aim to characterize the impact that both the assumed scattering phase function (SPF) and the polarization state of the illumination light source have on the accuracy of SFDI-derived optical properties when operating under diffuse or subdiffuse conditions, respectively. Approach: Through the use of a set of well-characterized optical phantoms, SFDI accuracy was assessed at four wavelengths (395, 545, 625, and 850 nm) and two different spatial frequencies (0.3 and 1.0 mm-1), which provided a broad range of diffuse and sub-diffuse conditions, using three different SPFs. To determine the effects of polarization, the SFDI accuracy was assessed using both unpolarized and cross-polarized illumination. Results: It was found that the assumed SPF has a direct and significant impact on the accuracy of the SFDI-derived optical properties, with the best choice of SPF being dictated by the polarization state. As unpolarized SFDI retains the sub-diffuse portion of the signal, optical properties were found to be more accurate when using the full SPF that includes forward and backscattering components. By contrast, cross-polarized SFDI yielded accurate optical properties when using a forward-scattering SPF, matching the behavior of cross-polarization to attenuate the immediate backscattering of sub-diffuse reflectance. Using the correct pairings of SPF and polarization enabled using a reflectance standard, instead of a more subjective phantom, as the reference measurement. Conclusions: These results provide the foundation for a more thorough understanding of SFDI and enable new applications of this technology in which sub-diffuse conditions dominate (e.g., μa/&#956's) or high spatial frequencies are required. [ABSTRACT FROM AUTHOR]

The scattering phenomena can be realized in a variety of everyday situations, including the rainbow pattern after a rainstorm, the dispersion of raindrops, information and communication (ICT) systems, radar cross section (RCS) measurement, and remote sensing. Inspired by the electromagnetic scattering features, this study explores the scattering characteristics of orbital angular momentum (OAM) carried by Gaussian vortex beam (GVB) for perfect electromagnetic conductor (PEMC) sphere by utilizing the generalized Lorenz–Mie theory (GLMT). Stemming from the integral localized approximation (ILA) method, the beam‐shape coefficients (BSCs) representing the incident GVB are obtained. Vortex beams carry distinct unique optical characteristics as compared to the other beam types as these possess OAM. Computations for the efficiencies (scattering and extinction) for a focused GVB are conducted and discussed to analyze the scattering phenomena of the electromagnetic fields outside the PEMC sphere. To ensure the accuracy of the results, scattering efficiency for Gaussian beam and plane wave is computed and compared using the GLMT for PEMC sphere. The OAM mode index, beam waist radius, and the scalar admittance of GVB are chosen as parameters to investigate their impact on the scattering dynamics (i.e., scattering and extinction efficiency). The numerical results show that OAM mode index, beam waist radius, and PEMC admittance have greater impact on optical efficiencies. Nonetheless, the trend of the scattering efficiency decreases irrespective of the extinction efficiency i.e., increases for OAM mode index. [ABSTRACT FROM AUTHOR]

Objective: The purpose of this study was to demonstrate heat transfer within oral soft tissues using different lasers under the effect of local anesthetics (LA). Methods: Bovine tongue slices were placed in between two glass slides and at a distance from a thermographic camera. In total, 2-cm-long 240 incisions were made along the surface of the tissue parallel to glass slides and the camera capture field. Incisions were performed using 445-nm and infrared (IR) lasers (970 nm and 980 nm on a continuous wave at 2W) with 320 μm-initiated (concentrated energy at the tip provided by a blue articulated paper and laser irradiation) and noninitiated (defused energy) fiber (30-sec irradiation period). LA was injected into the specimens before irradiation. The temperature changes in℃ (DT) and vertical and lateral heat transfer (in mm) were recorded at 10-sec intervals for 30 sec, using thermographic images. The amount of lateral and vertical heat transfer was measured. A repeated analysis of variance statistical comparison test was used to analyze differences between the lateral (width) and the vertical (height) heat transfer for initiated and noninitiated lasers and different lasers. Results: The maximum DT in℃ utilizing initiated tips of 970, 980, or 445 nm were 11.82 - 3.46, 7.66 - 3.24, and 18.94 - 7.01 and using noninitiated tips were 8.27 - 1.69, 8.87 - 2.40, and 12.31 - 8.65, respectively. Heat transfers (height/width) for initiated were 40.65 - 10.40/90.65 - 10.77 mm, 41.50 - 11.83/83.95 - 11.20 mm, and 33.70 - 9.10/95.10 - 11.17 mm and for noninitiated lasers were 52.95 - 6.89/96.10 - 11.17 mm, 47.75 - 7.41/93.75 - 14.96 mm, and 31.35 - 11.40/75.20 - 19.68 mm, respectively. A statistically significant difference was found between all lasers (p < 0.05) for initiated and noninitiated lasers (except for 970/980 nm for noninitiated lasers). Lower penetration depth (p < 0.05) at 445-nm diode and greater lateral heat spreading (p < 0.05) were identified under LA especially utilizing noninitiated tips without significant difference in IR lasers. Conclusions: LA might negatively influence soft tissues creating scattering when noninitiated tips are used and IR diode laser technology. [ABSTRACT FROM AUTHOR]

We establish global-in-time averaging for the L 2 -critical dispersion-managed nonlinear Schrödinger equation in the fast dispersion management regime. In particular, in the case of nonzero average dispersion, we establish averaging with any subcritical data, while in the case of a strictly positive dispersion map, we obtain averaging for data in  L 2 . [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the following fourth order Schrödinger equation with mixed dispersion on M N , an N-dimensional Cartan-Hadamard manifold. Namely we consider 4NLS i ∂ t ψ = - Δ M 2 ψ + β Δ M ψ + λ | ψ | 2 σ ψ in R × M , ψ (0 , ·) = ψ 0 ∈ X , where β ≥ 0 , λ = { - 1 , 1 } , 0 < σ < 4 / (N - 4) + , Δ M is the Laplace-Beltrami operator on M and X = L 2 (M) or X = H 2 (M) . At first, we focus on the case where M is the hyperbolic space H N . Using the fact that there exists a Fourier transform on this space, we prove the existence of a global solution to (4NLS) as well as scattering for small initial data provided that N ≥ 4 and 0 < σ < 4 / N if X = L 2 (H N) or 0 < σ < 4 / (N - 4) + if X = H 2 (H N) . Next, we obtained weighted Strichartz estimates for radial solutions to (4NLS) on a large class of rotationally symmetric manifolds by adapting the method of Banica and Duyckaerts (Dyn. Partial Differ. Equ., 07). Finally, we give a blow-up result for a rotationally symmetric manifold relying on a localized virial argument. [ABSTRACT FROM AUTHOR]

Ultrasound B-scan images are traditionally formed from the envelope of the received radiofrequency echoes, but the image texture is dominated by granular speckle patterns. Longstanding efforts at speckle reduction and deconvolution have been developed to lessen the detrimental aspects of speckle. However, we now propose an alternative approach to estimation (and image rendering) of the underlying fine grain scattering density of tissues based on power law constraints. The key steps are a whitening of the spectrum of the received signal while conforming to the original envelope shape and statistics, followed by a power law filtering in accordance with the known scattering behavior of tissues. This multiple step approach results in a high-spatial-resolution map of scattering density that is constrained by the most important properties of scattering from tissues. Examples from in vivo liver scans are shown to illustrate the change in image properties from this framework. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive review of research conducted on the Method of Auxiliary Sources (MAS) over a period of the last 22 years, i.e., since the last up-to-date survey was published. MAS is a very attractive numerical technique due to its simple algorithmic structure and the generally low computational cost it requires in terms of memory and CPU time; this is why it has been applied to a vast variety of cases, as concluded by the long citations list included. After a short introduction summarizing the fundamental concepts of the method, references since 2002 are categorized, briefly described, and commented on. This work is intended to assist every researcher who is involved in MAS computations, providing an exhaustive, to the best of the authors' knowledge, list of related publications. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS. [ABSTRACT FROM AUTHOR]

In this work we present a formalism based on scalar Green's functions to deal with electromagnetic scattering problems. Although the formulations of the Mie theory and Born approximations in terms of electromagnetic scattering are well known and relevant, they have certain disadvantages: complexity, computational time, few symmetries, etc. Therefore, the study with scalar Green's functions allows dealing with these problems with greater simplicity and efficiency. However, the information provided by the vector formulation is sacrificed. Nevertheless, different cases of electromagnetic scattering of dielectric media with different dimensions, geometries and refractive indices will be presented. Thus, we will be able to verify the capacity of this scalar method in predicting light-scattering problems. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for a class of coupled system of the four-dimensional cubic focusing nonlinear Schrödinger equations was investigated. By exploiting the double Duhamel method and the long-time Strichartz estimate, the global well-posedness and scattering were proven for the system below the ground state. In our proof, we first established the variational characterization of the ground state, and obtained the threshold of the global well-posedness and scattering. Second, we showed that the non-scattering is equivalent to the existence of an almost periodic solution by following the concentration-compactness/rigidity arguments of Kenig and Merle [17] (Invent. Math., 166 (2006), 645–675). Then, we obtained the global well-posedness and scattering below the threshold by excluding the almost periodic solution. [ABSTRACT FROM AUTHOR]

Germanium (Ge) is a system-forming material of IR photonics for the atmospheric transparency window of 8–14 µm. For optics of the 3–5 µm range, more widespread silicon (Si), which has phonon absorption bands in the long-wave region, is predominantly used. A technology for growing Ge single crystals has been developed, allowing the production of precision optical parts up to 500 mm in diameter. Ge is used primarily for the production of transparent optical parts for thermal imaging devices in the 8–14 µm range. In addition, germanium components are widely used in a large number of optical devices where such properties as mechanical strength, good thermal properties, and climatic resistance are required. A very important area of application of germanium is nonlinear optics, primarily acousto-optics. The influence of doping impurities and temperature on the absorption of IR radiation in germanium is considered in detail. The properties of germanium photodetectors are reported, primarily on the effect of photon drag of holes. Optical properties in the THz range are considered. The features of optical properties for all five stable isotopes of germanium are studied. The isotopic shift of absorption bands in the IR region, caused by phonon phenomena, which was discovered by the authors for the first time, is considered. [ABSTRACT FROM AUTHOR]

Traditional underwater polarization differential imaging methods use a fixed polarization direction to suppress the background scattered light; however, the polarization angle of the background scattered light may change in different underwater environments, limiting their effectiveness and real-time performance. In this paper, an improved underwater polarization differential imaging method is proposed, in which the polarization angle with the highest frequency of occurrence is selected as the polarization angle of the backscattered light by Stokes vector analysis. Then, the polarization images of the two best orthogonal polarization directions are obtained by combining the polarizer Mueller matrix and processed differentially. Compared with the traditional method, this method can suppress the backscattered light more accurately and effectively and improve the quality and real-time performance of underwater imaging. This method will have an important impact on imaging applications in complex underwater scenes. [ABSTRACT FROM AUTHOR]

Abstract Attributed scattering problems have been found to be helpful in inverse synthetic aperture radar (ISAR) imaging and target recognition problems. In this model, the scattering centres are divided into two categories: localised and distributed. Localised scattering centres are those that are concentrated in a small area, while distributed scattering centres are spread out over a larger area. Several methods have been proposed to estimate the scattering centres which aim to accurately identify the location and characteristics of the scattering centres. However, detecting a distributed scattering centre remains a challenging task. A novel technique is proposed based on sparse signals to improve the detection of distributed scattering centres from localised ones. This technique takes advantage of the sparsity of the signals to accurately identify the location of the distributed scattering centres. Experimental results demonstrate the superiority of algorithm in detecting distributed scattering centres. This improved detection capability has significant implications for ISAR imaging and target recognition problems.

This study explored the time asymptotic behavior of the Schrödinger equation with an inhomogeneous energy-critical nonlinearity. The approach follows the concentration-compactness method due to Kenig and Merle. To address the primary challenge posed by the singular inhomogeneous term, we utilized Caffarelli-Kohn-Nirenberg weighted inequalities. This work notably expanded the existing literature by applying these techniques to higher spatial dimensions without requiring any spherically symmetric assumption.

This work studies a coupled non-linear Schrödinger system with a singular source term. First, we investigate the question of the local existence of solutions. Second, one proves the existence of global solutions which scatter in some Sobolev spaces. Finally, one establishes the existence of non-global solutions. The main difficulty here is to overcome the regularity problem in the non-linearity. Indeed, because of the singularity of the source term, the classical contraction method in the energy space fails in such a regime. So, this paper is to fill such a gap in the literature. The argument follows ideas in T. Cazenave and I. Naumkin (Comm. Contemp. Math., 19 (2017), 1650038). This consists to remark that the singularity problem is only near the origin. So, one needs to impose that the solution stays away from zero. This is not trivial, since there is no maximum principle for the Schrödinger equation. The existence of global solutions which scatter follows with the pseudo-conformal transformation via the existence of local solutions. Finally, the existence of non-global solutions follows with the classical variance method.