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This paper continues the previous work of the author and contains the results concerning the relations for a wide class of special functions related to multidimensional Poisson and polynomial random walks.
Recent years have witnessed the development of single-molecule localization microscopy as a generic tool for sampling diverse biologically relevant information at the super-resolution level. While current approaches often rely on the target-specific alteration of the point spread function to encode the multidimensional contents of single fluorophores, the details of the point spread function in an unmodified microscope already contain rich information. Here we introduce a data-driven approach in which artificial neural networks are trained to make a direct link between an experimental point spread function image and its underlying, multidimensional parameters, and compare results with alternative approaches based on maximum likelihood estimation. To demonstrate this concept in real systems, we decipher in fixed cells both the colors and the axial positions of single molecules in regular localization microscopy data.
Automated aircraft control has traditionally been divided into distinct "functions" that are implemented separately (e.g., autopilot, autothrottle, flight management); each function has its own fault-tolerant computer system, and dependencies among different functions are generally limited to the exchange of sensor and control data. A by-product of this "federated" architecture is that faults are strongly contained within the computer system of the function where they occur and cannot readily propagate to affect the operation of other functions. More modern avionics architectures contemplate supporting multiple functions on a single, shared, fault-tolerant computer system where natural fault containment boundaries are less sharply defined. Partitioning uses appropriate hardware and software mechanisms to restore strong fault containment to such integrated architectures. This report examines the requirements for partitioning, mechanisms for their realization, and issues in providing assurance for partitioning. Because partitioning shares some concerns with computer security, security models are reviewed and compared with the concerns of partitioning.
Angiogenesis is a complex cellular process involving multiple regulatory growth factors and growth factor receptors. Among them, the ligands for the endothelial-specific tunica intima endothelial receptor tyrosine kinase 2 (Tie2) receptor kinase, angiopoietin-1 (Ang1) and Ang2, play essential roles in balancing vessel stability and regression during both developmental and tumor-induced angiogenesis. Despite possessing a high degree of sequence identity, Ang1 and Ang2 have distinct functional roles and cell-signaling characteristics. Here, we present the crystal structures of Ang1 both unbound and in complex with the Tie2 ectodomain. Comparison of the Ang1-containing structures with their Ang2-containing counterparts provide insight into the mechanism of receptor activation and reveal molecular surfaces important for interactions with Tie2 coreceptors and associated signaling proteins. Using structure-based mutagenesis, we identify a loop within the angiopoietin P domain, adjacent to the receptor-binding interface, which confers the specific agonist/antagonist properties of the molecule. We demonstrate using cell-based assays that an Ang2 chimera containing the Ang1 loop sequence behaves functionally similarly to Ang1 as a constitutive Tie2 agonist, able to efficiently dissociate the inhibitory Tie1/Tie2 complex and elicit Tie2 clustering and downstream signaling.
Under microgravity, the usual methods of placing granular solids into, or extracting them from, containers or storage vessels will not function. Alternative methods are required to provide a motive force to move the material. New configurations for microgravity regolith storage vessels that do not resemble terrestrial silos, hoppers, or tanks are proposed. The microgravity-compatible bulk-material storage vessels and exit feed configurations are designed to reliably empty and feed cohesive material to transfer vessels or conveying ducts or lines without gravity. A controllable motive force drives the cohesive material to the exit opening(s), and provides a reliable means to empty storage vessels and/or to feed microgravity conveying lines. The proposed designs will function equally well in vacuum, or inside of pressurized enclosures. Typical terrestrial granular solids handling and storage equipment will not function under microgravity, since almost all such equipment relies on gravity to at least move material to an exit location or to place it in the bottom of a container. Under microgravity, there effectively are no directions of up or down, and in order to effect movement of material, some other motive force must be applied to the material. The proposed storage vessels utilize dynamic centrifugal force to effect movement of regolith whenever material needs to be removed from the storage vessel. During simple storage, no dynamic motion or forces are required. The rotation rate during emptying can be controlled to ensure that material will move to the desired exit opening, even if the material is highly cohesive, or has acquired an electrostatic charge. The general concept of this Swirl Action Utilized for Centrifugal Ejection of Regolith (SAUCER) microgravity storage unit/dynamic feeder is to have an effective slot-hopper (based on the converging angles of the top and bottom conical section of the vessel) with an exit slot around the entire periphery of the SAUCER. The basic shape of such a unit is like two Chinese straw hats (douli) - one upside down, on the bottom, and another on top; or two wokpans, one upright on the bottom and another inverted on top, with a small gap between the upright and inverted pans or hats (around the periphery). A stationary outer ring, much like an unmounted bicycle tire, surrounds the gap between the two coaxial, nearly conical pieces, forming the top and bottom of the unit.
In this chapter we focus on methodological and computational aspects that are key to accurately modeling the spectroscopic and thermodynamic properties of molecular systems containing actinides within the density functional theory (DFT) framework. Our focus is on properties that require either an accurate relativistic all-electron description or an accurate description of the dynamical behavior of actinide species in an environment at finite temperature, or both. The implementation of the methods and the calculations discussed in this chapter were done with the NWChem software suite (Valiev et al. 2010). In the first two sections we discuss two methods that account for relativistic effects, the ZORA and the X2C Hamiltonian. Section 1.2.1 discusses the implementation of the approximate relativistic ZORA Hamiltonian and its extension to magnetic properties. Section 1.3 focuses on the exact X2C Hamiltonian and the application of this methodology to obtain accurate molecular properties. In Section 1.4 we examine the role of a dynamical environment at finite temperature as well as the presence of other ions on the thermodynamics of hydrolysis and exchange reaction mechanisms. Finally, Section 1.5 discusses the modeling of XAS (EXAFS, XANES) properties in realistic environments accounting for both the dynamics of the system and (for XANES) the relativistic effects.
Four ruthenium water oxidation catalysts that bear carboxylate and sulfonate groups in the active site have been synthesized and analyzed for their catalytic activity. Here, the sulfonate‐containing catalysts show higher electrochemical activity in pH 7 phosphate buffer with 4 times larger catalytic current, improved durability with sacrificial oxidant, and increased solubility compared to similar species containing two carboxylate groups. Density functional theory calculations suggest that the sulfonate group provides a more favorable geometry for water nucleophilic attack, which is both the energetically most favorable mechanism calculated and the experimentally predicted mechanism under electrochemical conditions. Further experimental studies have been performed to show that under certain conditions catalysts can perform well electrochemically under pH conditions as low as 1.6 and that various structural components can greatly change solubility and catalytic operation.
The conformational flexibility of three covalently linked alcohol dimers, composed of xanthenol units and diphenyl ether (DPE(OH) 2 ), 9,9-dimethylxanthene (XAN(OH) 2 ), or biphenyl (BP(OH) 2 ) linkers was studied. The relative orientation of the two alcohol units (In-In, In-Out, and Out-Out conformers) in the model compounds was investigated using NMR spectroscopy, X-ray crystallography, and density functional theory (DFT) calculations. Diols containing rigid linkers, such as XAN(OH) 2 and BP(OH) 2 , favor the formation of an In-In conformer in solution, and the interconversion between different conformers was slow on the NMR timescale. Interestingly, XAN(OH) 2 adopted an In-Out conformation in the crystalline solid state, possibly due to additional intermolecular interactions. More flexible DPE(OH) 2 was found to freely interconvert on the NMR timescale. This study provides important structural information that can be utilized in catalysis, metal-ligation, and other applications.
The effect of the composition and structure of oligodimethylsiloxanes containing carboxy- and amino-functional substituents at the silicon atom on their colloidal-chemical properties was studied. It was established that their colloidal-chemical properties are affected not only by the nature and concentration of functional groups, but also by the molecular weight of the organosilicon compound.
The time-fractional heat conduction equation with the Caputo derivative and with heat absorption term proportional to temperature is considered in a sphere in the case of central symmetry. The fundamental solution to the Dirichlet boundary value problem is found, and the solution to the problem under constant boundary value of temperature is studied. The integral transform technique is used. The solutions are obtained in terms of series containing the Mittag-Leffler functions being the generalization of the exponential function. The numerical results are illustrated graphically.
We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string. - Highlights: • First exact solution of Maxwell’s equations for massless charges in arbitrary motion. • Explicit expressions of electromagnetic fields and potentials. • Derivations are rigorous and based on distribution theory. • The form of the field depends heavily on whether the motion is bounded or unbounded. • The electromagnetic field contains unexpected Dirac-delta-function contributions.
Several global optimization methods are reviewed that attempt to ensure that the integral Gibbs energy of a closed isothermal isobaric system is a global minimum to satisfy the necessary and sufficient conditions for thermodynamic equilibrium. In particular, the integral Gibbs energy function of a multicomponent system containing non-ideal phases may be highly non-linear and non-convex, which makes finding a global minimum a challenge. Consequently, a poor numerical approach may lead one to the false belief of equilibrium. Furthermore, confirming that one reaches a global minimum and that this is achieved with satisfactory computational performance becomes increasingly more challenging in systems containing many chemical elements and a correspondingly large number of species and phases. Several numerical methods that have been used for this specific purpose are reviewed with a benchmark study of three of the more promising methods using five case studies of varying complexity. A modification of the conventional Branch and Bound method is presented that is well suited to a wide array of thermodynamic applications, including complex phases with many constituents and sublattices, and ionic phases that must adhere to charge neutrality constraints. Also, a novel method is presented that efficiently solves the system of linear equations that exploits the unique structure of the Hessian matrix, which reduces the calculation from a O(N 3 ) operation to a O(N) operation. As a result, this combined approach demonstrates efficiency, reliability and capabilities that are favorable for integration of thermodynamic computations into multi-physics codes with inherent performance considerations.
The current design for the ITER Low Field Side Reflectometer (LFSR) diagnostic system contains six circular waveguides that function as both launch and receive antennas. The front end of LFSR system, interfacing with the plasma facing DFW and its supporting diagnostic shielding Modules (DSM), is integrated into Equatorial Port Plug 11(EPP#11). In-vessel LFSR configuration is mainly divided into two sections, i.e. Front Antenna Unit (FAU) and in-vessel Transmission Line (TL) components. During plasma normal operation, the 14 MeV neutrons from D-T fusion reactions penetrate into the port plug and LFSR components. Neutronics code ATTILA is used for assessing the volumetric heating of in-vessel components. The maximum normal heat load due to radiation and the charge exchange from plasma is 0.35 MW/m 2 , which has to be applied on those surfaces affected by a viewing factor consistent with the aperture surface position and orientation. The front antenna unit (FAU) needs the active cooling to handle the radiant and nuclear heating from the plasma. Due to the specific viewing aperture layout at the front-end of in-vessel LFSR, the cooling channel design is challenging. The thermal-hydraulic iterations are performed to achieve the desirable temperature distribution of the water cooled front antenna units. The progressive ratcheting effects of the FAU subjected to cyclic thermal loading are examined by the preliminary non-linear elastic-plastic analysis.
Plasma control design increasingly depends on fast simulations able to connect to operational plasma control system (PCS) software for iterative development. GSevolve is a nonlinear free-boundary simulation that evolves the Grad-Shafranov equilibrium including current and pressure profiles, and can connect to all versions of the DIII-D PCS operational on devices around the world. Its ability to simulate the evolution of current continuously from open to closed field lines enables GSevolve to simulate full-discharge control from breakdown through plasma termination. GSevolve is compliant with the Plasma Control System Simulation Platform (PCSSP), a Matlab/Simulink®-based environment that serves as the primary framework for development of the ITER Plasma Control System (PCS). The code employs a novel response function-updating scheme to achieve fast simulations. The plasma evolves linearly until a significant shape change triggers a nonlinear update of the response while enforcing a prescribed accuracy. Old responses are recalled if the plasma changes back to an old shape. The equilibrium is a function of a state vector containing axisymmetric conductor currents and parameters related to parallel and perpendicular currents, which evolves according to an efficient state space circuit formulation. Control design and validation results are presented for simulations of DIII-D and EAST, connected to their corresponding versions of the DIII-D PCS.
A model-independent treatment of dark-matter particle elastic scattering has been developed, yielding the most general interaction for WIMP-nucleon low-energy scattering, and the resulting amplitude has been embedded into the nucleus, taking into account the selection rules imposed by parity and time-reversal. One finds that, in contrast to the usual spin-independent/spin-dependent (SI/SD) formulation, the resulting cross section contains six independent nuclear response functions, three of which are associated with possible velocity-dependent interactions. We find that current experiments are four orders of magnitude more sensitive to derivative couplings than is apparent in the standard SI/SD treatment, which necessarily associated such interactions with cross sections proportional to v 2 T ∼ 10 −6 , where v T is the WIMP velocity relative to the center of mass of the nuclear target.
Ionic liquids are tunable solvents composed entirely of ions that have properties desirable as electrolytes for lithium batteries such as non-flammability and a large electrochemical stability window. Solvate ionic liquids are a subclass of ionic liquids that consist of a glyme-based solvent and lithium salt in an equimolar ratio, where Li + cation-glyme solvation interactions result in ionic liquid-like properties. LiG4TFSi is a well-studied solvate ionic liquid consisting of equimolar amounts of lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) and tetraglyme (G4). In this work, pyrrolidinium ionic liquids with ether-functionalized side chains were synthesized containing either one ether (EO1) moiety or three ether (EO3) moieties and mixed with LiG4TFSI to form a new class of electrolyte mixtures. Their physical and transport properties, as well as ion solvation structures, were characterized by electrochemical, thermal, rheological, and spectroscopic measurements. The conductivity of the electrolyte mixture composed of EO1:LiTFSI:G4 in a 1:1:1 molar ratio is 2.54 mS/cm at 30 °C, compared to 1.53 mS/cm for LiG4TFSI, an increase of 67%. A significant decrease in the conductivity to 0.279 mS/cm is observed for the EO3:LiTFSI:G4 mixture in a 1:1:0.4 molar ratio. Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) measurements revealed that the EO1 cation diffuses significantly faster than the EO3 cation in their respective mixtures. Liquid-state 13 C NMR experiments indicate that Li + cations preferentially coordinate with tetraglyme. Li + cations do not coordinate with the EO1 cation and only coordinate with EO3 ether side chains at lower concentrations of tetraglyme. We hypothesize that the oligoether EO3 cation competes with G4 and TFSI - for lithium cation solvation in G4 deficient compositions, leading to a largely adverse effect on the mass transport properties of the electrolyte.
Polymeric materials containing amidine motifs are of high interest due to their ability to reversibly capture and release CO 2 at ambient temperature. Here, in this study, we probe physical and chemical responses of styrene-based copolymers containing linear amidine motifs as functions of CO 2 and inert gas exposures and temperature. A copper-catalyzed azide–alkyne cycloaddition “click” reaction involving N′-propargyl-N,N-dimethylacetamidine is used to modify random copolymers, resulting in an array of linear amidine motifs along the chain backbone with the amount of CO 2 -active amidine controlled by the copolymer composition. Through thermogravimetric measurements, we demonstrate that the amidine-functionalized copolymers efficiently capture CO 2 upon exposure to a stream of CO 2 (at 27 °C) and release it at a slightly elevated temperature (50 °C) when exposed to an inert gas stream (N 2 ). In addition to displaying a maximum adsorption capacity of 22 wt % in the presence of pure CO 2 , the copolymers show composition-dependent direct air capture (DAC) behaviors. Small molecule analogs are used to definitively understand degradation via chemical hydrolysis of the amidine moiety, which leads to insolubility and a large reduction in CO 2 adsorption capacity (1.7 wt %). Neutron vibrational spectroscopy and DFT calculations confirm that CO 2 binds strongly to the amidine motif, inducing a strong bending of the CO 2 molecule from its linear geometry. The coupled insights into mechanisms and behaviors of CO 2 adsorption in amidine-functionalized polymers provides a foundation for future investigations of CO 2 -responsive polymers and soft materials to improve carbon capture and sequestration technologies.
Organometallic iridium catalysts can be used in conjunction with bispinacolatodiboron (B 2 Pin 2 ) to effect the borylation of a variety of substrates such as arenes, alkanes, heteroarenes, and oxygenates. Recently, efforts have also focused on integrating these catalysts into porous supports, such as metal–organic frameworks (MOFs). While the mechanism of homogeneous borylation systems has been thoroughly investigated experimentally and computationally, analogous studies in MOF-supported iridium catalysts have not been conducted. In this paper, we report the mechanistic investigation of a phenanthroline-iridium catalyst immobilized in the organic linker of Universitetet i Oslo (UiO)-67 (Zr 6 O 4 (OH) 4 (BPDC) 4 (PhenDC) 2 , BPDC = biphenyl-4,4'-dicarboxylate, PhenDC = 1,10-phenanthroline-4,4'-dicarboxylate). By using benzene as a model substrate, variable time normalization analysis (VTNA) of the kinetic data suggested a rate law consistent with zero-order in B 2 Pin 2 , and first-order in arene. A primary kinetic isotope effect (KIE) in the time course of benzene-d 6 borylation also provided complementary information about the role of the arene in the rate-determining step of the reaction. Characterization by techniques such as X-ray absorption spectroscopy (XAS) confirmed the presence of Ir(III), while pair distribution function (PDF) analysis suggested structures containing an Ir–Cl bond, further substantiated by X-ray photoelectron spectroscopy (XPS). Analysis of postcatalysis materials by inductively coupled plasma–optical emission spectroscopy (ICP-OES) revealed low boron accumulation, which may indicate an absence of boron in the resting state of the catalyst. Finally, in comparing borylation of benzene and toluene, a slight selectivity for benzene is observed, which is similar to the analogous homogeneous reaction, indicating the influence of substrate sterics on reactivity.