Detailed Calculations Research Articles

Dissipative quintessential cosmic inflation

In this paper we construct a dissipative quintessential cosmic inflation. For this purpose, we add a multiplicative dissipative term in the standard quintessence field Lagrangian. We consider the specific form of dissipation as the time integral including the Hubble parameter and an arbitrary function that describes the dissipative properties of the quintessential scalar field. Inflation parameters and observables are calculated under slow-roll approximations and a detailed calculation of the cosmological perturbations is performed in this setup. We consider different forms of potentials and calculate the scalar spectral index and tensor-to-scalar ratio for a constant as well as variable dissipation function. To check the reliability of this model, a numerical analysis on the model parameters space is done in confrontation with recent observational data. By comparing the results with observational joint datasets at 68% and 95% confidence levels, we obtain some constraints on the model parameters space, specially the dissipation factor with e-folds numbers N=55 and N=60. As some specific results, we show that the power-law potential with a constant dissipation factor and N=60 is mildly consistent with observational data in some restricted domains of the model parameter space with very small and negative dissipation factor and a negligible tensor-to-scalar ratio. But this case with N=55 is consistent with observation considerably. For power-law potential and variable dissipation factor as Q=αϕn, the consistency with observation is also considerable with a reliable tensor-to-scalar ratio. The quadratic and quartic potentials with variable dissipation function as Q=αϕn are consistent with Planck2018 TT, TE, EE+lowE+lensing data at the 68% and 95% levels of confidence for some intervals of the parameter n.

Optical axis-driven field enhancement in a hyperbolic medium.

Field enhancement of applied electric field is the foundation for the variety of applied domains at a nanoscale level. Traditionally, efforts to achieve field enhancement have required the use of complicated metamaterial-based structures with a transition behavior. Here, the electromagnetic field solution of the TM-polarized wave that interacts with an optical-axis-driven hyperbolic medium with a transition behavior is established. Detailed calculations reveal that such field enhancement can be achieved over a broad range of incident angles (i.e., near critical angle). Definitely, such flexibility of the incident angle for achieving the field enhancement enriches the understanding and provides novel prospective toward its practical realization.

Density functional theory study on frustrated Lewis pairs catalyzed C‐H activation of heteroarenes: Mechanism variation tuning by electronic effect

AbstractUnreactive C‐H bond activation is a new horizon for frustrated Lewis pairs (FLPs) chemistry. Although concerted mechanism (Science 2015, 349, 513) and stepwise carbene mechanism (Org. Lett. 2018, 20, 1102) have been proposed for the FLPs catalyzed C‐H bond activation of 1‐methylpyrrole, the influence of electronic properties of FLPs on the reaction mechanism is far away from well‐understood. In this study, an assortment of P‐B type FLPs with different electronic characteristic was employed to study the catalyzed C‐H bond activation of 1‐methylpyrrole by using density functional theory calculations. Detailed calculations demonstrated that the reactivity variation and the reaction mechanism binary of FLPs catalyzed C‐H activation can be varied by tuning electronic effect of Lewis base center. On the one hand, the concerted C‐H activation reactivity is mainly controlled by the electron donation of the lone pair of Lewis base center; thus, the FLPs with electron‐donating substituents (FLP1, FLP2, and FLP3) catalyzed the C‐H bond activation through concerted mechanism. On the other hand, the reactivity of stepwise carbene mechanism is mostly attributed to the vacant orbital of Lewis acid center; as a result, the FLP5 bearing ‐P(C6F5)2 preferred to catalyzed the bond activation through concerted mechanism. In contrast, a metathesis mechanism through strained four‐membered ring transition state is less feasible. These results should provide deeper insight and broader perspective to understand the structure and function of FLPs for rational design of FLPs catalyzed C‐H bond activation.

Unexpected tunable photoluminescence and emission mechanism during the gradual increase of cyclic glucose units

Excitation-dependent (λex-dependent) emission is one of the most common emission characteristics of nonconventional luminophores. Previously, we have reported D-xylose crystals has an obvious λex-dependent color tunable persistent room temperature phosphorescence (p-RTP) from blue to green, but its p-RTP emission at long wavelength is very weak. To further explore this attractive multicolor p-RTP behavior, and to enhance its tunability, the photoluminescence (PL) behavior of three common cyclodextrins (CDs), namely α-CD, β-CD and γ-CD, including solution and single crystals, were studied. Their single crystals demonstrate λex-dependent multicolor p-RTP properties in the order of β-CD>α-CD>γ-CD, rather than the strongest with the least glucose units (α-CD). Among them, the λex-dependent tunable p-RTP of β-CD and α-CD is superior to that of D-(+)-xylose single crystal. The above unexpected phenomena could be explained reasonably through detailed single crystal structure analysis and theoretical calculations. The emission behavior of solution and single crystals of CDs can be reasonably explained by the clustering-triggered emission (CTE) mechanism. Furthermore, CD-based covalent organic frameworks (COF) and supramolecules are readily fabricated, which own significantly enhanced p-RTP emission. Due to the intriguing PL property as well as hydrophilic rim and low biotoxicity of CDs, successful imaging of HCT116 cells and encryption applications were demonstrated. It is believed that the intrinsic PL properties of CDs, especially their regularly adjustable multicolor p-RTP that varies with the number of glucose units, have significant guidance for the development of a series of multicolor luminescent materials.

Breast tumor segmentation via deep correlation analysis of multi-sequence MRI.

Precise segmentation of breast tumors from MRI is crucial for breast cancer diagnosis, as it allows for detailed calculation of tumor characteristics such as shape, size, and edges. Current segmentation methodologies face significant challenges in accurately modeling the complex interrelationships inherent in multi-sequence MRI data. This paper presents a hybrid deep network framework with three interconnected modules, aimed at efficiently integrating and exploiting the spatial-temporal features among multiple MRI sequences for breast tumor segmentation. The first module involves an advanced multi-sequence encoder with a densely connected architecture, separating the encoding pathway into multiple streams for individual MRI sequences. To harness the intricate correlations between different sequence features, we propose a sequence-awareness and temporal-awareness method that adeptly fuses spatial-temporal features of MRI in the second multi-scale feature embedding module. Finally, the decoder module engages in the upsampling of feature maps, meticulously refining the resolution to achieve highly precise segmentation of breast tumors. In contrast to other popular methods, the proposed method learns the interrelationships inherent in multi-sequence MRI. We justify the proposed method through extensive experiments. It achieves notable improvements in segmentation performance, with Dice Similarity Coefficient (DSC), Intersection over Union (IoU), and Positive Predictive Value (PPV) scores of 80.57%, 74.08%, and 84.74% respectively.

Air-Stable Wafer-Scale Ferromagnetic Metallo-Carbon Nitride Monolayer.

The pursuit of robust, long-range magnetic ordering in two-dimensional (2D) materials holds immense promise for driving technological advances. However, achieving this goal remains a grand challenge due to enhanced quantum and thermal fluctuations as well as chemical instability in the 2D limit. While magnetic ordering has been realized in atomically thin flakes of transition metal chalcogenides and metal halides, these materials often suffer from air instability. In contrast, 2D carbon-based materials are stable enough, yet the challenge lies in creating a high density of local magnetic moments and controlling their long-range magnetic ordering. Here, we report a novel wafer-scale synthesis of an air-stable metallo-carbon nitride monolayer (MCN, denoted as MN4/CNx), featuring ultradense single magnetic atoms and exhibiting robust room-temperature ferromagnetism. Under low-pressure chemical vapor deposition conditions, thermal dehydrogenation and polymerization of metal phthalocyanine (MPc) on copper foil at elevated temperature generate a substantial number of nitrogen coordination sites for anchoring magnetic single atoms in monolayer MN4/CNx (where M = Fe, Co, and Ni). The incorporation of densely populating MN4 sites into monolayer MCN networks leads to robust ferromagnetism up to room temperature, enabling the observation of anomalous Hall effects with excellent chemical stability. Detailed electronic structure calculations indicate that the presence of high-density metal sites results in the emergence of spin-split d-bands near the Fermi level, causing a favorable long-range ferromagnetic exchange coupling through direct exchange interactions. Our work demonstrates a novel synthesis approach for wafer-scale MCN monolayers with robust room-temperature ferromagnetism and may shed light on practical electronic and spintronic applications.

Band Engineering of Perovskite Quantum Dot Solids for High-Performance Solar Cells.

CsPbI3 perovskite quantum dot (PQD) shows high potential for next-generation photovoltaics due to their tunable surface chemistry, good solution-processability and unique photophysical properties. However, the remained long-chain ligand attached to the PQD surface significantly impedes the charge carrier transport within the PQD solids, thereby predominantly influencing the charge extraction of PQD solar cells (PQDSCs). Herein, a ligand-induced energy level modulation is reported for band engineering of PQD solids to improve the charge extraction of PQDSCs. Detailed theoretical calculations and systemic experimental studies are performed to comprehensively understand the photophysical properties of the PQD solids dominated by the surface ligands of PQDs. The results reveal that 4-nitrobenzenethiol and 4-methoxybenzenethiol molecules with different dipole moments can firmly anchor to the PQD surface through the thiol group to modulate the energy levels of PQDs, and a gradient band structure within the PQD solid is subsequently realized. Consequently, the band-engineered PQDSC delivers an efficiency of up to 16.44%, which is one of the highest efficiencies of CsPbI3 PQDSCs. This work provides a feasible avenue for the band engineering of PQD solids by tuning the surface chemistry of PQDs for high-performing solar cells or other optoelectronic devices.

LES of Premixed Turbulent Combustion Using Filtered Tabulated Chemistry

AbstractThe filtered tabulated chemistry (FTACLES) approach utilizes data from pre-tabulated explicitly filtered 1D flame profiles for closure of the LES-filtered transport terms. Different methodologies are discussed to obtain a suitable progress variable c from detailed chemistry calculations of a methane/air flame. In this context, special focus is placed on the analytical modeling of the reaction source term using series of parameterized Gaussians. For increasing effective filter sizes in LES (i.e. including the flame thickening) the precise shape of the reaction rate profile becomes less and less relevant. In particular, it is shown that for one-step chemistry, a single Gaussian is sufficient to derive an explicitly expressible 1D flame profile with a prescribed laminar flame speed and thermal flame thickness. The resulting artificial flame profile is shown to have similarities with profiles based on carbon chemistry and detailed reaction mechanisms. Next, the behavior of the filtered c-transport equation is analyzed and several possible closure methods are compared for a wide range of filter widths. It is shown that the unclosed contribution of the filtered diffusion term can be combined with the subgrid convection term, thus simplifying the FTACLES formulation. The model is implemented in OpenFOAM and validated in 1D for a variety of LES filter sizes in combination with artificial flame thickening. A power-law-based wrinkling model is modified for use with artificial flame thickening and combined with the FTACLES model to enable 3D simulations of a premixed turbulent Bunsen burner. The comparison of 3D Large Eddy Bunsen flame simulations at increasing levels of turbulence intensity shows a good match to experimental results for most investigated cases. In addition, the results are mostly insensitive to the variation of the mesh size.

Anisotropic Electron-Phonon Interactions in 2D Lead-Halide Perovskites.

Two-dimensional (2D) hybrid organic-inorganic metal halide perovskites offer enhanced stability for perovskite-based applications. Their crystal structure's soft and ionic nature gives rise to strong interaction between charge carriers and ionic rearrangements. Here, we investigate the interaction of photogenerated electrons and ionic polarizations in single-crystal 2D perovskite butylammonium lead iodide (BAPI), varying the inorganic lamellae thickness in the 2D single crystals. We determine the directionality of the transition dipole moments (TDMs) of the relevant phonon modes (in the 0.3-3 THz range) by the angle- and polarization-dependent THz transmission measurements. We find a clear anisotropy of the in-plane photoconductivity, with a ∼10% reduction along the axis parallel with the transition dipole moment of the most strongly coupled phonon. Detailed calculations, based on Feynman polaron theory, indicate that the anisotropy originates from directional electron-phonon interactions.

Spectral deferred correction method for fractional initial value problem with Caputo–Hadamard derivative

This paper considers an efficient and accurate spectral deferred correction (SDC) method for the initial value problem (IVP) with Caputo–Hadamard derivative. We first apply the basic idea of the SDC method to derive the numerical scheme. Then the iteration matrix which is the key to convergence of the proposed scheme can be obtained for the linear problem. Detailed computation of history term is presented using the spectral collocation method based on mapped Jacobi log orthogonal functions (MJLOFs). Finally, numerical simulations for both linear and nonlinear cases are shown to verify the feasibility and efficiency of the proposed method.

Environmental responsive peroxidase-like activity of MoS2@halloysite nanotubes mediated by piezoelectric effect

Nanozymes, as a class of synthetic enzymes, have the characteristics of abundant raw materials and powerful environmental adaptability, potentially serving as substitutes for natural enzymes. Herein, the MoS2 nanosheets were anchored on the surface of alkali activated halloysite nanotubes by utilizing a facile hydrothermal process, resulting in the formation of MoS2@halloysite (MoS2@HNTs) core-shell nanocomposites. The catalytic effect of material on peroxidase under the mechanical stress of applied ultrasonic vibration was systematically investigated with 3,3′,5,5′-tetramethylbenzidine (TMB) as the substrate for chromogenic reaction. The results demonstrated that the established piezoelectric polarization effect generated by MoS2 with asymmetric crystal structure under mechanical force can promote the in-situ coloration of TMB. Concretely, MoS2@HNTs possessing higher Michaels constant (3.42 mmol L-1) and reaction velocity (3.16 × 10–6 mol L-1 min-1) exhibited enhanced peroxidase-like activity compared to pristine MoS2 microspheres. This may be attributed to the fact that halloysite dispersed the MoS2 nanosheets, exposing more reactive sites, and the nanocomposites produced more pronounced structural deformation under mechanical stress. The detailed experiments and theoretical calculation have elucidated the structure-activity relationship and microscopic mechanism among the microstructures, piezoelectric polarization effects and peroxidase catalytic effects of materials. This work provides an advanced prototype for the research of environmental responsive enzyme-like catalytic effects of mineral-based nanozymes with the regulation of external environmental factors.

Multiple chiral doublet bands in 104Rh

Two new negative-parity bands have been identified in the odd-odd 104Rh nucleus. According to their experimentally observed properties, they have the same π(1g9/2)−1⊗ν(1h11/2)1 high-j configuration as the previously known negative-parity chiral doublet bands. This observation raises the possibility of the existence of multiple chiral doublet bands, MχD, in this nucleus. Comparing the properties of the observed bands with results of detailed theoretical calculations, one can conclude that the lower energy parts of bands 1 and 2 are chiral partner bands with the π(1g9/2)−1⊗ν(1h11/2)1 two-quasiparticle configuration, while bands 3 and 4 are chiral partner bands with the π(1g9/2)−1⊗ν(1g7/2)−2(1h11/2)1 four-quasiparticle configuration. Thus, MχD based on different configurations is observed in 104Rh.

A nanoscale photonic thermal transistor for sub-second heat flow switching

Control of heat flow is critical for thermal logic devices and thermal management and has been explored theoretically. However, experimental progress on active control of heat flow has been limited. Here, we describe a nanoscale radiative thermal transistor that comprises of a hot source and a cold drain (both are ~250 nm-thick silicon nitride membranes), which are analogous to the source and drain electrodes of a transistor. The source and drain are in close proximity to a vanadium oxide (VOx)-based planar gate electrode, whose dielectric properties can be adjusted by changing its temperature. We demonstrate that when the gate is located close ( < ~1 µm) to the source-drain device and undergoes a metal-insulator transition, the radiative heat transfer between the source and drain can be changed by a factor of three. More importantly, our nanomembrane-based thermal transistor features fast switching times ( ~ 500 ms as opposed to minutes for past three-terminal thermal transistors) due to its small thermal mass. Our experiments are supported by detailed calculations that highlight the mechanism of thermal modulation. We anticipate that the advances reported here will open new opportunities for designing thermal circuits or thermal logic devices for advanced thermal management.

Railway vibration – fast physics-based models for the prediction of ground vibration and the identification of track damage

The following applications of machine learning/AI for railway vibration will be discussed: 1. The prediction of the wave propagation from a railway line (completely physics based for surface lines, for tunnel lines (partially) physics-based ML for surface lines). 2. The track behaviour for the emission of train-induced ground vibration (physics based for homogeneous soil, ML for layered soil). 3. Track damage detection and quantification from FRF and moving load response. 4. Bridge damage detection and localisation from modal analysis and moving load response. 5. The use of axle-box acceleration for the identification of track/sub-soil condition and bridge resonances. Prediction calculation of railway vibration usually needs time-consuming finite element, boundary element and wavenumber domain calculations. For a user-friendly prediction software, fast calculations are needed. Several time-consuming detailed calculations should be used to develop simpler and fast models. The dynamic stiffness of isolated or un-isolated railway tracks from detailed calculations with a continuous soil is approximated with the simpler Winkler soil. The vehicle-track resonance (P2 resonance) rules the effect of the mitigation measures, and it can also be used for the on-board monitoring of the track and sub-soil condition. For the identification of track damage such as gaps between sleepers, track slabs and layers, detailed models with a continuous soil have been updated to get the best fit to the measured frequency response functions from hammer tests and the deformation pattern from the moving load response. Whereas the track damage can be locally identified, this is more difficult for bridges where the modal analysis gives mainly global information. The influence lines of the inclination for statically passing vehicles (locomotive, truck, compaction ) have been used to localise bridge damage (stiffness variations). The on-board monitoring of rail bridges needs special conditions (regular trains with special speeds) to excite and measure the bridge resonance.

Desymmetrization of Inert meso-Diethers through Copper-Catalyzed Asymmetric Allylic Alkylation with Grignard Reagents.

We have developed a highly regio-, diastereo-, and enantioselective Cu-catalyzed desymmetrization of inert meso-diethers using Grignard reagents. Moreover, previous inaccessible sterically hindered organometallic reagents are realized in the reaction with broad secondary alkyl Grignard reagents. Finally, detailed control experiments and density functional theory calculations revealed the desymmetrization of meso-diethers exploits a direct anti-SN2' pathway, in the absence of an in situ-generated allyl bromine intermediate. The following oxidative addition is the crucial rate-determining and enantioselectivity-determining step.

Global climate modeling of the Jupiter troposphere and effect of dry and moist convection on jets

Aims. The atmosphere of Jupiter is characterized by banded jets, including an equatorial super-rotating jet, by an intense moist con-vective activity, and by perturbations exerted by vortices, waves, and turbulence. Even after space exploration missions to Jupiter and detailed numerical modeling of Jupiter, questions remain about the mechanisms underlying the banded jets and the role played by dry and moist convection in maintaining these jets. Methods. We report three-dimensional simulations of the Jupiter weather layer using a global climate model (GCM) called Jupiter-DYNAMICO, which couples hydrodynamical integrations on an icosahedral grid with detailed radiative transfer computations. We added a thermal plume model for Jupiter that emulates the effect of mixing of heat, momentum, and tracers by dry and moist convec-tive plumes that are left unresolved in the GCM mesh spacing with a physics-based approach. Results. Our Jupiter-DYNAMICO global climate simulations show that the large-scale Jovian flow, in particular the jet structure, could be highly sensitive to the water abundance in the troposphere and that an abundance threshold exists at which equatorial super-rotation develops. In contrast to our dry (or weakly moist) simulations, simulations that include the observed amount of tropospheric water exhibit a clear-cut super-rotating eastward jet at the equator and a dozen eastward mid-latitude jets that do not migrate poleward. The magnitudes agree with the observations. The convective activity simulated by our thermal plume model is weaker in the equatorial regions than in mid to high latitudes, as indicated by lightning observations. Regardless of whether they are dry or moist, our simulations exhibit the observed inverse energy cascade from small (eddies) to large scales (jets) in a zonostrophic regime.

Dark radiation isocurvature from cosmological phase transitions

Cosmological first order phase transitions are typically associated with physics beyond the Standard Model, and thus of great theoretical and observational interest. Models of phase transitions where the energy is mostly converted to dark radiation can be constrained through limits on the dark radiation energy density (parameterized by ΔN eff). However, the current constraint (ΔN eff < 0.3) assumes the perturbations are adiabatic. We point out that a broad class of non-thermal first order phase transitions that start during inflation but do not complete until after reheating leave a distinct imprint in the scalar field from bubble nucleation. Dark radiation inherits the perturbation from the scalar field when the phase transition completes, leading to large-scale isocurvature that would be observable in the CMB. We perform a detailed calculation of the isocurvature power spectrum and derive constraints on ΔN eff based on CMB+BAO data. For a reheating temperature of T rh and a nucleation temperature T *, the constraint is approximately ΔN eff ≲ 10-5 (T */T rh)-4, which can be much stronger than the adiabatic result. We also point out that since perturbations of dark radiation have a non-Gaussian origin, searches for non-Gaussianity in the CMB could place a stringent bound on ΔN eff as well.

RMSE POWER COEFFICIENT OF WIND TURBINES WITH INVERSE TOQUE-SPEED CONTROL

The Blade Element Momentum (BEM) method stands out among various turbine modelling techniques due to its integration of airfoil aerodynamics with momentum theory, allowing detailed force calculations on blade elements. While traditional methods like BEM and Wake Models are efficient for initial turbine design, advancements in computational power have enabled the use of Computational Fluid Dynamics (CFD) for more accurate simulations. Although these models are precise, they are computationally intensive, leading to the continued use of simpler empirical methods, such as the static power coefficient approach, in power system studies. Future research aims to validate and implement dynamic estimation models to account for wind variability and turbine control dynamics. Traditional constant torque-speed control strategies maintain a constant generator speed by using a fixed electromagnetic torque command and adjusting the pitch angle when wind speed exceeds the rated value. However, if the pitch control does not respond quickly enough, rotor acceleration can occur, leading to increased power beyond the generator’s rating. To mitigate this, the pitch control mechanism must react promptly to adjust the turbine's torque profile, ensuring convergence to the rated operating point and avoiding prolonged generator overload. To reduce the burden on the pitch-control system, an inverse torque-speed control approach is proposed, where the electromagnetic torque is dynamically adjusted based on real-time rotor speed data. This method aims to achieve rated power operation with improved responsiveness and reduced stress on the pitch-control mechanism.

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

Effect of inter-module connection properties on structural sway of high-rise modular buildings

The modular steel building is a rapidly evolving prefabricated structural system, consisting of discrete volumetric modules assembled with inter-module connections. Despite numerous studies on the design optimization of inter-module connections, research on the development of realistic connection models and the correlation between connection properties and the overall structural behavior is relatively scarce. This paper introduces a multiple-spring inter-module connection model and supplies detailed property calculations of different load transfer components. The model can effectively simulate different stiffness and strength levels at inter-module connections and predict relative dislocations between assembled modules. The model is then applied to analyze the structural sway of modular buildings under seismic loads. Influences of connection modelling methods and the real connecting abilities on structural sway responses are investigated through comparative analysis of connection and module drift deformations when using conventional pin or rigid constraint connection models and the proposed realistic multiple spring model. Results indicate that simplified pin or rigid constraints cannot accurately represent the actual load transfer mechanisms at inter-module connections. The horizontal link determines the composition extent of horizontally assembled columns and modules. The horizontal shear resistance is closely related to column loads and follows the downwardly increased mode, which induces different structural sway and module drift levels in modular buildings.