Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “two-component system”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Heterologous synthesis of a simplified nitrogenase analog in Escherichia coli

The heterologous synthesis of a nitrogen-fixing system in a non-diazotrophic organism is a long-sought-after goal because of the crucial importance of nitrogenase for agronomy, energy, and the environment. Here, we report the heterologous synthesis of a two-component nitrogenase analog fromAzotobacter vinelandii, which consists of the reductase component (NifH) and the cofactor maturase (NifEN), inEscherichia coli. Metal, electron paramagnetic resonance, and activity analyses verify the cluster composition and functional competence of the heterologously expressed NifH and NifEN. Nuclear magnetic resonance, nanoscale secondary ion mass spectrometry, and growth experiments further illustrate the ability of the NifH/NifEN system to reduce N 2 and incorporate the reduced N into the cellular mass. These results establish NifEN/NifH as a simplified nitrogenase analog that could be optimized and engineered to facilitate transgenic expression and biotechnological adaptations of this important metalloenzyme.

Science & Technology - Other Topics↗

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q , in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ ∝ I ν (S)/S ν , where I ν (S) is the modified Bessel function of the entropy S . For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z , …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. Further, the additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E , Q) for a set of the integrals of motion Q = { N, Z }, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K , which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Early Light Curve of the Type Ia Supernova 2021hpr in NGC 3147: Progenitor Constraints with the Companion Interaction Model

The progenitor system of Type Ia supernovae (SNe Ia) is expected to be a close binary system consisting of a carbon/oxygen white dwarf (WD) and a nondegenerate star or another WD. Here, we present results from high-cadence monitoring observations of SN 2021hpr in a spiral galaxy, NGC 3147, and constraints on the progenitor system based on its early multicolor light-curve data. First, we classify SN 2021hpr as a normal SN Ia from its long-term photometric and spectroscopic data. More interestingly, we found a significant "early excess" in the light curve over a simple power-law ~t 2 evolution. The early light curve evolves from blue to red to blue during the first week. To explain this, we fitted the early part of the BVRI-band light curves with a two-component model consisting of ejecta–companion interaction and a simple power-law model. The early excess and its color can be explained by shock-cooling emission due to a companion star having a radius of 8.84 ± 0.58 R ⊙ . We also examined Hubble Space Telescope preexplosion images, finding no detection of a progenitor candidate, consistent with the above result. However, we could not detect signs of a significant amount of stripped mass from a nondegenerate companion star (≲0.003 M ⊙ for Hα emission). The early excess light in the multiband light curve supports a nondegenerate companion in the progenitor system of SN 2021hpr. At the same time, the nondetection of emission lines opens the door for other methods to explain this event.

79 ASTRONOMY AND ASTROPHYSICS↗

Cross-family and phage-specific gene requirements for Klebsiella infection revealed by scalable RB-TnSeq genetic screens.

Bacteriophages are being cataloged at an accelerating pace and are recognized as key players in nutrient and energy cycling across ecosystems. Yet the bacterial genetic determinants that govern phage-host specificity and infection success remain poorly understood, particularly in clinically and ecologically important genera such as Klebsiella where prior receptor characterization has been almost entirely limited to capsulated strains. Here we used a randomly barcoded, genome-wide, loss-of-function transposon mutant library (RB-TnSeq) of Klebsiella sp. M5al, a naturally acapsular, nitrogen-fixing rhizobacterium, to generate the first systematic, cross-family map of phage receptor gene dependencies in Klebsiella. Challenging the library against 25 double-stranded DNA phages spanning five families in 213 parallel assays, we identified 42 bacterial genes associated with phage infection, of which 15 had no prior association with phage infection in any bacterial system. Disruption of surface receptor biosynthesis genes conferred cross-resistance across multiple phage families, while intracellular gene disruptions had predominantly phage-specific effects. Clonal validation of eight genes confirmed LPS outer core biosynthesis genes as primary receptor determinants alongside additional host factors spanning outer membrane transport, cofactor biosynthesis, and two-component signaling. Comparative analysis across all 25 phages revealed that phage genus rather than family is the stronger predictor of host gene dependency profiles, a finding with direct implications for the functional annotation of uncharacterized phage isolates and rational phage cocktail design. Together, these findings provide a community resource for linking phage genomic diversity to functional host interaction space in this ecologically and clinically important genus.

Gittrich, Marissa R↗

Spectroscopic investigation of cation effects in U(VI)-NO3- complexation in aqueous solutions

Understanding and manipulating uranyl speciation in aqueous solutions is critical for advancing chemical separation, sensing, and understanding environmental transport of uranyl. We report on the significant enhancement in the complexation of uranyl with nitrate in aqueous solutions containing quaternary ammonium cations leading to the formation of anionic complexes. We base this on the comparative study of the effect of monovalent cations (Na+, Li+, NH4+, and N(CH3)4+) on the complexation equilibria of uranyl-nitrate in solutions, probed by time-resolved laser induced fluorescence spectroscopy (TRLFS). Lifetime-corrected spectra, obtained by extrapolating the time-resolved spectra to t = 0, were used to study speciation to mitigate the effects of variations in the fluorescence lifetimes that depend on extraneous factors such as dynamic quenching. We demonstrate that the lifetime-corrected spectra can be used to determine uranyl speciation in aqueous solutions where the mono-nitrate complex forms, and in acetonitrile with N(CH3)4NO3 where di-nitrate and tris-nitrato species are formed. Aqueous solutions containing N(CH3)4+ are shown to promote the formation of higher complexes of uranyl compared to other inorganic nitrate salts based on the higher redshift in the spectra, poor fits to the two-component model, and the higher apparent formation constants. Comparing the trends in uranyl speciation in the presence of N(CH3)4+ in aqueous and acetonitrile solutions, it is proposed that the quaternary ammonium cations (quats) promote the formation of anionic complexes of uranyl by the ion-association mechanism. These results provide a basis for designing quat-assisted separation systems that target anionic actinide species in aqueous solutions.

Nayak, Srikanth (ORCID:0000000302135796)↗

Magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria: A DFT cluster expansion study

Magnetic contributions have the potential to significantly influence predicted phase stability within alloy and mineral mixing phase diagrams, yet have been historically challenging to incorporate due to a significant increase to phase space sampling. Here, in this work, we employ a computational protocol that includes spin orientation as an additional configurational component within multi-component cluster expansions between magnetic and non-magnetic metal oxide alloys [calculated using density functional theory (DFT) and the generalized gradient approximation]. This approach was used to determine the effect of magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria from first principles. Two-component cluster expansions of the magnetic components of eskolaite and hematite were first performed showing the ability of this method to properly calculate their respective magnetic properties. Two-component cluster expansions were then performed for non-magnetic Al(III) and ferromagnetic Cr(III) and Fe(III), and phase diagrams were calculated for later comparison. Finally, a non-magnetic Al(III) and “up” and “down” magnetic configurations for anti-ferromagnetic Cr(III) and Fe(III) were performed. Magnetic contributions to the calculated phase diagram for the corundumeskolaite system were shown to be inconsequential but are vital for accurate determination of the corundum-hematite solvus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Secular outflows from 3D MHD hypermassive neutron star accretion disc systems

Magnetized hypermassive neutron stars (HMNSs) have been proposed as a way for neutron star mergers to produce high electron fraction, high-velocity ejecta, as required by kilonova models to explain the observed light curve of GW170817. The HMNS drives outflows through neutrino energy deposition and mechanical oscillations, and raises the electron fraction of outflows through neutrino interactions before collapsing to a black hole (BH). Here, in this study, we perform 3D numerical simulations of HMNS–torus systems in ideal magnetohydrodynamics, using a leakage/absorption scheme for neutrino transport, the nuclear APR equation of state, and Newtonian self-gravity, with a pseudo-Newtonian potential added after BH formation. Due to the uncertainty in the HMNS collapse time, we choose two different parametrized times to induce collapse. We also explore two initial magnetic field geometries in the torus, and evolve the systems until the outflows diminish significantly ($\sim\!\! 1\!\! - \!\!2\ \mathrm{s}$). We find bluer, faster outflows as compared to equivalent BH–torus systems, producing M ∼ 10 −3 M ⊙ of ejecta with Y e ≥ 0.25 and v ≥ 0.25c by the simulation end. Approximately half the outflows are launched in disc winds at times $t\lesssim 500 \ \mathrm{ms}$, with a broad distribution of electron fractions and velocities, depending on the initial condition. The remaining outflows are thermally driven, characterized by lower velocities and electron fractions. Nucleosynthesis with tracer particles shows patterns resembling solar abundances in all models. Although outflows from our simulations do not match those inferred from two-component modelling of the GW170817 kilonova, self-consistent multidimensional detailed kilonova models are required to determine whether our outflows can power the blue kilonova.

79 ASTRONOMY AND ASTROPHYSICS↗

Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between 𝑁 = 0 and 𝑁 = 1 electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component 2/5 state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Bilayer graphene↗

Observation of Vortex Stripes in UTe 2

In conventional type-II superconductors, quantum vortices determine the magnetic response of the system and tend to form regular lattices. UTe 2 is a recently discovered heavy Fermion superconductor exhibiting many anomalous macroscopic behaviors, but whether it has a multicomponent order parameter remains open. Here, in this work, we study the vortices of UTe 2 by employing scanning superconducting quantum interference device microscopy. While a small out-of-plane magnetic field produces typical isolated vortices, a higher field generates vortex stripe patterns that evolve with the vortex density. The stripes form at different locations and along different directions in the surface plane when the field is along the b or c axis. The behavior is reproduced by our simulation based on an anisotropic two-component order parameter. This study shows that UTe 2 has a nontrivial disparity of multiple length scales, placing constraints on the multicomponent superconductivity.

UTe2↗

Tunable pairing with local spin-dependent Rydberg molecule potentials in an atomic Fermi superfluid

We explore the energy spectrum and eigenstates of two-component atomic Fermi superfluids with tunable pairing interactions in the presence of spin-dependent ultralong-range Rydberg molecule (ULRM) potentials, within the Bogoliubov–de Gennes formalism. The attractive ULRM potentials lead to local-density accumulation, while their difference results in a local polarization potential and induces the in-gap Yu-Shiba-Rusinov (YSR) states whose energies lie below the bulk energy gap. A transition from equal population to population imbalance occurs as the pairing strength falls below a critical value, accompanied by the emergence of local Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)–like states characterized by out-of-phase wave functions and lower energies compared to the YSR states. The negative contribution emanating from the FFLO-like states also causes a sign change in the gap function within the ULRM potentials. Depending on the Rydberg excitation, the transition towards population imbalance can be on either the BCS or the Bose-Einstein condensation side of the Fermi superfluid. Additionally, spin-polarized bound states arise along with oscillatory “clumpy states” to compensate for the local-density difference. Here, we discuss possible experimental realizations of the composite Rydberg-atom–Fermi-superfluid system.

Cold and ultracold molecules↗

17 O NMR Spectroscopy Reveals CO 2 Speciation and Dynamics in Hydroxide-Based Carbon Capture Materials

Carbon dioxide capture technologies are set to play a vital role in mitigating the current climate crisis. Solid-state 17 O NMR spectroscopy can provide key mechanistic insights that are crucial to effective sorbent development. In this work, we present the fundamental aspects and complexities for the study of hydroxide-based CO 2 capture systems by 17 O NMR. We perform static density functional theory (DFT) NMR calculations to assign peaks for general hydroxide CO 2 capture products, finding that 17 O NMR can readily distinguish bicarbonate, carbonate and water species. However, in application to CO 2 binding in two test case hydroxide-functionalised metal-organic frameworks (MOFs) – MFU-4l and KHCO 3 -cyclodextrin-MOF, we find that a dynamic treatment is necessary to obtain agreement between computational and experimental spectra. We therefore introduce a workflow that leverages machine-learning force fields to capture dynamics across multiple chemical exchange regimes, providing a significant improvement on static DFT predictions. In MFU-4l, we parameterise a two-component dynamic motion of the bicarbonate motif involving a rapid carbonyl seesaw motion and intermediate hydroxyl proton hopping. For KHCO 3 -CD-MOF, we combined experimental and modelling approaches to propose a new mixed carbonate-bicarbonate binding mechanism and thus, we open new avenues for the study and modelling of hydroxide-based CO 2 capture materials by 17 O NMR.

NMR spectroscopy↗

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated nitrogen atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. Furthermore, these results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian with Size-Intensive Picture Change

We present a simple relativistic exact 2-component (X2C) Hamiltonian that models two-electron picture-change effects using Lehtola’s superposition of atomic potentials (SAP) [S. Lehtola, J. Chem. Theory Comput. 15, 1593−1604 (2019)]. The SAP-X2C approach retains the low cost and technical simplicity of the popular 1-electron X2C (1eX2C) predecessor but is significantly more accurate and has a well-defined thermodynamic limit, making it applicable to extended systems (such as large molecules and periodic crystals). The assessment of the SAP-X2C-based Hartree−Fock total and spinor energies, spin−orbit splittings, equilibrium bond distances, and harmonic vibrational frequencies suggests that SAP-X2C is similar to the more complex atomic meanfield (AMF) X2C counterparts in its ability to approximate the 4-component Dirac−Hartree−Fock reference.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing the origin of the two-component structure of broad-line region by reverberation mapping of an extremely variable quasar

ABSTRACT The physical origins of quasar components, such as the broad-line region (BLR) and dust torus, remain under debate. To gain insights into them, we focused on changing-state quasars (CSQs) which provide a unique perspective through structural changes associated with accretion disc state transitions. We targeted SDSS J125809.31+351943.0, an extremely variable CSQ, to study its central core structure and kinematics. We conducted reverberation mapping with optical spectroscopy to explore the structure of the BLR and estimate the black hole mass. The results from Hβ reverberation mapping indicated a black hole mass of $10^{9.64^{+0.11}_{-0.20}}\rm {M_\odot }$. Additionally, we analysed variations in the optical to X-ray spectral indices, αox, before and after the state transition, to investigate the accretion disc. These variations in αox and the Eddington ratio (from 0.4 per cent to 2.4 per cent) exhibitied behaviour similar to state transitions observed in X-ray binary systems. Spectral analysis of Hβ revealed a predominantly double-peaked profile during dim periods, transitioning to include a single-peaked component as the quasar brightened, suggesting that Hβ contains a mixture of two components. Each of these components has its distinct characteristics: the first is a double-peaked profile that remains stable despite changes in the accretion rate, while the second is a variable single-peaked profile. Using time-lags from reverberation mapping, we estimated the spatial relationships between these BLR components, the accretion disc, and the dust torus. Our results suggest that the BLR consists of two distinct components, each differing in location and origin.

Nagoshi, Shumpei (ORCID:0000000326504322)↗

Correcting for Selection Biases in the Determination of the Hubble Constant from Time-Delay Cosmography

The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred ⁠H 0 . The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred H 0 by 8 per cent. Here, we test the assumption that the density profiles of galaxy–galaxy and galaxy–quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy–galaxy and galaxy–quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy–galaxy lenses have systematically higher mass-sheet components than galaxy–quasar lenses. For individual systems, λ int correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO hierarchical inference code, we find that H 0 is lowered by a further 3 per cent. Using a more recent measurement of velocity dispersions and our fiducial model for selection biases, we infer H 0 = 66 ± 4 (stat) ± 1 (model sys) ± 2 (measurement sys) km s -1 Mpc -1 for the TDCOSMO plus SLACS data set. The first residual systematic error is due to plausible alternative choices in modelling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.

79 ASTRONOMY AND ASTROPHYSICS↗

Relativistic Exact Two-Component Theory in the Generalized Pseudospectral Representation

We present a formulation and implementation of exact two-component (X2C) relativistic theory in the generalized pseudospectral representation. When combined with the Hartree-Fock-Slater framework, this approach enables efficient and accurate treatments of scalar-relativistic and spin-orbit effects in atomic electronic structures without the computational overhead of four-component methods. Benchmark calculations across light and heavy elements demonstrate that the our X2C scheme yields substantially more accurate relativistic corrections to core-electron binding energies than perturbational Breit-Pauli treatments while converging more rapidly with respect to basis size. The method provides an improved computational framework for modeling ultrafast x-ray-induced processes in heavy-element systems.

Wang, Xubo↗

Unified Description of Cuprate Superconductors by Fractionalized Electrons Emerging from Integrated Analyses of Photoemission Spectra and Quasiparticle Interference

Electronic structure of high-temperature superconducting cuprates is studied by analyzing experimental data independently obtained from two complementary spectroscopies: one, quasiparticle interference (QPI) measured by scanning-tunneling microscopy, and the other, angle-resolved photoemission spectroscopy (ARPES). We combine these two sets of data in a unified theoretical analysis. Through explicit calculations of experimentally measurable quantities, we show that a simple two-component fermion model (TCFM) representing electron fractionalization succeeds in reproducing various detailed features of these experimental data: ARPES and QPI data are concomitantly reproduced by the TCFM in full energy and momentum spaces. The measured QPI pattern reveals a signature characteristic of the TCFM, distinct from the conventional single-component prediction, supporting the validity of the electron fractionalization in the cuprates. The integrated analysis also solves the puzzles of ARPES and QPI data that are seemingly inconsistent with each other. The overall success of the TCFM offers a comprehensive understanding of the electronic structure of the cuprates, in particular, the unoccupied side of the spectra, of which momentum-resolved structure has long been unexplored experimentally. We further predict that a characteristic QPI pattern should appear in the unoccupied high-energy part if the fractionalization is at work. We propose that integrated-spectroscopy analyses offer a promising way to explore challenging issues of strongly correlated electron systems.

Sakai, Shiro [Sophia University; RIKEN Center for ↗