Results for “dynamical phase transitions” — Page 24

DOE OSTI2026

Theory of stimulated and spontaneous axion scattering.

We present a theory for nonlinear, resonant excitation of dynamical axions by counterpropagating electromagnetic waves in materials that break both 𝒫 and 𝒯 symmetries. We show that dynamical axions can mediate an exponential growth in the amplitude of the lower frequency (Stokes) beam. We also discuss spontaneous generation of a counterpropagating Stokes mode, enabled by resonant amplification of quantum and thermal fluctuations in the presence of a single pump laser. Remarkably, the amplification can be orders of magnitude larger than that obtained via stimulated Brillouin and Raman scattering processes, and can be modulated with the application of external magnetic fields, making stimulated axion scattering promising for optoelectronics applications.

Smith, M.↗

NASA NTRS2026

Incremental Learning for Passive Microwave Precipitation Retrievals using Advanced Technology Microwave Sounder

Spaceborne passive microwave (PMW) radiometry is central to global precipitation monitoring, yet retrieval uncertainties remain substantial, particularly for cross-track sounders whose variable footprints and channel configurations are optimized for atmospheric temperature and moisture profiling rather than precipitation. Consequently, existing operational products often exhibit angular-dependent biases, limited effective swath utilization, unrealistic rainfall probability distributions, and systematic misclassification of precipitation phase. These limitations are further compounded by the scarcity of globally accurate and representative precipitation observations, as training data from the Dual-frequency Precipitation Radar (DPR) and the Cloud Profiling Radar (CPR) are spatially sparse, lack uniform global coverage, and exhibit heterogeneous error characteristics across precipitation regimes. To address these challenges, this study presents a supervised retrieval algorithm that incrementally trains an ensemble of extreme gradient-boosted decision trees by augmenting base learners with pre-training on reanalysis data and post-training on coincident DPR and CPR observations matched with the Advanced Technology Microwave Sounder (ATMS). By transferring prior information from reanalysis to posterior constraints from radar observations and adopting a sequential detection–estimation strategy for precipitation phase and rate retrieval, the proposed approach yields retrievals across the full ATMS swath that are largely free from persistent deficiencies in current Global Precipitation Measurement (GPM) passive microwave operational products. In particular, the method resolves bimodal artifacts in rainfall retrievals and mitigates systematic high-latitude snowfall biases, including overestimation across the Arctic and underestimation across the Antarctic. Validation against independent Multi-Radar Multi-Sensor (MRMS) data over the Contiguous United States (CONUS) further demonstrates improved performance in precipitation phase detection and rate estimation relative to both reanalysis and current GPM PMW products.

Mahyar Garshasbi↗

DOE OSTI2026

Time Correlations from Steady-State Expectation Values

Recovering properties of correlation functions is typically challenging. On the one hand, experimentally, it requires measurements with a temporal resolution finer than the system’s dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a system parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable, and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to the experimental characterization of ultrafast systems and to the theoretical analysis of many-body models whose dynamics are hard to compute.

Górecki, Wojciech [INFN, Pavia] (ORCID:00000001991↗

DOE OSTI2023

Thermal Disorder‐Induced Strain and Carrier Localization Activate Reverse Halide Segregation

The reversal of halide ions is studied under various conditions. However, the underlying mechanism of heat-induced reversal remains unclear. This work finds that dynamic disorder-induced localization of self-trapped polarons and thermal disorder-induced strain (TDIS) can be co-acting drivers of reverse segregation. Localization of polarons results in an order of magnitude decrease in excess carrier density (polaron population), causing a reduced impact of the light-induced strain (LIS – responsible for segregation) on the perovskite framework. Meanwhile, exposing the lattice to TDIS exceeding the LIS can eliminate the photoexcitation-induced strain gradient, as thermal fluctuations of the lattice can mask the LIS strain. Under continuous 0.1 W cm -2 illumination (upon segregation), the strain disorder is estimated to be 0.14%, while at 80 °C under dark conditions, the strain is 0.23%. However, in situ heating of the segregated film to 80 °C under continuous illumination (upon reversal) increases the total strain disorder to 0.25%, where TDIS is likely to have a dominant contribution. Therefore, the contribution of entropy to the system's free energy is likely to dominate, respectively. Various temperature-dependent in situ measurements and simulations further support the results. These findings highlight the importance of strain homogenization for designing stable perovskites under real-world operating conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Fingerprinting Uranium Oxides with Electron Energy Loss Spectroscopy Supported by Theoretical Computations

Uranium oxides occur in a variety of phases that differ in crystal structure and uranium oxidation states. Electron energy loss spectroscopy (EELS) is one of the few techniques that has sufficient spatial resolution and sensitivity to electronic structure to distinguish amongst phases at the nanoscale. However, beam-sensitive materials such as uranium oxides are subject to spectral modification due to interactions with the electron beam. Therefore, theory support is essential to reliably exclude the impact of beam damage and generate true reference datasets. Here we use a comparison of theoretical and experimental spectra to probe the impact of beam damage on O K-edge and U N-edge (N6,7 and N4,5) EELS spectra of various single-valent and mixed-valence uranium oxide bulk phases. Using a low-dose experimental set-up, we show that the O K-edge theoretical spectra are in excellent agreement with experiment for both peak positions and relative intensities of respective peaks. In contrast, U N-edge features are less distinguishing due to the partially localized nature of the U 5f orbitals and overlapping multiplet and spin–orbit coupling effects. This work demonstrates that O K-edge EELS is sufficiently diagnostic to distinguish a wide range of uranium oxides and that the experimental approach used here minimizes beam damage and allows valence state discrimination across the U(IV), U(V) and U(VI) series. When combined with imaging modes available in electron mi-croscopy, the work enables detailed investigation and characterization of uranium redox transformations at the nanoscale.

Carbone, Jacopo↗

NASA NTRS1994

Astrophysical science with a spaceborne photometric telescope

The FRESIP Project (FRequency of Earth-Sized Inner Planets) is currently under study at NASA Ames Research Center. The goal of FRESIP is the measurement of the frequency of Earth-sized extra-solar planets in inner orbits via the photometric signature of a transit event. This will be accomplished with a spaceborne telescope/photometer capable of photometric precision of two parts in 100,000 at a magnitude of m(sub v) = 12.5. To achieve the maximum scientific value from the FRESIP mission, an astrophysical science workshop was held at the SETI Institute in Mountain View, California, November 11-12, 1993. Workshop participants were invited as experts in their field of astrophysical research and discussed the astrophysical science that can be achieved within the context of the FRESIP mission.

Granados, Arno F.↗

NASA NTRS2008

Spray Forming of NiTi and NiTiPd Shape-Memory Alloys

In the work to be presented, vacuum plasma spray forming has been used as a process to deposit and consolidate prealloyed NiTi and NiTiPd powders into near net shape actuators. Testing showed that excellent shape memory behavior could be developed in the deposited materials and the investigation proved that VPS forming could be a means to directly form a wide range of shape memory alloy components. The results of DSC characterization and actual actuation test results will be presented demonstrating the behavior of a Nitinol 55 alloy and a higher transition temperature NiTiPd alloy in the form of torque tube actuators that could be used in aircraft and aerospace controls.

Aero-Surface Controls↗

NASA NTRS2026

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

stagnation heat flux↗

NASA NTRS2026

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

inviscid theory↗

NASA NTRS1964

Thermal Design

An essential phase of the Explorer XIII development was a thermal study and design to provide an acceptable temperature environment for the electronics components and external surfaces of the satellite during ascent and in orbit. It was necessary to establish by preflight analysis and tests that tolerable temperatures could be maintained in three regimes of flight. In the first regime (from launch until release of the heat shield) the satellite was subjected to radiative and conductive heat from the shield. In the second regime, after release of the shield at 350,000 feet, the satellite was heated by free molecular flow. In the third regime - the orbit phase - it was necessary that temperatures within limits for a 1-year lifetime be established. In addition to these three regimes, a study was made to investigate the effect of elevated rocket-motor temperatures during launch and after burnout. This chapter will deal with some pertinent preflight estimates and correlation of these estimates with flight data.

Explorer XIII Satellite↗

DOE OSTI2025

Transforming Windows from Energy Liabilities to Zero-Energy Assets: Next-Generation Solutions for Buildings

Windows have traditionally contributed to a building's HVAC load, but they can also become a source of net energy gain or even operate as zero-energy components. For heating applications, highly insulating windows can harness more solar heat than the energy lost through them, transforming windows from energy liabilities to assets. Dynamic glazings provide further benefits by regulating solar heat gain, reducing cooling loads in summer and heating demands in winter. This simulation study focuses on developing the next generation of zero-energy windows (ZEW) for residential new construction. Through annual energy simulations across climate zones 1-8, ZEW performance benchmarks were established based on current code-level buildings, and we've identified the regions where meeting ZEW standards are most achievable. This work evaluates both static and dynamic window technologies, assessing their effects on annual energy use and cost. Key findings demonstrate that ZEW performance is achievable across diverse climate zones, with specific regional requirements. Most climate zones from 3-8 can achieve ZEW with specific configurations, while some warm climates (1-2) appear challenging for ZEW implementation. Climate zones 4-6 consistently allow for zero energy window implementation, offering multiple pathways through either static or dynamic window technologies. Colder climate zones (7-8) ZEW products allow for higher SHGC values while requiring low U-values.

Yu, Lili↗

NASA NTRS2026

The Contaminant Footprint of Landed Spacecraft: Toward an Inventory and Modelling Framework

All spacecraft generate and carry contaminants, i.e., unwanted and potentially harmful material. When a spacecraft lands and operates in near-vacuum, as onto Earth’s Moon, it introduces contaminants into its environment that may compromise mission science objectives and engineering performance. Contamination of solar system bodies may irrevocably degrade targets of unique value to planetary scientists, for instance, as lunar landed spacecraft introduce propellant effluents into the otherwise pristine ice of the Moon’s permanently shadowed regions. NASA’s planetary protection discipline seeks to ensure that solar system bodies are not contaminated, for scientific purposes, by terrestrial material (i.e., forward contamination). This interest aligns with planetary science interest in mitigating the transport of terrestrial contaminants onto solar system bodies and in controlling types of contamination that could compromise the scientific value of samples or measurements. NASA, and other entities that practice planetary science, have compelling and multidisciplinary interests in the preservation of special regions and sampling sites of high scientific value – including lunar permanently shadowed regions (PSRs) – from inadvertent contamination by any spacecraft, and in understanding the contamination of such regions by all spacecraft. Organic molecular contamination here represents a primary threat. Organic molecules will be introduced to solar system bodies by nominal landed spacecraft and crew processes – including by the action of descent and ascent engines; natural materials outgassing; and crew environmental and life support system sources. Molecular contaminants can also travel in the free-molecular sense at global scale across near-vacuum bodies, including into regions where they may be permanently trapped. This presentation will address a high-level study to identify sources of contaminants – in particular, organic material – generated by landed spacecraft along with the transport vectors by which these contaminants can reach sites of scientific interest on bodies like the Moon. A vision for an integrated modeling framework for the organic contamination footprint of spacecraft missions, individually and collectively, will also be described and presented along with initial conclusions related to organic molecular transport.

Gas Dynamics↗

DOE OSTI2026

Valorization of consolidated bioprocessing residues for bioplastics

This study demonstrates an organic solvent-free processing strategy to valorize consolidated bioprocessing (CBP) residues, from switchgrass and poplar biomass, into functional poly(butylene succinate) (PBS)-based biocomposites using high-shear homogenization (HSH). HSH transformed the switchgrass and poplar CBP residues (CBP-R) into fine, uniformly distributed particles and microfibers. The composites of PBS with homogenized switchgrass residues (H-CBP-R-SG) or homogenized poplar residues (H-CBP-R-P) at a 70/30 weight ratio exhibited improved processability and mechanical integrity, with the Young's modulus for the PBS/H-CBP-R-SG and PBS/H-CBP-R-P nearly doubling to 0.66 ± 0.07 GPa and 0.65 ± 0.04 GPa, respectively, compared to neat PBS (0.36 ± 0.02 GPa). Dynamic Mechanical Analysis (DMA) reveals a significant suppression of the tan δ peak magnitude, indicating that HSH-mediated physical activation facilitates stress transfer in composites typical of covalent chemical grafting systems. While the transition to a stiffness-dominated profile reduces ductility, the resulting composites exhibit the dimensional stability and resistance to thermal warping required for high-fidelity FDM 3D printing and injection molding. Beyond material performance, comprehensive techno-economic analysis (TEA) and life cycle assessment (LCA) confirmed that diverting CBP residues into composite products can improve the economic viability of the biorefinery without substantially increasing biorefinery global warming potential (GWP). At a 30 wt% blend ratio, incorporating residuals into PBS yielded a minimum selling price for the composite of $\$4.07$ per kg compared to the conventional bioplastic price of $\$5.00$ per kg. This approach aligns with circular bioeconomy principles by converting waste streams into value-added products. Furthermore, this innovative strategy addresses key challenges in bioplastic development, including cost, compatibility, and performance, while simultaneously advancing waste minimization strategies for sustainable manufacturing systems.

09 BIOMASS FUELS↗

NASA NTRSDate not supplied

Performance of a Regenerative Fuel Cell System for the Lunar Surface

Regenerative fuel cells (RFCs) are an attractive energy storage solution for lunar missions as a technology capable of providing a higher specific energy (i.e., W∙h/kg) than state-of-the-art packaged Li-ion battery systems. An RFC consists of the (1 & 2) electrochemical stacks (chemical to electrical energy conversion to supply electricity to an external load, i.e. the fuel cell reaction, and electrical to chemical energy conversion of supplied electrical power to dissociate water into hydrogen and oxygen gases, i.e. water electrolysis), (3) fluidic conditioning, (4) reactant storage, (5) avionics, (6) power management and distribution (PMAD), and (7) thermal management. NASA’s Glenn Research Center has designed, assembled, and tested a breadboard RFC sys-tem capable of operating autonomously for multiple simulated lunar day/night cycles in a laboratory environment. The system is comprised of a non-flow through proton exchange membrane (PEM) fuel cell stack and a liquid-anode feed PEM electrolyzer (EZ) stack designed to electrochemically compress the reactants at balanced pressures up to 12.4 MPa (1800 psia). The fluidic conditioning, avionics, PMAD, and thermal management sub-systems are largely comprised of commercial-off-the-shelf components for this system-level development effort. The hardware is controlled by a CubeSat space processor running an operational program based on core flight architecture that can control the RFC hardware autonomously through a state machine with fault monitoring. The testing results highlighted here were completed with the system in an open-loop configuration such that reactants generated through water electrolysis were vented while gas cylinders supplied fuel cell operation. The breadboard operated autonomously, but there were five unplanned transitions to a safe state that required a manual restart after reviewing the data, determining a root cause, and implementing a solution. Four of the transitions were caused by the thermal management subsystem and the fifth was caused by a water management control issue in the EZ sub-system. The RFC system operated for over 550 hours with the final cycle being slightly abbreviated due to reasons unrelated to system performance.

Kerrigan Cain↗

NASA NTRSDate not supplied

Performance of a Regenerative Fuel Cell System for the Lunar Surface

Regenerative fuel cells (RFCs) are an attractive energy storage solution for lunar missions as a technology capable of providing a higher specific energy (i.e., W∙h/kg) than state-of-the-art packaged Li-ion battery systems. An RFC consists of the (1 & 2) electrochemical stacks (chemical to electrical energy conversion to supply electricity to an external load, i.e. the fuel cell reaction, and electrical to chemical energy conversion of supplied electrical power to dissociate water into hydrogen and oxygen gases, i.e. water electrolysis), (3) fluidic conditioning, (4) reactant storage, (5) avionics, (6) power management and distribution (PMAD), and (7) thermal management. NASA’s Glenn Research Center has designed, assembled, and tested a breadboard RFC sys-tem capable of operating autonomously for multiple simulated lunar day/night cycles in a laboratory environment. The system is comprised of a non-flow through proton exchange membrane (PEM) fuel cell stack and a liquid-anode feed PEM electrolyzer (EZ) stack designed to electrochemically compress the reactants at balanced pressures up to 12.4 MPa (1800 psia). The fluidic conditioning, avionics, PMAD, and thermal management sub-systems are largely comprised of commercial-off-the-shelf components for this system-level development effort. The hardware is controlled by a CubeSat space processor running an operational program based on core flight architecture that can control the RFC hardware autonomously through a state machine with fault monitoring. The testing results highlighted here were completed with the system in an open-loop configuration such that reactants generated through water electrolysis were vented while gas cylinders supplied fuel cell operation. The breadboard operated autonomously, but there were five unplanned transitions to a safe state that required a manual restart after reviewing the data, determining a root cause, and implementing a solution. Four of the transitions were caused by the thermal management subsystem and the fifth was caused by a water management control issue in the EZ sub-system. The RFC system operated for over 550 hours with the final cycle being slightly abbreviated due to reasons unrelated to system performance.

Kerrigan Cain↗

DOE OSTI2025

Numerical simulation of frost formation and heat transfer on fin-and-tube heat exchangers in turbulent cross-flow

Frost formation in fin-and-tube heat exchangers in turbulent cross-flow presents significant challenges in industrial refrigeration applications, affecting heat transfer efficiency and operational reliability. The purpose of this work is to investigate frost deposition and growth on a staggered bank of a fin-and-tube freezer coil under turbulent forced convection conditions. The focus here is on investigating conditions that closely replicate real-world scenarios in large walk-in industrial freezers. Using a direct numerical simulation approach, we examine the flow dynamics and thermal behaviour in the presence of frost, considering turbulent regimes characterized by a Reynolds number in the range 1050 ≤ R e D , avg ≤ 4800 , with the characteristic length being the outer diameter of the tube and the velocity being the bulk fluid velocity between the plates (fins). Computational fluid dynamics simulations are employed to resolve the interactions between turbulent airflow and the frost layer. Our approach incorporates a modified immersed boundary method and a slow-time acceleration technique to address the complex dynamic interface between the continuously evolving frost layer and the flowing air stream. Our findings indicate that frost forms more on the sides of the finned surfaces (plates) and less on the tubes themselves. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics↗

DOE OSTI2026

Purpose, Design, and Analysis of the NSTX-U Centerstack Casing Lateral Support Shims

The National Spherical Torus Experiment Upgrade (NSTX-U) centerstack casing surrounds the central magnet core of NSTXU. It provides the inner vacuum boundary of the plasma chamber and supports the radially inboard plasma facing components lining the plasma chamber. The casing is supported like a cantilever, fixed at the lower flange by a connection to the TF Bundle through a G-10 ring. It is flexibly supported at the top by bellows, and insulated shims intended to react the largest part of the inventory of the disruption loads at the upper support, thereby protecting the upper and lower connections from excessive loads. A large part of the qualification of the casing and tiles requires addressing and quantifying disruption loads. These have been estimated based on extensions of the behavior of NSTX during its run period roughly 15 years ago. Structural qualification of the Upgrade used these estimates of the loading as input to calculations to demonstrate adequacy for a “most probable” disruption. The estimates are included in a requirements document to guide conservative design of all components loaded by disruptions. However, the changes made for the upgrade made the extrapolation of disruption behavior uncertain. Disruptions include axisymmetric loading from axisymmetric currents induced in the vessel shells. In addition, more complex currents called Halo currents are a result of plasma poloidal currents impinging on the casing. The halo currents add another layer of uncertain behavior and net lateral loading to the casing. As a result, NSTX-U is equipped with a number of instruments intended to assess the nature and severity of disruptions. The casing shims are required for lateral support of the casing, but these have also been converted to load cells to provide another measure of the magnitude of symmetric and asymmetric loading. Some of the logic in the development of the requirements document are presented. Electromagnetic analysis of axisymmetric and halo loading is described. Global simulations of the casing transient dynamic response, and local analysis and testing of the shim/load cell are included. The shim load cells and other instrumentation will be an important guide in planning NSTX-U experiments beyond its next run period expected in late 2026 or early 2027.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2018

Initial Jitter Analysis of Lynx, a Proposed Future Large Astrophysics Facility

Lynx is an X-Ray telescope large-mission concept for consideration in NASA's 2020 Astrophysics Decadal Survey. A conceptual structural design is evolving that leverages the success and lessons learned from Chandra and that takes into account unique needs of Lynx. Space optics systems require extreme stability. Any motion in-service (thermal effects, structural dynamics, etc.) impacts performance. An initial analysis was performed to predict the first-cut dynamic responses, jitter, at two selected points on the Lynx observatory. One point is on the Lynx X-ray Mirror Assembly (LMA) and the other, on the focal plane Integrated Science Instrument Module (ISIM). Relative motion between these two points was predicted along with vibration spectra. This information will be used in upcoming analyses of the LMA and the ISIM.

J Brent Knight↗