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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.

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At least 1,459 records · Page 81
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Statistical model based iterative reconstruction (MBIR) in clinical CT systems: Experimental assessment of noise performance

Purpose: To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system. Methods: Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo{sup ®}, GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods. Results: (1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a “redder” NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose){sup −β} with the component β ≈ 0.25, which violated the classical σ ∝ (dose){sup −0.5} power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2. Conclusions: The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Universal Human Papillomavirus Typing Assay: Whole-Genome Sequencing following Target Enrichment

We designed a universal human papillomavirus (HPV) typing assay based on target enrichment and whole-genome sequencing (eWGS). The RNA bait included 23,941 probes targeting 191 HPV types and 12 probes targeting beta-globin as a control. We used the Agilent SureSelect XT2 protocol for library preparation, Illumina HiSeq 2500 for sequencing, and CLC Genomics Workbench for sequence analysis. Mapping stringency for type assignment was determined based on 8 (6 HPV-positive and 2 HPV-negative) control samples. Using the optimal mapping conditions, types were assigned to 24 blinded samples. eWGS results were 100% concordant with Linear Array (LA) genotyping results for 9 plasmid samples and fully or partially concordant for 9 of the 15 cervical-vaginal samples, with 95.83% overall type-specific concordance for LA genotyping. eWGS identified 7 HPV types not included in the LA genotyping. Since this method does not involve degenerate primers targeting HPV genomic regions, PCR bias in genotype detection is minimized. With further refinements aimed at reducing cost and increasing throughput, this first application of eWGS for universal HPV typing could be a useful method to elucidate HPV epidemiology.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

An Evaluation of the Economic and Resilience Benefits of a Microgrid in Northampton, Massachusetts

Recent developments and advances in distributed energy resource (DER) technologies make them valuable assets in microgrids. This paper presents an innovative evaluation framework for microgrid assets to capture economic benefits from various grid and behind-the-meter services in grid-connecting mode and resilience benefits in islanding mode. In particular, a linear programming formulation is used to model different services and DER operational constraints to determine the optimal DER dispatch to maximize economic benefits. For the resiliency analysis, a stochastic evaluation procedure is proposed to explicitly quantify the microgrid survivability against a random outage, considering uncertainties associated with photovoltaic (PV) generation, system load, and distributed generator failures. Optimal coordination strategies are developed to minimize unserved energy and improve system survivability, considering different levels of system connectedness. The proposed framework has been applied to evaluate a proposed microgrid in Northampton, Massachusetts that would link the Northampton Department of Public Works, Cooley Dickenson Hospital, and Smith Vocational Area High School. The findings of this analysis indicate that over a 20-year economic life, a 441 kW/441 kWh battery energy storage system, and 386 kW PV solar array can generate $2.5 million in present value benefits, yielding a 1.16 return on investment ratio. Results of this study also show that forming a microgrid generally improves system survivability, but the resilience performance of individual facilities varies depending on power-sharing strategies.

25 ENERGY STORAGE↗
DOE OSTI2015

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, where the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.

Ma, Xiao↗
DOE OSTI2016

Toward Linear Stability Analysis of Upper Plenum Flows

Linear stability analysis is a tool used to help identify the sensitivity of a particular domain to perturbations and evaluate the system dynamics as a transition, if any, occurs. The development of a time invariant base flow for future use in a linear stability analysis is the focus of this investigation. A test case, with a Reynolds number of 100, was brought to a steady state using the spectral element code Nek5000 and the method of selective frequency damping. The convergence criteria for this method is the volume averaged value of the forcing function which, after approximately 80,000 time-steps, decreased to 3.6x10{sup -4}. Analysis shows that the case has yet to have reached the tolerance desired, 1x10{sup -6}. With the simulation in the process of converging a preliminary perturbation analysis was conducted. Due to the low Reynolds number of this case, 100, it was hypothesized that the flow would be linearly stable. This preliminary stability analysis only focused on the largest fundamental mode and the energy growth of that perturbation over time. Upon evaluation of the perturbation energy, which was shown to be monotonically decreasing in time, it was concluded that, despite not yet being converged, the system is in fact linearly stable. Future work includes evaluating the domain at higher Reynolds numbers, solving the eigenvalue problem created when the linearized Navier-Stokes are written in operator form and calculating the energy evolution of the optimal perturbation. (authors)

42 ENGINEERING↗
DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Digital memcomputing: From logic to dynamics to topology

Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear, point-dissipative dynamical systems engineered so that periodic orbits and chaos can be avoided. A given logic problem is first mapped into this type of dynamical system whose point attractors represent the solutions of the original problem. A DMM then finds the solution via a succession of elementary instantons whose role is to eliminate solitonic configurations of logical inconsistency (“logical defects”) from the circuit. By employing a supersymmetric theory of dynamics, a DMM can be described by a cohomological field theory that allows for computation of certain topological matrix elements on instantons that have the mathematical meaning of intersection numbers on instantons. We discuss the “dynamical” meaning of these matrix elements, and argue that the number of elementary instantons needed to reach the solution cannot exceed the number of state variables of DMMs, which in turn can only grow at most polynomially with the size of the problem. These results shed further light on the relation between logic, dynamics and topology in digital memcomputing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Co-optimized machine-learned manifold models for large eddy simulation of turbulent combustion

Many modeling approaches in large eddy simulation (LES) of turbulent combustion employ a projection of the thermochemical state onto a low-dimensional manifold within state space to reduce the number of transported variables and hence computational cost. Flamelet-generated manifolds (FGM) is an example of a well-established, physics-based approach, but increasingly, principal component analysis (PCA) is being used as a data-driven method for generating manifold models. For both approaches, the nonlinear relationship between the location on the predefined manifold and the outputs of interest, such as reaction rates, can be tabulated or encoded in a neural network. This work proposes a new approach for manifold modeling that extends these existing approaches. A modified neural network structure simultaneously encodes the definition of the manifold variables, the nonlinear mapping, and the subfilter closure for LES. This allows all three of these aspects of the model to be co-optimized, generating a model from any source of combustion thermochemical state data. The manifold parameterizing variables are constrained to be linear combinations of species, as in FGM and PCA-based models, to aid in interpretability and implementation. For LES, subfilter variances of the manifold variables are also included as inputs. Two types of a priori analysis are performed to evaluate the new approach. In the first, the model is trained on data from one-dimensional premixed flames. In this case, the approach recovers the behavior of flamelet-based manifold approaches, and in fact slightly improves performance by identifying an optimized progress variable. The approach is also applied to data from direct numerical simulations of spherical ignition kernels in isotropic turbulence. For any specified manifold dimensionality, the new approach provides substantially lower prediction errors than a PCA-based model developed from the same data set. Additionally, the LES formulation of the new approach can provide accurate predictions for filtered reaction rates across a variety of filter widths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Approximate Synthesis of Distributed Optimal Control for Hyperbolic Equations with Rapidly Oscillating Coefficients

We study the problem of finding approximations to the optimal control with respect to a quadratic-type quality criterion in the form of feedback (synthesis) for a linear-quadratic problem in the from of a hyperbolic equation with rapidly oscillating coefficients and distributed control on the right-hand side. On the basis of the exact formula of synthesis, its approximate version (based on the replacement of the rapidly oscillating variables by averaged quantities) is substantiated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimization of DARHT Axis 1 Injector Voltage

The Dual-Axis Radiographic Hydrodynamic Test (DARHT) facility provides flash radiography capabilities using two electron Linear Induction Accelerators (LIA’s). Axis-1 of DARHT produces a 20- MeV, 2-kA, 80-ns-FWHM electron beam. The strict requirements for flash radiography require a detailed understanding of the LIA’s performance, including precision measurements of the injector electron beam energy. The technique for time resolved measurement of the electron beam energy using electron Permanent Magnet Spectrometer (ePMSpec) has been developed. The electron energy then is used to infer the voltage produced by the injector pulsed power. The injector pulsed power of DARHT I consists of a 1.5-MV, glycol-insulated Blumlein that is pulsecharged by a step-up transformer and switched by four, laser-triggered spark gaps. A series of increasing impedance transmission lines are used to transform the output voltage of the Blumlein to a maximum of 3.8MV at the diode. Figure 1a shows a graphic of the Axis-1 prime power tank, Blumlein and downstream transmission lines. The injector pulse power is designed to produce voltage on a velvet cathode located in the vacuum vessel. The specifications of the voltage-pulse flat-top over 60ns is +/-1%. A key element in the high-voltage circuit is the ethylene glycol Blumlein. The outer volume, adjacent to the laser triggered switches of the Blumlein, is a peaking capacitor. This is an independent volume that contains a mixture of ethylene glycol and water to make it an adjustable capacitor of 380 to 750 pF.

43 PARTICLE ACCELERATORS↗
DOE OSTI2017

Optimization of wind plant layouts using an adjoint approach

Abstract. Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flow physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.

17 WIND ENERGY↗
DOE OSTI2024

Benchmarking Optimizers for Qumode State Preparation with Variational Quantum Algorithms

Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in qumodes due to advancements in the field and their potential applications. However there is a notable gap in the literature specifically addressing this area. This paper aims to bridge this gap by providing performance benchmarks of various optimizers used in state preparation with Variational Quantum Algorithms. We conducted extensive testing across multiple scenarios, including different target states, both ideal and sampling simulations, and varying numbers of basis gate layers. Our evaluations offer insights into the complexity of learning each type of target state and demonstrate that some optimizers perform better than others in this context. Notably, the Powell optimizer was found to be exceptionally robust against sampling errors, making it a preferred choice in scenarios prone to such inaccuracies. Additionally, the Simultaneous Perturbation Stochastic Approximation optimizer was distinguished for its efficiency and ability to handle increased parameter dimensionality effectively.

Kan, Shuwen [Fordham University]↗
DOE OSTI2021

Computational framework for behind-the-meter DER techno-economic modeling and optimization: REopt Lite

The energy system is undergoing a major transformation with the global emphasis on decarbonization. Distributed generation is projected to play a significant role in the new energy system, and energy models are informing how distributed generation can be integrated reliably and economically. In this work, we present an end-to-end computational framework for distributed energy resource (DER) modeling, REopt Lite™, which captures the interface of technology, economics, and policy in the energy modeling process. We describe the problem space, the building blocks of the model, the scaling capabilities of the design, the optimization formulation, and the extensibility of the model. We present a framework for accelerating the techno-economic analysis of behind-the-meter distributed energy resources to enable rapid planning and decision-making, thereby enabling greater renewable energy deployment. This computation framework is open-sourced to facilitate transparency, flexibility, and wider collaboration opportunities within the worldwide energy modeling community.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

CONTROLLED END GAS AUTO IGNITION WITH EXHAUST GAS RECIRCULATION ON A STOICHIOMETRIC, SPARK IGNITED, NATURAL GAS ENGINE

The goal of this study is to address fundamental limitations to achieving diesel-like efficiencies in heavy duty on-highway natural gas (NG) engines. Engine knock and misfire are barriers to pathways leading to higher efficiency engines. This study explores enabling technologies for development of high efficiency stoichiometric, spark ignited, natural gas engines. These include design strategies for fast and stable combustion and higher dilution tolerance. Additionally, advanced control methodologies are implemented to maintain stable operation between knock and misfire limits. To implement controlled end- gas autoignition (C-EGAI) strategies a Combustion Intensity Metric (CIM) is used for ignition control with the use of a Woodward large engine control module (LECM). Tests were conducted using a single cylinder, variable compression ratio, cooperative fuel research (CFR) engine with baseline conditions of 900 RPM, engine load of 800 kPa indicated mean effective pressure (IMEP), and stoichiometric air/fuel ratio. Exhaust gas recirculation (EGR) tests were performed using a custom EGR system that simulates a high pressure EGR loop and can provide a range of EGR rates from 0 to 40%. The experimental measurements included the variance of EGR rate, compression ratio, engine speed, IMEP, and CIM. These five variables were optimized through a Modified Box- Benken design Surface Response Method (RSM), with brake efficiency as the merit function. A positive linear correlation between CIM and f-EGAI was identified. Consequently, CIM was used as the feedback control parameter for C-EGAI. As such, implementation of C-EGAI effectively allowed for the utilization of high EGR rates and CRs, controlling combustion between a narrower gap between knock and lean limits. The change from fixed to parametric ignition timing with CIM targeted select values of f-EGAI with an average coefficient of variance (COV) of peak pressure of 5.4. The RSM efficiency optimization concluded with operational conditions of 1080 RPM, 1150 kPa IMEP, 10.55:1 compression ratio, and 17.8% EGR rate with a brake efficiency of 21.3%. At this optimized point of peak performance, a f-EGAI for C-EGAI was observed at 34.1% heat release due to auto ignition, a knock onset crank angle value of 10.3° aTDC and ignition timing of - 24.7° aTDC. This work has demonstrated that combustion at a fixed f-EGAI can be maintained through advanced ignition control of CIM without experiencing heavy knocking events.

Cooperative Fuel Research Engine, Auto Ignition, E↗
DOE OSTI2014

Poster — Thur Eve — 28: Enabling trajectory-based radiotherapy on a TrueBeam accelerator with the Eclipse treatment planning system

The TrueBeam linear accelerator platform has a developer's mode which permits the user dynamic control over many of the machine's mechanical and radiation systems. Using this research tool, synchronous couch and gantry motion can be programmed to simulate isocentric treatment with a shortened SAD, with benefits such as smaller projected MLC leaf widths and an increased dose rate. In this work, water tank measurements were used to commission a virtual linear accelerator with an 85 cm SAD in Eclipse, from which several arc-based radiotherapy treatments were generated, including an inverse optimized VMAT delivery. For each plan, the pertinent treatment delivery information was extracted from control points specified in the Eclipse-exported DICOM files using the pydicom package in Python, allowing construction of an XML control file. The dimensions of the jaws and MLC positions, defined for an 85 cm SAD in Eclipse, were scaled for delivery on a conventional SAD linear accelerator, and translational couch motion was added as a function of gantry angle to simulate delivery at 85 cm SAD. Ionization chamber and Gafchromic film measurements were used to compare the radiation delivery to dose calculations in Eclipse. With the exception of the VMAT delivery, ionization chamber measurements agreed within 3.3% of the Eclipse calculations. For the VMAT delivery, the ionization chamber was located in an inhomogeneous region, but gamma evaluation of the Gafchromic film plane resulted in a 94.5% passing rate using criteria of 3 mm/3%. The results indicate that Eclipse calculation infrastructure can be used.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2019

Optimizing multi-modal, non-axisymmetric plasma response metrics with additional coil rows on DIII-D

The expansion of the DIII-D tokamak operational space via the addition of new non-axisymmetric coil rows is investigated using the linear MHD plasma response code MARS-F. The plasma response to magnetic perturbations imposed by five distinct low- and high-field side coil geometries is modeled for toroidal mode numbers up to n = 6. A set of linear (~δB^2: resonant, kink mode amplitude) and quadratic (~δB: core and edge integrated NTV torque) plasma metrics are defined and compared directly for the various coil geometries. Coil size is also scanned as a secondary optimization variable. An in-vessel coil located at the low-field side midplane is identified as the most efficient plasma response actuator across all metrics and toroidal mode numbers. The multi-row combination of this new midplane (M) coil with the existing DIII-D non-axisymmetric coil set is considered in numerical optimization studies to quantify the impact of this new coil on modeled plasma response metrics. The addition of the M coil is shown to significantly increase the actuator efficiency in maximizing individual plasma response metrics as well as maximizing multi-modal ratios of response metrics, e.g. maximizing resonant modes or edge NTV torque while minimizing kink modes or core NTV torque. The ex-vessel midplane (C) coil is also observed to have an outsize effect on multi-modal optimization due to its uniquely narrow poloidal spectra, and the expansion of optimization space due to the combined use of the two existing in-vessel coil rows with both the M and C coils is notably larger than either coil's individual contribution even though both share similar poloidal locations. This four-row system is expected to greatly extend abilities to understand and optimize the control of transients and rotation on the DIII-D tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Helium: lifting high-performance stencil kernels from stripped x86 binaries to halide DSL code

Highly optimized programs are prone to bit rot, where performance quickly becomes suboptimal in the face of new hardware and compiler techniques. In this paper we show how to automatically lift performance-critical stencil kernels from a stripped x86 binary and generate the corresponding code in the high-level domain-specific language Halide. Using Halide's state-of-the-art optimizations targeting current hardware, we show that new optimized versions of these kernels can replace the originals to rejuvenate the application for newer hardware. The original optimized code for kernels in stripped binaries is nearly impossible to analyze statically. Instead, we rely on dynamic traces to regenerate the kernels. We perform buffer structure reconstruction to identify input, intermediate and output buffer shapes. Here, we abstract from a forest of concrete dependency trees which contain absolute memory addresses to symbolic trees suitable for high-level code generation. This is done by canonicalizing trees, clustering them based on structure, inferring higher-dimensional buffer accesses and finally by solving a set of linear equations based on buffer accesses to lift them up to simple, high-level expressions. Helium can handle highly optimized, complex stencil kernels with input-dependent conditionals. We lift seven kernels from Adobe Photoshop giving a 75 % performance improvement, four kernels from Irfan View, leading to 4.97 x performance, and one stencil from the mini GMG multigrid benchmark netting a 4.25 x improvement in performance. We manually rejuvenated Photoshop by replacing eleven of Photoshop's filters with our lifted implementations, giving 1.12 x speedup without affecting the user experience.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Optimization and large scale computation of an entropy-based moment closure

We present computational advances and results in the implementation of an entropy-based moment closure, M N , in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as P N , but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the M N algorithm that do not appear for the P N algorithm. We also observe that in weak scaling tests, the ratio in time to solution of M N to P N decreases.

97 MATHEMATICS AND COMPUTING↗