SEARCH · Engineering Papers

Results for “Profiling optimization”

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.

SourceResearch connectionFrom yearThrough year

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

At least 307 records · Page 17

All sources NASA NTRS DOE OSTI

NASA NTRS1983

Radial diffusion in Saturn's radiation belts - A modeling analysis assuming satellite and ring E absorption

A modeling analysis is carried out of six experimental phase space density profiles for nearly equatorially mirroring protons using methods based on the approach of Thomsen et al. (1977). The form of the time-averaged radial diffusion coefficient D(L) that gives an optimal fit to the experimental profiles is determined under the assumption that simple satellite plus Ring E absorption of inwardly diffusing particles and steady-state radial diffusion are the dominant physical processes affecting the proton data in the L range that is modeled. An extension of the single-satellite model employed by Thomsen et al. to a model that includes multisatellite and ring absorption is described, and the procedures adopted for estimating characteristic satellite and ring absorption times are defined. The results obtained in applying three representative solid-body absorption models to evaluate D(L) in the range where L is between 4 and 16 are reported, and a study is made of the sensitivity of the preferred amplitude and L dependence for D(L) to the assumed model parameters. The inferred form of D(L) is then compared with that which would be predicted if various proposed physical mechanisms for driving magnetospheric radial diffusion are operative at Saturn.

Hood, L. L.↗

DOE OSTI2021

Progress on Optimizing Wind Farms and Rotor Designs Using Adjoints

Modern wind plants are increasingly tasked with multiple performance objectives. In addition to designing plants that maximize power output and minimize the levelized cost of energy (LCOE), the design and operation of wind plants is increasingly influenced by challenges regarding grid integration of variable generation renewables. This places a growing emphasis on making wind plants more controllable and predictable. WindSE is a Reynolds-averaged Navier-Stokes (RANS) model designed around analytical gradient and adjoint methods, with the ability to capture terrain-induced effects, as shown in Figure 1. The recent addition of an unsteady solver with an actuator line method (ALM) and ongoing work to enable massively parallel optimizations gives it a unique niche to explore coupled plant-level controls and design problems. This code is an open source python package built on the FEniCS framework that utilizes fast, parallel PETSc solvers to model fluid flow throughout wind-farm scale domains. Two recent studies performed using WindSE demonstrate the capability to optimize under a wide variety of flow conditions and objective functions. In the first, we present an optimization focused on modifying the layout of a wind farm with a fixed number of turbines for maximum total power output [1]. This study highlights the ability to quickly perform simulations using the steady Navier-Stokes solver combined with rotors represented as actuator disks while also stressing the importance of capturing terrain-induced effects. Gradient-based optimization using the RANS equations is viable due to the inclusion of efficiently computed adjoint derivatives. We interpret the physical results of the optimal layout and also discuss the computational cost of scaling to larger problems. In the second study, we present the capabilities of the unsteady Navier-Stokes solver, where rotor-blade profiles represented by actuator lines are optimized to enhance wake steering effects and overall power production [2]. We quantify the wind plant performance gains obtained from this type of simultaneous control co-design optimization as compared to optimizing the blade design and yaw independently. Figure 2 shows the differences between a baseline two-turbine system and an optimized system where we fine-tune the blade chord profile. Results and challenges from each study are quickly summarized and used to motivate the current development efforts within WindSE. Current and future work is focused on enabling higher-resolution studies with more degrees of freedom through parallelization of both the simulation and optimization algorithms. We present benchmarking results to show that WindSE performs well in both weak- and strong-scaling tests and further demonstrate that the optimizer obtains the same convergence rates in both shared- and distributed-memory environments. Using larger wind farms, we can study deep-array effects within an optimization context, allowing the use of objective functions that have been previously unstudied. As an example, we present ongoing work on a blockage metric which characterizes the loss of available kinetic energy due to wake effects from multiple upstream turbines.

adjoint optimization↗

DOE OSTI2020

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗

DOE OSTI2024

Virtual Tokamak for Test and Development of Plasma Control Applied to NSTX-U

Safe and efficient operation of tokamak experiments depends on shot preparation prior to the experiment to maximize performance and avoid issues that are predictable consequences of known physics. The General Atomics TokSys toolbox is used to test and develop the plasma control system (PCS) on numerous tokamaks around the world. Tokamaks that use a version of the DIII-D PCS can connect it to a TokSys simulation and control a virtual version of the tokamak with the real PCS. Recent upgrades to the simulation include more detailed profile and transport modeling to support design and implementation of optimized scenarios. The simulation combines a module called “Profiles” that simulates the 1D profiles of density, pressure, and current and a module called “GSevolve'' that evolves the 2D Grad-Shafranov equilibrium. The “Profiles'' module primarily uses simplified models for fueling, heating, and current. The TRANSP code provides precomputed diffusion coefficients and heating/current drive profiles from radio-frequency and neutral beam sources for the scenarios being simulated. The fidelity of a simulation can be enhanced by analyzing it with TRANSP and making corrections to the precomputed values and iterating until convergence. Simulations of the National Spherical Torus Upgrade (NSTX-U) are presented. It is shown that the simulation reproduces the experimental profile evolution. Here, the simulation has also been upgraded to reproduce the experimental outcome at points of bifurcation. This is demonstrated with a simulation of vertical displacement in NSTX-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Development of near-optimal advanced control sequences for chiller plants with water-side economizers in U.S. Climates (ASHRAE RP-1661)

Various advanced control sequences for chiller plants with water-side economizers (WSE) have been proposed in literature, but the evaluation and optimization of those controls is limited. It is possible to maximize energy savings by selecting different sequences and related parameters based on the plant configuration, load, and climate. This paper addresses this gap by developing near-optimal advanced control sequences for chiller plants with WSEs. First, advanced control sequences for chiller plants with WSEs are categorized into condenser water, chilled water, and hybrid controls and representative sequences from each category are identified. Next, 504 different scenarios are optimized. These scenarios represent all possible combinations of two plant configurations, a constant or variable load profile, three advanced control sequences, and seven optimization parameter combinations in six climate zones. The results show the recommended near-optimal sequences can reduce energy consumption by up to 15% relative to the baseline depending on the configuration, load profile, and climate. Specifically, the CW-CHW sequence is recommended for the majority of systems because it is often the most energy efficient and/or reduces the runtime of chillers. The methodology in this paper provides practical guidance for achieving energy savings through near-optimal control of chiller plants with WSEs.

42 ENGINEERING↗

DOE OSTI2022

Dose-finding studies in drug development for rare genetic diseases

The small patient populations inherent to rare genetic diseases present many challenges to the traditional drug development paradigm. One major challenge is generating sufficient data in early phase studies to inform dose selection for later phase studies and dose optimization for clinical use of the drug. However, optimizing the benefit-risk profile of drugs through appropriate dose selection during drug development is critical for all drugs, including those being developed to treat rare diseases. Recognizing the challenges of conducting dose finding studies in rare disease populations and the importance of dose selection and optimization for successful drug development, we assessed the dose-finding studies and analyses conducted for drugs recently approved for rare genetic diseases. Of the 40 marketing applications for new molecular entity (NME) drugs and biologics approved by the United States Food and Drug Administration for rare genetic diseases from 2015 to 2020, 21 (53%) of the development programs conducted at least one dedicated dose-finding study. In addition, the majority of drug development programs conducted clinical studies in healthy subjects and included population pharmacokinetic and exposure–response analyses; some programs also conducted clinical studies in patient populations other than the disease for which the drug was initially approved. The majority of primary endpoints utilized in dedicated dose-finding studies were biomarkers, and the primary endpoint of the safety and efficacy study matched the primary endpoint used in the dose finding study in 9 of 13 (69%) drug development programs where primary study endpoints were assessed. Our study showed that NME drug development programs for rare genetic diseases utilize multiple data sources for dosing information, including studies in healthy subjects, population pharmacokinetic analyses, and exposure–response analyses. In addition, our results indicate that biomarkers play a key role in dose-finding studies for rare genetic disease drug development programs. Our findings highlight the need to develop study designs and methods to allow adequate dose-finding efforts within rare disease drug development programs that help overcome the challenges presented by low patient prevalence and other factors. Furthermore, the frequent reliance on biomarkers as endpoints for dose-finding studies underscores the importance of biomarker development in rare diseases.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Methods of controllable interstitial oxygen doping in niobium

A method for vacuum heat treating Nb, such as is used in superconducting radio frequency cavities, to engineer the interstitial oxygen profile with depth into the surface to conveniently optimize the low-temperature rf surface resistance of the material. An example application is heating of 1.3 GHz accelerating structures between 250-400° C. to achieve a very high quality factor of 5×1010 at 2.0 K. With data supplied by secondary ion mass spectrometry measurements, application of oxide decomposition and oxygen diffusion theory was applied to quantify previously unknown parameters crucial in achieving the oxygen alloy concentration profiles required to optimize the rf surface resistance. RF measurements of vacuum heat treated Nb superconducting radio frequency cavities confirmed the minimized surface resistance (higher Q0) previously expected only from 800° C. diffusive alloying with nitrogen.

Palczewski, Ari D.↗

DOE OSTI2026

Profile Generation for GPU Targets

GPU accelerators are ubiquitous, but their ecosystem is far less evolved than the host one. Compiler heuristics are often tuned for CPUs and reused for GPU. Similarly, tooling and more evolved optimization techniques are historically not available on GPU targets. In this work, we address one of these shortcomings and enable profile generation and profile-guided optimizations (PGO) for GPU targets. While this is only a single step towards a CPU equivalent ecosystem for offload devices, it shows how old misconceptions on the limitations of GPUs are often not warranted anymore. Through our implementation in LLVM/Offload, we enable device-side PGO for full scientific applications and open up tooling opportunities, including code coverage analysis and compiler-built-in roofline analysis. Our evaluation highlights the performance implications of profile generation, the insights gained from these profiles, and the (missed) opportunities in utilizing the information for GPU compilation.

McDonough, Ethan Luis [Lawrence Livermore National↗

DOE OSTI2022

Real-Time Ecodriving Control in Electrified Connected and Autonomous Vehicles Using Approximate Dynamic Programing

Connected and automated vehicles (CAVs), particularly those with a hybrid electric powertrain, have the potential to significantly improve vehicle energy savings in real-world driving conditions. In particular, the ecodriving problem seeks to design optimal speed and power usage profiles based on available information from connectivity and advanced mapping features to minimize the fuel consumption over an itinerary. This paper presents a hierarchical multilayer model predictive control (MPC) approach for improving the fuel economy of a 48 V mild-hybrid powertrain in a connected vehicle environment. Approximate dynamic programing (DP) is used to solve the receding horizon optimal control problem, whose terminal cost is approximated with the base policy obtained from the long-term optimization. The controller was tested virtually (with deterministic and Monte Carlo simulation) across multiple real-world routes, demonstrating energy savings of more than 20%. The controller was then deployed on a test vehicle equipped with a rapid prototyping embedded controller. In-vehicle testing confirm the energy savings obtained in simulation and demonstrate the real-time ability of the controller.

Automation & Control Systems↗

DOE OSTI2023

Techno-Economic Optimization of Advanced Energy Plants with Integrated Thermal, Mechanical, and Electro-Chemical Storage (Final Report)

The increasing use of renewable energy sources is leading to increased cycling of fossil-fueled power plants (FFPP) that are designed to operate at base-loaded conditions. Integrating energy storage facilities with the FFPPs can be helpful in reducing load-following operation of FFPPs. Decentralized deployment of energy storage facilities at the FFPP level has considerable advantages due to possibilities of smaller storage capacities, immediate benefits realized by the host power plant due to the increase in the efficiency, cleaner emission and higher plant life to name a few. Most importantly, deployment at the FFPP level can exploit the existing equipment items and facilities at the host power plant, thus reducing the CAPEX and reducing the storage capacity. However, realization of these benefits will critically depend on novel configuration/integration strategies with the least impact on the power plant operation and its configuration. Furthermore, dynamics of the entire integrated system including both the FFPP and the storage technologies must be taken into account to obtain the cost-optimal solution. With these motivations, the objective of this project was to complete a focused evaluation of decentralized deployments of energy storage facilities at the FFPP level. Promising thermal, chemical, mechanical, and electro-chemical storage technologies were evaluated with due consideration of their transient response to obtain various optimal system concepts that can minimize the levelized cost of storage. For thermal storage, cryogenic energy storage along with high temperature heat storage in molten salt as well as phase change material were evaluated. For mechanical storage, cryogenic air storage and pumped hydro storages were evaluated. For chemical storage, hydrogen storage was evaluated. For electrochemical storage, the team evaluated sodium sulfur, vanadium redox flow battery as well as Li-ion batteries. Integration of these storage technologies with the natural gas combined cycle (NGCC) and supercritical pulverized coal (SCPC) plants was considered. Six technologies, namely molten salt, cryogenics, compressed air, pumped hydro, H2 storage and Li-ion battery storage, were downselected based on their levelized cost of storage. It was observed that the ranking of the optimal storage technology can differ based on the host power plant technology even when same demand/supply/price profile for electricity are considered. It was also observed that as the variability in power demand varies, the ranking of the optimal storage technologies vary. However, for the same demand and LMP profile, top six optimal storage technologies for NGCC vs SCPC plants did not differ much even though LCOS for the same technology and optimal size of a given storage technology did differ. Detailed techno-economic assessment of these six technologies was undertaken.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRSDate not supplied

Noise Reduction Trajectory Analysis of a Supersonic Business Jet using Novel Optimization Tools

Proposals to reduce airport noise during takeoff and landing for supersonic aircraft using methods such as variable noise reduction systems add complexity to conceptual flight models. To better optimize these takeoff and landing profiles for noise certification, new modeling methods are explored in this paper with the end goal of more effectively determining the sensitivities of airframe, propulsion, and mission design variables on overall airport noise. Takeoff and landing trajectories are modeled for a notional supersonic business jet concept developed by NASA for use in environmental impact studies conducted by the International Civil Aviation Organization. Optimization tools capable of gradient-based optimal control and collocation solving methods are examined with the aim of achieving faster solutions in a more comprehensive design space. The benefits and limitations of these new methods are compared with existing methods used in previous studies of the airplane concept. It is found that the new modeling methods match closely when compared with existing tools for a standard takeoff and landing case, with a cumulative effective perceived noise difference of 0.1 EPNdB. Comparisons between takeoff trajectories with a variable noise reduction system match within 0.8 EPNdB and 1.3 EPNdB, due to highlighted differences in the modeling approaches.

supersonic↗

DOE OSTI2024

Developing Near Optimal Control Sequences for Chiller Plants with Water-side Economizers: A Case Study in a Warm and Marine Climate

Various advanced control sequences for chiller plants with water-side economizers (WSE) have been proposed in literature, but the optimization of those controls is limited. It is possible to maximize energy savings by developing near-optimal control sequences, which are dependent on several factors such as the load profile. To address these gaps, we first identify an advanced control sequence and three key control parameters for chiller plants with WSE. Next, optimizations are performed to minimize energy consumption for seven combinations of control parameters. A chiller plant with WSE system in a warm and marine climate is studied and two load profiles are considered. The system and controls are modeled using the Modelica Buildings library. The results show optimizing the selected control parameters can reduce energy consumption by up to 11% depending on the load profile. Specifically, optimizing the cooling tower efficiency threshold in the condenser water reset control can significantly reduce energy savings for the variable load profile by efficiently shifting the load from the cooling tower to the chiller. This paper provides practical guidance for developing near-optimal control sequences for chiller plant with WSE systems considering impacts such as the load profile.

chiller plant↗

NASA NTRS2009

Angle of Attack Modulation for Mars Entry Terminal State Optimization

From the perspective of atmospheric entry, descent, and landing (EDL), one of the most foreboding destinations in the solar system is Mars due in part to its exceedingly thin atmosphere. To benchmark best possible scenarios for evaluation of potential Mars EDL system designs, a study is conducted to optimize the entry-to-terminal-state portion of EDL for a variety of entry velocities and vehicle masses, focusing on the identification of potential benefits of enabling angle of attack modulation. The terminal state is envisioned as one appropriate for the initiation of terminal descent via parachute or other means. A particle swarm optimizer varies entry flight path angle, ten bank profile points, and ten angle of attack profile points to find maximum-final-altitude trajectories for a 10 30 m ellipsled at 180 different combinations of values for entry mass, entry velocity, terminal Mach number, and minimum allowable altitude. Parametric plots of maximum achievable altitude are shown, as are examples of optimized trajectories. It is shown that appreciable terminal state altitude gains (2.5-4.0 km) over pure bank angle control may be possible if angle of attack modulation is enabled for Mars entry vehicles. Gains of this magnitude could prove to be enabling for missions requiring high-altitude landing sites. Conclusions are also drawn regarding trends in the bank and angle of attack profiles that produce the optimal trajectories in this study, and directions for future work are identified.

Lafleur, Jarret M.↗

DOE OSTI2025

A methodology for decay heat characterization in molten salt reactors

Accurate decay heat prediction in molten salt reactors (MSRs) faces dual challenges: complex operational uncertainties and the need for interpretable models compatible with engineering workflows. This work presents a hybrid machine learning and segmented polynomial methodology that addresses both requirements through three key innovations. First, a modular data architecture encodes MSR-specific operational parameters (power density: 1-100 W cm -3 , humidity: 0-0.1 wt %, air ingress: 0-0.1 mol %) with uncertainty-aware temporal discretization spanning 15 orders of magnitude. Second, region-optimized machine learning models achieve 92.3 % root mean square error (RMSE) reduction over conventional polynomials while maintaining physical interpretability through automated piecewise equation generation. Third, dual front-end interfaces accelerate safety analyses — a Jupyter environment enables researchers to explore 10,000+ parameter combinations via interactive widgets, while a Streamlit web application reduces design iteration cycles through production-grade visualization tools. Operational deployment demonstrates prediction times of only a couple hundred milliseconds for 10 4 years decay profiles, enabling real-time optimization of spent fuel container designs.

42 - ENGINEERING↗

DOE OSTI2024

Error field predictability and consequences for ITER

Abstract ITER coil tolerances are re-evaluated using the modern understanding of coupling to least-stable plasma modes and an updated center-line-traced model of ITER’s coil windings. This reassessment finds the tolerances to be conservative through a statistical, linear study of n = 1 error fields (EFs) due to tilted, shifted misplacements and nominal windings of central solenoid and poloidal field coils within tolerance. We also show that a model-based correction scheme remains effective even when metrology quality is sub-optimal, and compare this to projected empirical correction schemes. We begin with an analysis of the necessity of error field correction (EFC) for daily operation in ITER using scalign laws for the EF penetration threshold. We then consider the predictability of EF dominant mode overlap across early planned ITER scenarios and, as measuring EFs in high power scenarios can pose risks to the device, the potential for extrapolation to the ITER Baseline Scenario (IBS). We find that carefully designing a scenario matching currents proportionally to those of the IBS is far more important than plasma shape or profiles in accurately measuring an optimal correction current set.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Invertible Neural Networks for Aerodynamic Design of Wind Turbine Blades

The state-of-the-practice methods for aerodynamic design of wind turbine blads use linearized blade element momentum theory (BEM) to optimize the twist and chord profiles from a pre-selected set of 2D airfoil shapes. In this work, we apply invertible neural network (INN) tools to enable the rapid inverse aerodynamic design of wind turbine blades including component airfoils. The INN is trained on data obtained through the use of robust automated mesh generation and the HAMSTR computational fluid dynamics solver with advanced turbulence and transition models validated for turbine applications. Our design technique is a significant improvement over the state-of-the-practice linearized blade element momentum (BEM) techniques in capturing 3D nonlinear aerodynamic effects that are critical for optimal design of the rotors. This is made possible by developing sparse, invertible neural networks (INNs) for inverse design and optimization that realize a 100x cost reduction compared to adjoint-based computational fluid dynamics (CFD) approaches, while enabling increased robustness of the final design. We demonstrate the INN tool for design of a section of the NREL 5-MW blade. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of wind turbine blades.

aerodynamic design↗

NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land on asteroids are becoming popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site. The problem under investigation is how to design a fuel-optimal powered descent trajectory that can be quickly computed on- board the spacecraft, without interaction from ground control. An optimal trajectory designed immediately prior to the descent burn has many advantages. These advantages include the ability to use the actual vehicle starting state as the initial condition in the trajectory design and the ease of updating the landing target site if the original landing site is no longer viable. For long trajectories, the trajectory can be updated periodically by a redesign of the optimal trajectory based on current vehicle conditions to improve the guidance performance. One of the key drivers for being completely autonomous is the infrequent and delayed communication between ground control and the vehicle. Challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies and low thrust vehicles. There are two previous studies that form the background to the current investigation. The first set looked in-depth at applying convex optimization to a powered descent trajectory on Mars with promising results.1, 2 This showed that the powered descent equations of motion can be relaxed and formed into a convex optimization problem and that the optimal solution of the relaxed problem is indeed a feasible solution to the original problem. This analysis used a constant gravity field. The second area applied a successive solution process to formulate a second order cone program that designs rendezvous and proximity operations trajectories.3, 4 These trajectories included a Newtonian gravity model. The equivalence of the solutions between the relaxed and the original problem is theoretically established. The proposed solution for designing the asteroid powered descent trajectory is to use convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process to design the fuel optimal trajectory. The solution to the convex optimization problem is the thrust profile, magnitude and direction, that will yield the minimum fuel trajectory for a soft landing at the target site, subject to various mission and operational constraints. The equations of motion are formulated in a rotating coordinate system and includes a high fidelity gravity model. The vehicle's thrust magnitude can vary between maximum and minimum bounds during the burn. Also, constraints are included to ensure that the vehicle does not run out of propellant, or go below the asteroid's surface, and any vehicle pointing requirements. The equations of motion are discretized and propagated with the trapezoidal rule in order to produce equality constraints for the optimization problem. These equality constraints allow the optimization algorithm to solve the entire problem, without including a propagator inside the optimization algorithm.

Pinson, Robin M.↗

DOE OSTI2024

Ultra-Long Distance BOTDA Sensor System Employing Hybrid Amplification and Advanced Noise Reduction Techniques

Brillouin Optical Time Domain Analysis (BOTDA) sensor systems play a pivotal role in distributed sensing, which enables precise measurements of strain and temperature across extensive fiber lengths. This research offers a comprehensive strategy to extend the sensing range of BOTDA systems beyond tens of kilometers while maintaining high spatial resolutions. Such enhanced sensing is realized through the integration of distributed Raman amplification, inline amplification using erbium-doped fiber amplifiers (EDFA), and advanced noise reduction techniques. Optimizing Raman pump and probe wave profiles ensures the robustness of Brillouin scattering signals, effectively countering attenuation-induced losses. Additionally, enhancing weak Brillouin signals by strategically placing EDFAs at optimal fiber locations keeps sensor sensitivity high. Leveraging inherent redundancy in measured data as a function of frequency and fiber distance, the non-local means (NLM) filter removes noise while preserving essential physical information. In summary, this research has shown a holistic exploration of extending BOTDA’s distance sensing capabilities up to 150 km with spatial resolutions of 8 meters.

Bhatta, Hari↗