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At least 397 records · Page 22

The Failure of Correlation to Describe Out-of-Plane Carbon=Carbon Bending

Carbon-carbon multiply bonded systems are improperly described with standard correlation methods and basis sets. For computations of vibrational modes, the out-of- plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior for the first time. A combined 1-particle and n-particle basis set effect conspire to produce these non-physical results. When moving from sp2 to sp3 hybridization in the carbon atoms, the larger number of basis functions overcorrects the energy. This is exacerbated by correlation methods. These allow for occupation of the π and π∗ orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space can be further and non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem with at least Hartree-Fock based methods of all flavors in describing carbon. Beyond being a flaw in quantum chemical theory, other repercussions will be present in computations regarding spectroscopy as well as energy and environmental studies where highly-accurate hydrocabon vibrational transitions or thermochemical data are needed.

Fortenberry, Ryan C.↗

Combustion Processes in Hybrid Rocket Engines

In recent years, there has been a resurgence of interest in the development of hybrid rocket engines for advanced launch vehicle applications. Hybrid propulsion systems use a solid fuel such as hydroxyl-terminated polybutadiene (HTPB) along with a gaseous/liquid oxidizer. The performance of hybrid combustors depends on the convective and radiative heat fluxes to the fuel surface, the rate of pyrolysis in the solid phase, and the turbulent combustion processes in the gaseous phases. These processes in combination specify the regression rates of the fuel surface and thereby the utilization efficiency of the fuel. In this paper, we employ computational fluid dynamics (CFD) techniques in order to gain a quantitative understanding of the physical trends in hybrid rocket combustors. The computational modeling is tailored to ongoing experiments at Penn State that employ a two dimensional slab burner configuration. The coordinated computational/experimental effort enables model validation while providing an understanding of the experimental observations. Computations to date have included the full length geometry with and with the aft nozzle section as well as shorter length domains for extensive parametric characterization. HTPB is sed as the fuel with 1,3 butadiene being taken as the gaseous product of the pyrolysis. Pure gaseous oxygen is taken as the oxidizer. The fuel regression rate is specified using an Arrhenius rate reaction, which the fuel surface temperature is given by an energy balance involving gas-phase convection and radiation as well as thermal conduction in the solid-phase. For the gas-phase combustion, a two step global reaction is used. The standard kappa - epsilon model is used for turbulence closure. Radiation is presently treated using a simple diffusion approximation which is valid for large optical path lengths, representative of radiation from soot particles. Computational results are obtained to determine the trends in the fuel burning or regression rates as a function of the head-end oxidizer mass flux, G=rho(e)U(e), and the chamber pressure. Furthermore, computation of the full slab burner configuration has also been obtained for various stages of the burn. Comparisons with available experimental data from small scale tests conducted by General Dynamics-Thiokol-Rocketdyne suggest reasonable agreement in the predicted regression rates. Future work will include: (1) a model for soot generation in the flame for more quantitative radiative transfer modelling, (2) a parametric study of combustion efficiency, and (3) transient calculations to help determine the possible mechanisms responsible for combustion instability in hybrid rocket motors.

Venkateswaran,S.↗

Sizing and Performance Analysis of a MegaWatt-Class Electrified Aircraft Propulsion (EAP) System for a Parallel Hybrid Turboprop Concept

Aircraft electrification has emerged as a pivotal research and development focus in the 21st century, gaining international momentum as a strategic approach to curtail fuel consumption and emissions in the civil aviation sector. Under the Electrified Powertrain Flight Demonstration (EPFD) project, NASA and industry partners are raising the technical readiness, addressing integration challenges and gathering data for future standards and regulations for demonstrate Megawatt (MW) class Electrified Aircraft Propulsion (EAP) systems which can be utilized on regional turboprop or single aisle transports. With the rapid emergence of novel EAP concepts, risk reduction efforts are focused on developing the capabilities to evaluate the impacts of electrification at the conceptual design level where high variability in the EAP system architecture must be accounted for. This paper details an integrated, approach to parametric sizing of multi-MW EAP systems with the primary goal of assessing vehicle-level performance sensitivities to variations in electrical system component-level performance metrics. The focus of this work is to investigate the degree to which EAP component parameters such as specific power, efficiency, and energy density impact range and overall fuel savings.

EAP↗

Electron-ion hybrid instabilities driven by velocity shear in a magnetized plasma

The stability of a magnetized plasma is investigated in which a sheared electron flow channel is present. The flow's peak velocity and shear scale length are denoted by V and L, respectively. If the velocity channel is perpendicular to the confining magnetic field and L is less than the ion Larmor radius, an electrostatic instability develops whose frequency is on the order of the lower hybrid frequency. It is concluded that velocity shear is the only source of free energy. Further, it is shown that density gradients do not stabilize this mode. It follows that the mode presented in this work can not be identified with the well-known modified two-stream instability. If the velocity channel is parallel to the confining magnetic field and the plasma is weakly magnetized, an instability driven by velocity shear is shown to exist.

Romero, H.↗

Fundamental Phenomena on Fuel Decomposition and Boundary-Layer Combustion Precesses with Applications to Hybrid Rocket Motors: Experimental Investigation - Part 1

This final report summarizes the major findings on the subject of 'Fundamental Phenomena on Fuel Decomposition and Boundary-Layer Combustion Processes with Applications to Hybrid Rocket Motors', performed from 1 April 1994 to 30 June 1996. Both experimental results from Task 1 and theoretical/numerical results from Task 2 are reported here in two parts. Part 1 covers the experimental work performed and describes the test facility setup, data reduction techniques employed, and results of the test firings, including effects of operating conditions and fuel additives on solid fuel regression rate and thermal profiles of the condensed phase. Part 2 concerns the theoretical/numerical work. It covers physical modeling of the combustion processes including gas/surface coupling, and radiation effect on regression rate. The numerical solution of the flowfield structure and condensed phase regression behavior are presented. Experimental data from the test firings were used for numerical model validation.

Kuo, Kenneth K.↗

High Energy Cutting and Stripping Utilizing Liquid Nitrogen

The Aerospace Industry has endeavored for decades to develop hybrid materials that withstand the rigors of mechanized flight both within our atmosphere and beyond. The development of these high performance materials has led to the need for environmentally friendly technologies for material re-work and removal. The NitroJet(TM) is a fluid jet technology that represents an evolution of the widely used, large-scale water jet fluid jet technology. It involves the amalgamation of fluid jet technology and cryogenics technology to create a new capability that is applicable where water jet or abrasive jet (water jet plus entrained abrasive) are not suitable or acceptable because of technical constraints such as process or materials compatibility, environmental concerns and aesthetic or legal requirements. The NitroJet(TM) uses ultra high-pressure nitrogen to cut materials, strip numerous types of coatings such as paint or powder coating, clean surfaces and profile metals. Liquid nitrogen (LN2) is used as the feed stream and is pressurized in two stages. The first stage pressurizes sub cooled LN2 to an intermediate pressure of between 15,000 and 20,000 psi at which point the temperature of the LN2 is about -250 F. The discharge from this stage is then introduced as feed to a dual intensifier system, which boosts the pressure from 15,000 - 20,000 psi up to the maximum operating pressure of 55,000 psi. A temperature of about -220 F is achieved at which point the nitrogen is supercritical. In this condition the nitrogen cuts, strips and abrades much like ultra high-pressure water would but without any residual liquid to collect, remove or be contaminated. Once the nitrogen has performed its function it harmlessly flashes back into the atmosphere as pure nitrogen gas. The system uses heat exchangers to control and modify the temperature of the various intake and discharge nitrogen streams. Since the system is hydraulically operated, discharge pressures can be easily varied over a very wide range providing considerable flexibility for various operations. The NitroJet(TM) is an advance on the nitrogen fluid jet technology initially developed at the Idaho National Engineering Laboratory in Idaho Falls, Idaho. NitroCision(R) first introduced the NitroJet(TM) into a commercial setting in 2003 and there has been considerable interest from many diverse sectors of government and industry since then. While the current system is an industrial system with the size and mass normally associated with industrial applications, a smaller system that is much more compact is being contemplated for those applications that do not need the full capabilities of the larger system. The NitroJet(TM) can be deployed as a fixed or mobile system with multiple end effectors capable of cutting, stripping, cleaning, and surface profiling either in robotic or manual applications.

Hume, Howard↗

Environmentally Friendly Coating Technology for Autonomous Corrosion Control

This work concerns the development of environmentally friendly encapsulation technology, specifically designed to incorporate corrosion indicators, inhibitors, and self-healing agents into a coating, in such a way that the delivery of the indicators and inhibitors is triggered by the corrosion process, and the delivery of self-healing agents is triggered by mechanical damage to the coating. Encapsulation of the active corrosion control ingredients allows the incorporation of desired autonomous corrosion control functions such as: early corrosion detection, hidden corrosion detection, corrosion inhibition, and self-healing of mechanical damage into a coating. The technology offers the versatility needed to include one or several corrosion control functions into the same coating.The development of the encapsulation technology has progressed from the initial proof-of-concept work, in which a corrosion indicator was encapsulated into an oil-core (hydrophobic) microcapsule and shown to be delivered autonomously, under simulated corrosion conditions, to a sophisticated portfolio of micro carriers (organic, inorganic, and hybrid) that can be used to deliver a wide range of active corrosion ingredients at a rate that can be adjusted to offer immediate as well as long-term corrosion control. The micro carriers have been incorporated into different coating formulas to test and optimize the autonomous corrosion detection, inhibition, and self-healing functions of the coatings. This paper provides an overview of progress made to date and highlights recent technical developments, such as improved corrosion detection sensitivity, inhibitor test results in various types of coatings, and highly effective self-healing coatings based on green chemistry.

Coatings↗

Corrosion-Activated Micro-Containers for Environmentally Friendly Corrosion Protective Coatings

This work concerns the development of environmentally friendly encapsulation technology, specifically designed to incorporate corrosion indicators, inhibitors, and self-healing agents into a coating, in such a way that the delivery of the indicators and inhibitors is triggered by the corrosion process, and the delivery of self-healing agents is triggered by mechanical damage to the coating. Encapsulation of the active corrosion control ingredients allows the incorporation of desired autonomous corrosion control functions such as: early corrosion detection, hidden corrosion detection, corrosion inhibition, and self-healing of mechanical damage into a coating. The technology offers the versatility needed to include one or several corrosion control functions into the same coating.The development of the encapsulation technology has progressed from the initial proof-of-concept work, in which a corrosion indicator was encapsulated into an oil-core (hydrophobic) microcapsule and shown to be delivered autonomously, under simulated corrosion conditions, to a sophisticated portfolio of micro carriers (organic, inorganic, and hybrid) that can be used to deliver a wide range of active corrosion ingredients at a rate that can be adjusted to offer immediate as well as long-term corrosion control. The micro carriers have been incorporated into different coating formulas to test and optimize the autonomous corrosion detection, inhibition, and self-healing functions of the coatings. This paper provides an overview of progress made to date and highlights recent technical developments, such as improved corrosion detection sensitivity, inhibitor test results in various types of coatings, and highly effective self-healing coatings based on green chemistry. The NASA Kennedy Space Centers Corrosion Technology Lab at the Kennedy Space Center in Florida, U.S.A. has been developing multifunctional smart coatings based on the microencapsulation of environmentally friendly corrosion indicators, inhibitors and self-healing agents. This allows the incorporation of autonomous corrosion control functionalities, such as corrosion detection and inhibition as well as the self-healing of mechanical damage, into coatings. This paper presents technical details on the characterization of inhibitor-containing particles and their corrosion inhibitive effects using electrochemical and mass loss methods.Three organic environmentally friendly corrosion inhibitors were encapsulated in organic microparticles that are compatible with desired coatings. The release of the inhibitors from the microparticles in basic solution was studied. Fast release, for immediate corrosion protection, as well as long-term release for continued protection, was observed.The inhibition efficacy of the inhibitors, incorporated directly and in microparticles, on carbon steel was evaluated. Polarization curves and mass loss measurements showed that, in the case of 2MBT, its corrosion inhibition effectiveness was greater when it was delivered from microparticles.

Corrosion Control↗

Hybrid Propulsion In-Situ Resource Utilization Test Facility Results for Performance Characterization

Hybrid propulsion presents a promising alternative to conventional systems for in-space propulsion applications using In-Situ Propellant Production (ISPP). A hybrid propulsion test facility has been built at the NASA Jet Propulsion Laboratory (JPL) with the capability to evaluate ISPP oxidizers (gaseous mixtures of O2 and CO2) and modify fuel type and chamber geometry. This work is the result of a continuing effort at JPL to characterize the burn characteristics and performance of different propellant combinations and motor configurations in order to refine and support preliminary designs. Twelve tests using gaseous oxygen and two paraffin based fuels (Black Paraffin and SP1X) from the 2015 campaign are presented. Different reduction techniques are compared in an effort to determine the uncertainty associated with deriving a regression rate law and evaluating c* efficiency with the collected data.

Mechentel, F. S.↗

Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation

Recently, the makespan-minimization problem of compiling a general class of quantum algorithms into near-term quantum processors has been introduced to the AI community. The research demonstrated that temporal planning is a strong solution approach for the studied class of quantum circuit compilation (QCC) problems. In this paper, we explore the use of methods from operations research, specifically constraint programming (CP), as an alternative and complementary approach to temporal planning. We also extend previous work by introducing two new problem variations that incorporate important characteristics identified by the quantum computing community. We apply temporal planning and CP to the baseline and extended QCC problems as both stand-alone and hybrid approaches. The hybrid method uses solutions found by temporal planning to warm-start CP, leveraging the ability of temporal planning to find satisficing solutions to problems with a high degree of task optionality, an area that CP typically struggles with. These solutions are then used to seed the CP formulation which significantly benefits from inferred bounds on planning horizon and task counts provided by the warm-start. Our extensive empirical evaluation indicates that while stand-alone CP is not competitive with temporal planning, except for the smallest problems, CP in a hybrid setting is beneficial for all temporal planners in all problem classes.

quantum circuit compilation↗

Recovery Timescales of the Dayside Martian Magnetosphere to IMF Variability

In this work we revisit an event observed by Mars Atmosphere and Volatile Evolution MissioNin the solar wind where the interplanetary magneticfield (IMF) rotates around the Mars‐Sun axis during∼6 min. Based on a time‐dependent LATMOS Hybrid Simulation, we determine recovery timescales of thedayside Martian magnetosphere normalized by the IMF variability timescale. Particularly, wefind thatsuch recovery timescales range between 8 s and 11 min for an∼90° IMF rotation that lasted 50 s (observed aspart of the 6‐min time interval), depending on the considered magnetospheric region. We alsofind thatthe O+plume recovery timescales range between 40 and 120 s, taking greater values for further downstreamdistances (at least up to 1RMdownstream from the terminator plane). This range is on the order of themagnetosheath O+gyroperiod, showing the kinetic nature of the plume recovery process.

Romanelli, N.↗

Hybrid Particle-Element Simulation of Impact on Composite Orbital Debris Shields

This report describes the development of new numerical methods and new constitutive models for the simulation of hypervelocity impact effects on spacecraft. The research has included parallel implementation of the numerical methods and material models developed under the project. Validation work has included both one dimensional simulations, for comparison with exact solutions, and three dimensional simulations of published hypervelocity impact experiments. The validated formulations have been applied to simulate impact effects in a velocity and kinetic energy regime outside the capabilities of current experimental methods. The research results presented here allow for the expanded use of numerical simulation, as a complement to experimental work, in future design of spacecraft for hypervelocity impact effects.

Fahrenthold, Eric P.↗

Flexural Fatigue Testing and Qualification of Hybrid PAN-pitch Composite Materials with High Through-Thickness Thermal Conductivity

Carbon-fiber-reinforced polymers (CFRPs) considered for motor components within future electric vertical takeoff and landing (eVTOL) vehicles require not only a high strength-to-weight ratio but also a high through-thickness thermal conductivity (TC) to dissipate heat. Previously, CFRPs incorporating pitch CF interleaves demonstrated an increased through-thickness TC relative to the baseline composite, but the effect on flexural fatigue life was not evaluated. For this work, T700S/TC275–1 braided carbon fiber/epoxy prepreg baseline (no interleave), YSH–60A pitch interleave, and YS–80A pitch interleave configurations were tested for fatigue life. A combination of ASTM International Standards D7264 and D3479 were used to develop a reliable testing method. An Instron® (Illinois Tool Works Inc.) 8501 servohydraulic system with a fatigue test fixture was set up with a 16:1 span:thickness ratio, load ratio R set to 0.1, and frequency of 4 Hz. High-cycle fatigue testing was completed, and it was found that YSH–60A interleave performed slightly better than YS–80A below 100,000 cycles but showed no differences above 100,000 cycles. In all cases, the baseline CFRP had superior fatigue life performance both in terms of stress handled and total cycles to failure. These fatigue testing data will inform future use of hybrid CFRP materials by highlighting the tradeoff between increased through-thickness TC and fatigue life. Testing guidelines, equipment, and parameters for static and fatigue tests were successfully outlined for CFRPs.

composites↗

Electronic hardware implementations of neutral networks

This paper examines some of the present work on the development of electronic neural network hardware. In particular, the investigations currently under way at JPL on neural network hardware implementations based on custom VLSI technology, novel thin film materials, and an analog-digital hybrid architecture are reviewed. The availability of such hardware will greatly benefit and enhance the present intense research effort on the potential computational capabilities of highly parallel systems based on neural network models.

Thakoor, A. P.↗

Time-Accurate Computational Fluid Dynamics Simulation of a Pair of Moving Solid Rocket Boosters

Since the Columbia accident, the threat to the Shuttle launch vehicle from debris during the liftoff timeframe has been assessed by the Liftoff Debris Team at NASA/MSFC. In addition to engineering methods of analysis, CFD-generated flow fields during the liftoff timeframe have been used in conjunction with 3-DOF debris transport methods to predict the motion of liftoff debris. Early models made use of a quasi-steady flow field approximation with the vehicle positioned at a fixed location relative to the ground; however, a moving overset mesh capability has recently been developed for the Loci/CHEM CFD software which enables higher-fidelity simulation of the Shuttle transient plume startup and liftoff environment. The present work details the simulation of the launch pad and mobile launch platform (MLP) with truncated solid rocket boosters (SRBs) moving in a prescribed liftoff trajectory derived from Shuttle flight measurements. Using Loci/CHEM, time-accurate RANS and hybrid RANS/LES simulations were performed for the timeframe T0+0 to T0+3.5 seconds, which consists of SRB startup to a vehicle altitude of approximately 90 feet above the MLP. Analysis of the transient flowfield focuses on the evolution of the SRB plumes in the MLP plume holes and the flame trench, impingement on the flame deflector, and especially impingment on the MLP deck resulting in upward flow which is a transport mechanism for debris. The results show excellent qualitative agreement with the visual record from past Shuttle flights, and comparisons to pressure measurements in the flame trench and on the MLP provide confidence in these simulation capabilities.

Strutzenberg, Louise L.↗

NASA Hybrid Thermally Efficient Core (HyTEC) Phase 2 Q3’GFY25 to Q2’GFY26 Unlimited Rights Annual Report for CLIN 1 and 2

The HyTEC Phase 2 Project focuses on the development and demonstration of high-power density, small engine core gas turbine engine technologies. The focus of HyTEC on these small engine core technologies will provide direct benefits to the next single-aisle class aircraft in terms of thermal efficiency, as well as integrate with other technologies, through increased hybridization, as they mature to provide substantial continuous fuel burn reductions during the aircraft lifecycle. These advances will strengthen the US position in the commercial aviation engine market and enable cost benefits in commercial aviation. In Government fiscal year 26 the HyTEC Project was closed and contract moved to the Subsonic Vehicle Technologies and Tools Project. GE Aerospace is executing two major work plans as part of the HyTEC Phase 2 contract. The first is Contract Line-Item Number (CLIN) 001 and its objective is to mature High Pressure Turbine (HPT) aerodynamics technology to TRL 5 through multiple rigs so that it may be incorporated into a complete TRL 6 evaluation and unlock learnings for the engine core demonstration as applicable. CLIN 002, the second work plan, is to design, procure and test a cost shared portion of technologies on the TRL6 Compact Core test vehicle. The compact core demonstrated through HyTEC Phase 2 along with the HPT rig TRL advancement directly matures the technologies being developed as part of the CFM RISE demonstrator program which is targeting a more than 20% fuel burn reduction at the engine level versus today’s state of the art. The RISE program’s objective is to advance both the novel Open Fan architecture, compact core technologies and advanced systems such as hybrid electric needed to achieve the desired fuel burn reduction to TRL6 ahead of a new product introduction in the single-aisle class aircraft in the 2030s timeframe.

gas turbine engine↗

Evaluation of Electrical System Requirements for Implementing Turbine Electrified Energy Management

Turbine Electrified Energy Management (TEEM) is a concept concerned with the management of energy in an electrified propulsion system. The management of energy in the hybrid-electric architecture has potential to benefit the turbomachinery and the aircraft it powers. The concept is particularly useful for improving operability during transient operation and could be leveraged to design a better performing engine. The concept utilizes electric machines coupled to the engine shafts and an electric power distribution system that includes energy storage. A controller is used to decide when and how energy is moved around the electrified propulsion system, particularly when considering energy conversion between mechanical and electrical forms. Prior work has shown that the electric machines can be used to supply/or extract supplemental power to/from the engine shafts to improve their operability and achieve or enable propulsion efficiency and performance benefits. However, the previous studies did not consider the practical constraints of the electrical machines and energy storage devices that are required for implementing the TEEM system architecture concept. This paper presents an integrated engine and electrical system model that is used to evaluate the electrical system requirements. The model captures the physics of the conceptual, Advanced Geared Turbofan 30,000lbf (AGTF30) engine, which features advanced technologies such as a compact gas turbine and a variable area fan nozzle. For this work, the engine is augmented with electrical system components that allow for the implementation of the TEEM concept. The evaluation presented suggests the potential of the TEEM concept to provide performance benefits for a turbofan engine.

hybrid electric propulsion↗

Holodeck Testbed Project

The main objective of the Holodeck Testbed is to create a cost effective, realistic, and highly immersive environment that can be used to train astronauts, carry out engineering analysis, develop procedures, and support various operations tasks. Currently, the Holodeck testbed allows to step into a simulated ISS (International Space Station) and interact with objects; as well as, perform Extra Vehicular Activities (EVA) on the surface of the Moon or Mars. The Holodeck Testbed is using the products being developed in the Hybrid Reality Lab (HRL). The HRL is combining technologies related to merging physical models with photo-realistic visuals to create a realistic and highly immersive environment. The lab also investigates technologies and concepts that are needed to allow it to be integrated with other testbeds; such as, the gravity offload capability provided by the Active Response Gravity Offload System (ARGOS). My main two duties were to develop and animate models for use in the HRL environments and work on a new way to interface with computers using Brain Computer Interface (BCI) technology. On my first task, I was able to create precise computer virtual tool models (accurate down to the thousandths or hundredths of an inch). To make these tools even more realistic, I produced animations for these tools so they would have the same mechanical features as the tools in real life. The computer models were also used to create 3D printed replicas that will be outfitted with tracking sensors. The sensor will allow the 3D printed models to align precisely with the computer models in the physical world and provide people with haptic/tactile feedback while wearing a VR (Virtual Reality) headset and interacting with the tools. Getting close to the end of my internship the lab bought a professional grade 3D Scanner. With this, I was able to replicate more intricate tools at a much more time-effective rate. The second task was to investigate the use of BCI to control objects inside the hybrid reality ISS environment. This task looked at using an Electroencephalogram (EEG) headset to collect brain state data that could be mapped to commands that a computer could execute. On this Task, I had a setback with the hardware, which stopped working and was returned to the vendor for repair. However, I was still able to collect some data, was able to process it, and started to create correlation algorithms between the electrical patterns in the brain and the commands we wanted the computer to carry out. I also carried out a test to investigate the comfort of the headset if it is worn for a long time. The knowledge gained will benefit me in my future career. I learned how to use various modeling and programming tools that included Blender, Maya, Substance Painter, Artec Studio, Github, and Unreal Engine 4. I learned how to use a professional grade 3D scanner and 3D printer. On the BCI Project I learned about data mining and how to create correlation algorithms. I also supported various demos including a live demo of the hybrid reality lab capabilities at ComicPalooza. This internship has given me a good look into engineering at NASA. I developed a more thorough understanding of engineering and my overall confidence has grown. I have also realized that any problem can be fixed, if you try hard enough, and as an engineer it is your job to not only fix problems but to embrace coming up with solutions to those problems.

Arias, Adriel↗