Long has over 260 publications under his name including journals and conference papers. His research works are focused on various aspects of applied mathematics, and computational science with a particular emphasis on computational fluid dynamics, modernizing STEM education, artificial intelligence, rarefied gas dynamics, and parallel computing.[7] He showed in many research studies that the object oriented approach of C++ is extremely powerful compared to obsolete approaches such as those using the FORTRAN programming language.[8]
Long has extensively focused his research on computational science particularly computational fluid dynamics, and massively parallel computers, and has developed efficient algorithms for solving mathematical model equations. In 1989, he conducted a research study which explained the solution method aimed at the solution of 3D and Navier-Stokes equations with the massively parallel connection machine.[9] He has also solved the Boltzmann equation with the use of Connection Machine, Bhatnagar-Gross-Krook (BGK) model and accurate results were acquired.[10] This led to the Gordon Bell prize in 1993.[11] Later on, he presented an in-depth evaluation of the gas dynamic models, and discussed the Navier-Stokes method and a molecular simulation methods.[12]
Long, along with E. Alpman showed that the Reynolds stress turbulence model was a complete model, he examined separated turbulent flow simulations.[13] Another aspect of computational science that holds prominence in his work is flow-associated noise prediction. He developed a new efficient computational aeroacoustics algorithm for the prediction of aerodynamic noise.[14] He also showed that the four-dimensional integral equation for aeroacoustics can be used to simulate unsteady aerodynamics in the time domain.[15] Together with V. Ahuja, he also developed algorithms and software to solve Maxwell's equations for electromagnetic propagation on parallel computers.[16]
While working on the emotion modeling for mobile robots, he developed a computational model for Temperament and Emotions on Robots. A relationship between emotions, and temperament was built which the previous models on robotics cognitive often overlooked. Having modeled emotions, he implemented the reinforcement effects in his model, so as in the absence of reinforcers emotions return to their standard steady-values. It was demonstrated from his research work that this model carries the potential to be coupled to cognitive architecture, and has been tested, and incorporated into the SS-RICS at the Army Research Laboratory.[17] In 2019, he presented a review of artificial general intelligence (AGI), characterized the current AGI as Narrow AI which focuses on purpose-built applications, formulated by the cumulation of well-recognized algorithms, and proposed a framework as well.[18] Focusing his research on building more intelligent, and autonomous system for the unmanned vehicles, he along with his student, Scott D Hanford built a cognitive robotic system based on the soar cognitive architecture for mobile robot navigation. The cognitive robotic system (CRS) was tested in both outdoor, and indoor navigation missions. For the outdoor setting, it was demonstrated that the Soar agent was able to successfully navigate autonomously to the destination while avoiding obstacles, even with a low information about the environment. It was revealed that the Soar agent had the capability to modify its approach upon the failure of a previous applied approach in avoiding an obstacle. For the indoor search navigation mission, the Soar agent also exhibited success in locating the specific object in the building. This research study highlighted how the implementation of soar in the CRS displayed features of planning, reasoning, intelligent behavior on the autonomous missions, and have implications for the artificial intelligence field.[19] He has also researched possibility of conscious robots with an in-depth analysis on consciousness from the philosophical, neurological, and psychological aspects. It was demonstrated from this research that the hybrid parallel architecture would be befitting for the formulation of conscious robot in order to approximate the complex human brain system.[20]
Long's research works have focused on the neural networks as well. He developed the effective algorithms for the massively-parallel neural networks with the neuron model known as the Hodgkin-Huxley equations. In the research study conducted in 2012, he used C++ and MPI for the efficient scaling up to human-level size networks. Other simple neuron models have failed to accurately simulate the biological neurons.[21] Having discussed that, he also explored the computational costs, and the potential capabilities of neuron models, by reviewing three neuron models namely; Hodgkin–Huxley model, Izhikevich model, and leaky integrate-and-fire model. It was suggested that leaky integrate-and-fire model requires less computations as compared to the Hodgkin–Huxley model but was much too simple, and the Izhikevich model is not useful since it is usually solved using time steps that are unstable and do not actually solve the equations outlined.[22]
Long has also explored molecular simulations with James Bernhard Anderson, and presented the accurate rate expressions for simulations of gas-phase chemical reactions,[23] as well as predicted the ultrafast detonations with the Monte Carlo simulation method.[24]
Long has worked on making STEM education better, and recommends modernizing engineering education. At the 2019 IEEE Aerospace Conference, he presented a research paper that highlighted how Russia, and China are progressing with updated modern discipline whereas US has been too slow to incorporate computing, artificial intelligence, and software systems to their curriculum.[25] He also added that the curriculum highly needs an upgrade with more software engineering certifications, and educational programs.[26]
