Double-Step Shape Invariance in Quantum Mechanics

 An article recently published in the journal Axioms explored the double-step shape invariance of radial Jacobi-Reference (JRef) potential and the violation of conventional supersymmetric (SUSY) quantum mechanics rules.

Background

Laguerre-reference (LRef) and JRef are the two implicit potential families that are exactly solvable in terms of confluent hypergeometric or hypergeometric functions. These potentials are referred to as LRef and JRef potentials as they are quantized through classical Laguerre and classical Jacobi polynomials, respectively, using degree-dependent indices.

The JRef potential can be converted into a distinct rational function, referred to as the CGK potential, by the Darboux transformation with a nodeless eigenfunction as the transformation function. This implies that the exactly solvable potential like JRef is not shape-invariant, contradicting the renowned assertion of Gendenshtein that all exactly solvable potentials must be shape-invariant.

SUSY Rule Violation

This paper revealed some significant form-invariance features of the JRef canonical Sturm-Liouville equation (CSLE) in the particular density function case with the simple pole at the origin. It was proven that the CSLE preserves its form under the two second-order Darboux-Crum transformations (DCTs), with specially chosen basic quasi-rational solutions (q-RSs) pairs representing the seed functions to ensure that their analytical continuations do not possess zeros in the complex plane.

Additionally, both transformations often decrease or increase by two the exponent difference (ExpDiff) for the pole mentioned while keeping the other two parameters unchanged. The change can be more complicated if the ExpDiff for the original CSLE's pole is smaller than two at the origin. Researchers observed that bound energy levels are not preserved by DCTs according to conventional SUSY rules.

Specifically, they concluded that first-order differential expressions are generated by the mentioned second-order DCTs in the hypergeometric functions' space after the replacement of Crum Wronskians (CWs) by the Krein determinants (KDs). The predicted differential equations for the principal Frobenius solutions (PFSs) near the origin were explicitly confirmed using the conventional contiguous relations for hypergeometric series.

This mentioned anomalous case presented a good example of the breakup of the conventional SUSY quantum mechanics rules for DCTs between limit point (LP) and limit circle (LC) regions.

The Study and Findings

In this study, the researchers split the DCT into the two sequential Darboux deformations of the Liouville potentials associated with the CSLEs to understand the anomaly. Specifically, the anomaly source was explained by decomposing the second-order DCT into two sequential Liouville-Darboux transformations (LDTs).

The two different Liouville transformations on the infinite interval (1, inf) and on the finite interval (0, 1) then resulted in the supplementary double-step shape-invariant potential pair defined on the real axis and on the positive semi-axis, respectively. These potentials were solvable by the Heun equation's polynomial solutions.

The researchers observed that the initial CSLE was turned into the Heun equation written in canonical form by the first Darboux transformation, while the second transformation yielded the hypergeometric equation's canonical form. Additionally, the first of these transformations/first LDT placed the ExpDiff into the LC range, and then the second transformation/second LDT kept the pole/the given spectral problem within the LC region, which violated the conventional SUSY quantum mechanics prescriptions.

Significance of the Work

The significance of this study extends beyond the specific findings outlined here. It presented a specific illustration of the recently developed SUSY theory of the Gauss-reference (GRef) potentials representing the Liouville potentials for the confluent rational CSLE (RCSLE) with a single pole in the finite plane that is commonly placed at the origin, or two Fuchsian RCSLEs with three second-order poles, including infinity.

The RCSLE is referred to as Routh-reference (RRef), LRef, or JRef if it possesses q-RSs consisting of generalized Routh, Jacobi, or Laguerre polynomials. Most importantly, the eigenfunctions of the LRef and JRef CSLEs are composed of infinite sequences of classical Laguerre and classical Jacobi polynomials, with the polynomial indices typically reliant on the polynomial degrees in all three cases, while the RRef CSLE is quantized based on Romanovski/pseudo-Jacobi polynomials' finite orthogonal sequences.

In this work, the form-invariant RCSLE concept was extended to the JRef CSLE with the density function. The Liouville transformation can be performed independently on the three quantization intervals (−∞, 0), (1, ∞), and (0, 1), which leads to three Liouville potentials, including the radial potential studied in this work and the two branches of the linear tangent polynomial (LTP) potential on the line, which were found to be shape-invariant due to the action of second-order DCTs with basic solution pairs as the seed functions.

To summarize, this study effectively explained the breakdown of SUSY rules for the radial potential with a centrifugal barrier in the LC range.

Journal Reference

Natanson, G. (2024). Double-Step Shape Invariance of Radial Jacobi-Reference Potential and Breakdown of Conventional Rules of Supersymmetric Quantum Mechanics. Axioms, 13(4), 273.

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Tweak to Schrödinger's cat equation could unite Einstein's relativity and quantum mechanics, study hints

 Physicists have proposed modifications to the infamous Schrödinger's cat paradox that could help explain why quantum particles can exist in more than one state simultaneously, while large objects (like the universe) seemingly cannot.

The universe's largest structures appear to follow the rules of Einstein's relativity, while the smallest objects obey quantum mechanics. Can proposed changes to the infamous Schrödinger's cat equations help unite the two theories? (Image credit: TheDigitalArtist / Pixabay)

Theoretical physicists have proposed a new solution to the Schrödinger's cat paradox, which may allow the theories of quantum mechanics and Einstein's relativity to live in better harmony.

The bizarre laws of quantum physics postulate that physical objects can exist in a combination of multiple states, like being in two places at once or possessing various velocities simultaneously. According to this theory, a system remains in such a "superposition" until it interacts with a measuring device, only acquiring definite values as a result of the measurement. Such an abrupt change in the state of the system is called a collapse.

Physicist Erwin Schrödinger summarized this theory in 1935 with his famous feline paradox — using the metaphor of a cat in a sealed box being simultaneously dead and alive until the box is opened, thus collapsing the cat's state and revealing its fate.

However, applying these rules to real-world scenarios faces challenges — and that's where the true paradox arises. While quantum laws hold true for the realm of elementary particles, larger objects behave in accordance with classical physics as predicted by Einstein's theory of general relativity, and are never observed in a superposition of states. Describing the entire universe using quantum principles poses even greater hurdles, as the cosmos appears entirely classical and lacks any external observer to serve as a measuring device for its state.

"The question is can the Universe, which does not have a surrounding environment, be in such a superposition?" lead author Matteo Carlesso, a theoretical physicist at the University of Trieste in Italy, told Live Science in an email. "Observations say no: everything goes along the classical predictions of General Relativity. Then, what is breaking such a superposition?"

Related: Quantum 'yin-yang' shows two photons being entangled in real-time

To tackle this question, Carlesso and his colleagues proposed modifications to the  Schrödinger equation, which governs how all states, including those in superposition, evolve over time.

"Specific modifications of the Schrödinger equation can solve the problem," Carlesso said. In particular, the team added terms to the equation that captured how the system interacts with itself, as well as adding some other specific terms. This in turn leads to superposition breaking down.

"Such effects are stronger the larger the system," Carlesso added.

Crucially, these modifications have little impact on microscopic quantum systems, such as atoms and molecules, but allow larger systems — like the universe itself — to collapse at frequent intervals, giving them definite values that fit with our observations of the cosmos. The team described their modified Schrödinger equation in February in the Journal of High Energy Physics.

In their tweaked version of quantum physics, the researchers eliminated the distinction between objects subject to measurement and measuring devices. Instead, they proposed that each system's state undergoes spontaneous collapse at regular intervals, leading to the acquisition of definite values for some of their attributes.

For large systems, spontaneous collapse occurs frequently, rendering them classical in appearance. Subatomic objects interacting with these systems become part of them, leading to rapid collapse of their state and the acquisition of definite coordinates, akin to measurement.

"With no action from external entities, any system localizes (or collapses) spontaneously in a particular state. In place of having a cat being dead AND alive, one finds it dead OR alive," Carlesso said.

The new model may explain why our universe's space-time geometry doesn't exist in a superposition of states and obeys the classical equations of Einstein's relativity.

"Our model describes a quantum Universe, which eventually collapsed thus becoming effectively classical," Carlesso said. "We show that spontaneous collapse models can explain the emergence of a classical Universe from a quantum superposition of Universes, where each of these Universes has a different space-time geometry."


While this theory may explain why the universe seems to be governed by classical laws of physics, it doesn't make new predictions about large-scale physical processes.

However, it does make predictions about how atoms and molecules will behave, albeit with minimal deviations from conventional quantum mechanics.

As a result, testing their modified quantum model won't be so simple. Future work will be aimed at coming up with such tests.

"Together with experimental collaborators, we are trying to test the effects of the collapse modifications or derive bounds on their parameters. This is completely equivalent to testing the limits of quantum theory."

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Breathing New Life into Buildings: The Future of HVAC Design by Mechanical Engineers

 

It is undeniable that in today’s world, where the focus is on environmental impact and energy efficiency, HVAC systems in buildings are undergoing a significant transformation.

Mechanical engineers are at the forefront of this change, whose innovative approaches to HVAC design are redefining climate control in our living and working spaces.

“The necessity for efficient HVAC systems has never been more pronounced,” says mechanical engineer Ioannis Kalfagiannis. With years of experience in mechanical engineering, he has seen firsthand the evolution of HVAC systems.

Kalfagiannis adds: “With the rise in global temperatures and heightened awareness of energy consumption, the demand for more efficient, eco-friendly HVAC solutions has grown exponentially.

“Now, the goal is no longer just to provide comfort but to do so sustainably.”

Kalfagiannis, an Intermediate Mechanical Building Services Design Engineer at Arup, is currently based in London but has worked on billion-dollar building projects in the United States, Dubai and Denmark.

Celebrated for his exceptional analytical abilities, Kalfagiannis can adeptly address and resolve intricate problems while crafting comprehensive engineering specifications. His extensive technical expertise encompasses various areas, including computer-aided Design (CAD), HVAC designs, energy modeling, and building information modeling.

These multifaceted skills underscore his proficiency in detailed engineering aspects and contribute significantly to his ability to lead and innovate in his field.

Kalfagiannis is also proficient in software like AutoCAD, Revit, and IES and is familiar with various standards and codes, such as ASHRAE, NFPA, and CIBSE Guides.

His academic credentials are equally impressive. Kalfagiannis holds a Master’s degree in Global BIM Management from the Zigurat Global Institute of Technology – University of Barcelona, an MSc in Energy & Sustainability from Heriot-Watt University, Edinburgh, and a BSc in Mechanical Engineering from the Technological Institute of East Macedonia & Thrace, Kavala, Greece.

“What we’re looking at today is a complete rethinking of how we heat and cool our spaces,” says Kalfagiannis.

“Now we need to consider not only the mechanics but how to integrate technology, sustainability, and design.”

One of the most significant advancements in HVAC design is the integration of smart systems and artificial intelligence. Kalfagiannis’s work often involves the use of AI to optimize system performance: “By incorporating AI, we can create systems that learn and adapt to their environment, significantly reducing energy consumption,” he explains.

Kalfagiannis is also a strong advocate for customizable and modular HVAC designs: “Every building has its own unique set of needs and challenges. A one-size-fits-all approach is no longer viable,” he says.

His designs often involve modular components that can be easily adapted or upgraded as needs change: For example, if there is a future need, you can meet the cooling load in a building by adding one extra plate in a plate heat exchanger, which is more cost-effective than buying an additional chiller. This saves money, space and embodied carbon.”

Kalfagiannis excels at integrating renewable energy sources into HVAC systems. He frequently incorporates solar and geothermal energy into his designs.

One such project where he could put this into practice was on the VIP Resorts of the Exclusive Club Skorpios Island and the New Integrated Training Center project in Doha, Qatar. His designs for the HVAC systems demonstrate his skill in creating efficient and sustainable solutions.

He says: High performing buildings have become the forefront for developers all over the world.

To deliver highly energy-efficient buildings, you have to go through the details. Every parameter counts. Back in the day, mechanical engineers used to use oversized equipment; however, times have changed.

Today engineers have to go through detailed and very intense energy modelling to promote efficiency and evaluate operating energy.

Then through value engineering, they save resources and time for the client. Designing for extreme weather conditions doesn’t work anymore and is updated.

Kalfagiannis adds, “Renewable energy is the future. Integrating these sources into HVAC systems is not only environmentally responsible but also cost-effective in the long run.”

His innovations also focus on improving indoor air quality, a crucial aspect of HVAC systems that has gained importance due to global health concerns: “We have to engineer systems for comfort, as well as creating environments that contribute to the well-being of their occupants,” Kalfagiannis states.

He emphasizes the importance of considering the building as a whole adding: “The efficiency of any HVAC system is greatly influenced by the building’s insulation and the materials used in its construction.”

To ensure this is considered, his approach often involves working closely with architects to ensure that the building and HVAC system complement each other.

However, it is not always straightforward: “The most difficult part can often be dealing with people that have different backgrounds, as well as working with architects or structural engineers,” Kalfagiannis confesses.

“They understandably want to put the design first, and I have to try and convince them that my proposal is going to work!”

Despite advancements, Kalfagiannis also acknowledges challenges, particularly in retrofitting older buildings with new technologies. “The biggest challenge often lies in integrating new systems into existing structures in an efficient and cost-effective way,” he explains.

Examples of his experience in this area include the Novo Nordisk Pharmaceutical Facility in Denmark and F35 Dormitory at USAF Lakenheath Base, UK.

He also had to employ sophisticated techniques when he worked on the New York Police Department 69th Coney Island Precinct.

Here, he sized and specified mechanical equipment for the older building, showcasing his adaptability to different project demands.

“I’m very familiar with building codes and standards,” says Kalfagiannis, which is how I ensure we can stay within the parameters necessary.”

He adds, “I also use a wide variety of software, especially design software like AutoCAD or Revit for sketches and Blue Beam.”

Kalfagiannis is passionate about educating the next generation of mechanical engineers: “It’s essential that we equip young engineers with not only technical knowledge but also an understanding of environmental responsibility,” he says.

He has mentored hundreds of individuals to support them in their careers and build their skills: “When I was starting my career in Greece I didn’t have someone to call a mentor. The main reasons behind that were the economic crisis the country was going through and the high competition among peers and coworkers.”

Kalfagiannis adds: “I found it overwhelming and stressful. One of my goals is to embrace the young engineers joining the industry. Everyone has the right to feel lost when starting a career, but you have to remind them that they are not lost, rather just early in the process.

“Educating is part of my work ethic. I care about my team, especially the young fellows.

“I also emphasize a laid-back, friendly style, and fostering a sense of camaraderie among my team. I want them to see me as a friend, to develop a friendship relationship.”

Kalfagiannis’s approach not only creates a positive work environment but also ensures the mutual respect and collaboration necessary for successful project delivery.

Despite the rewarding aspects of his career, Kalfagiannis also doesn’t shy away from discussing the stressors of his job, particularly the tight deadlines and the intense focus required to resolve complex technical issues.

However, he finds immense satisfaction in overcoming these challenges: “It’s the best feeling when I achieve my goals. It makes my day,” he shares.

Looking to the future, Kalfagiannis sees a world where HVAC systems are integral to the sustainability of buildings: “We’re heading towards a future where buildings are not just passive structures but active contributors to energy efficiency and environmental health,” he predicts.

Kalfagiannis acknowledges the role of regulations and standards in driving innovation in the field: “Regulatory bodies play a crucial role in setting benchmarks for efficiency and environmental impact. These standards push the industry towards innovation,” he points out.

A key to Kalfagiannis’s success is his belief in interdisciplinary collaboration. “The future of HVAC is not just in the hands of mechanical engineers. It requires a collaborative approach, integrating insights from architecture, environmental science, and technology,” he stresses.

Dylan Mendes is the Commissioning Project Engineer and Construction Project Manager for Fulcrum Group. He collaborated with Kalfagiannis on the project for the 69th Police Precinct NYPD: “Mr. Kalfagiannis excelled in his role as a Mechanical Building Services Design Engineer on the project, showcasing outstanding skill and professionalism.

“Our collective goal was to lower the building’s energy usage substantially, boost operational efficiency and cut costs. Mr. Kalfagiannis was thorough in his approach, conducting in-depth energy surveys, simulations, and feasibility studies to pinpoint effective energy-saving strategies.

“He was instrumental in selecting and implementing new energy-efficient boilers, air handling units, and circulation pumps equipped with variable-frequency drives.

“His adeptness in developing detailed mechanical layouts, including new plant rooms and coordination drawings, was a key factor in the project’s successful completion.”

Ali Abbani is Senior Mechanical Engineer at Arup and worked with Kalfagiannis on the Triton project, which incorporated refurbishing a 12-story office building in central London: “Kalfagiannis showcased remarkable skill and commitment in his professional capacity. His duties encompassed precise calculations of heating and cooling loads, assessment of solar and internal gains, and thorough examination of the British Council for Offices’ specification guide.

“He also skillfully selected and detailed fan coil units to precisely match specific cooling requirements, expertly coordinated services, and effectively developed 3D models.

“His significant contributions played a crucial role in the triumphant realization of the project, demonstrating his expertise in mechanical engineering and project management.”

Kalfagiannis represents the pinnacle of mechanical engineering and HVAC design innovation: “My work is about creating sustainable, efficient, and healthy environments as well as comfort,” he says.

“As we move forward, insight and innovation will be crucial in shaping a world where buildings shelter us and support our planet’s health and resources.”

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New generation of aircraft mechanics hoping to fill gaps amid worker shortage

Another student, Justin Bosco, said his love for aircraft started as a child.

"When I was younger there was a program called Operation Purple, where they would send military kids to a summer camp for a week," he said. "The Army National Guard came in one year and brought a Blackhawk helicopter, and little 8-year-old me was like that’s the coolest thing ever."

Among the pros of being an aircraft mechanic, Bosco said the job is very interesting, every day is different, and the money can't be complained about, "especially with everyone retiring."



Those retirements are helping drive the shortage of mechanics as nearly one-third of the current aircraft mechanic workforce is at or near retirement.
AMERICAN AIRLINES PILOTS APPROVE NEW CONTRACT THAT INCLUDES PAY BOOST, BENEFITS

"We had the baby boomer generation, and that’s what filled the workforce. So this is you know, the next large wave. All the people now are going to need to start filling in all the spots that are being vacated by people retiring or at that age," said Matthew Harter, the SWIC Aviation Maintenance Technology Program coordinator.

Harter said the shortage of technicians could impact travel.

"If they don’t have enough mechanics, they can’t produce a certain amount of hours that inspections take, so they may have to down planes or extend planes maintenance activities longer," said Harter.

AIRLINES SEEK TO EXTEND CUTS TO FLIGHTS IN NEW YORK-AREA AIRPORTS AMID STAFFING SHORTAGE

Some commercial airlines like Delta and American don’t anticipate issues. Delta said they’re getting ahead of the shortage with a strong pipeline of workers through partnerships with schools and other recruiting efforts.. "We have a great team that goes out and helps with our forecasting to make sure we have enough of a spread. And then if we have to, we’ll add more schools in to the partnerships, and we’ll start drawing from other universities," said Joseph McDermott, Delta Air Lines' vice president of cabin operations and support services.
In the meantime, the future mechanics are ready to get to work.

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"I’m glad that there are jobs available, but I really hope that a lot of people [are] joining us so that we don’t have to end up with having to work overtime and being stressed out," Hagstrom said.

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Elon’s Department of Engineering launches mechanical engineering concentration

The mechanical engineering concentration complements existing coursework and is the most popular engineering degree worldwide. Assistant Professor Blake Hament was hired this summer to add to existing curriculum and faculty expertise.

New this academic year, Elon’s Department of Engineering will offer a mechanical engineering concentration with the Bachelor of Science in Engineering degree program — a sign of the program’s continued growth and rise to prominence.

Mechanical engineering is the most popular among engineering disciplines globally and is in high demand by employers. The new concentration complements Elon’s general engineering degree with an emphasis on technical proficiency through courses in mechanics, dynamics, thermodynamics, materials science and structural analysis.

The Engineering program also offers concentrations in biomedical engineering, computer engineering and environmental engineering.

“Mechanical engineering is the most popular and versatile engineering discipline and broadly appeals to prospective students who are interested in engineering,” said Scott Wolter, associate professor and chair of the Department of Engineering. “Many of the courses required of a mechanical engineering concentration have been taught at Elon for many years, and several of our faculty and staff hold mechanical engineering degrees.”

Elon’s B.S. in Engineering program offers a general engineering degree applicable to a wide variety of careers and fields. The program’s rigorous emphasis on fundamental skills fused with liberal arts perspectives produces graduates with technical prowess, broad critical thinking and collaborative dexterity needed to solve complex problems in the 21st century.

Current and prospective students are expected to enroll in the mechanical engineering concentration, having expressed interest in surveys and on tours with department faculty.

Complementing existing courses in statics and dynamics, mechanics of solids, fluid mechanics and thermodynamics, faculty have added new courses in manufacturing engineering, controls and dynamic systems, and introduction to heat and mass transfer.

Assistant Professor Blake Hament joined the department faculty this summer to create and teach some of these new courses. Hament earned his doctorate in mechanical engineering from the University of Nevada – Las Vegas, where he specialized in robotics research in the Drones and Autonomous Systems Lab. Hament worked in research and development for companies including Boston Dynamics, Tesla and Lockheed Martin Space while completing his doctorate. He obtained a Master of Science in curriculum and instruction – secondary science, also at the University of Nevada – Las Vegas, and his Bachelor of Science in physics at Duke University.

“We are excited to have Dr. Hament join us,” Wolter said. “His prior and planned work in mobile robotics, such as drones, humanoids and quadrupeds, has already generated interest among many of our students and is certain to draw visitors to his labs in Innovation Hall.”

Hament is particularly interested in ways drones and quadruped robots can be utilized to improve construction safety and in engineering-controlled environments for agricultural use that require less water, less pesticides and less transportation than traditional farming practices. One of his favorite projects was designing a drone that could carry and spray a high-pressure hose.

“It posed an interesting physics and dynamics problem,” Hament said. “Pressurized water hoses kick back almost like a firearm, and that’s challenging to equip to a free-flying drone. It was a fun problem to solve.”

Hament is developing the EGR 4160 Controls and Dynamic Systems course for spring 2024. That course will provide hands-on learning around designing controls “for everything from HVAC, to industrial controls for manufacturing, to robots and aerospace vehicles,” he said.

“I’m very excited to be joining the Elon community,” Hament said. “Elon has established an impressive tradition of teaching, scholarship and mentorship, and I look forward to collaborating with all the amazing students, faculty and staff across campus.”

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LyondellBasell Acquires Mechanical Recycling Assets and Plans Operations in California

mechanical recycling assets containing rigid plastics recycling processing lines from PreZero, a global recycling leader and waste management service provider. The transaction includes leasing the processing facility in Jurupa Valley, Calif., which has a production capacity of approximately 50 million pounds per year for recycled materials.

"This acquisition further strengthens our U.S. presence and will deliver value for our customers and plastic recycling rates in the West Coast," said Yvonne van der Laan, LyondellBasell executive vice president, Circular and Low Carbon Solutions. "We will build upon our existing experience in plastic recycling in Europe and deliver a state-of-the-art, mechanical recycling facility to meet growing demand for recycled products in the U.S."

LYB plans to operate its newly-acquired mechanical recycling plant in California to manufacture post-consumer recycled resins using plastic waste feedstock. LYB will offer these recycled polymers under its CirculenRecover brand, part of the company's Circulen portfolio of products that enable the circular economy. LYB expects to commence operations at its new facility in 2025.

The transaction supports the company's efforts to build a circular economy for plastic, help end plastic waste in the environment and meet customers' growing demand for sustainable products. Together with the previously announced equity stake in the and investment in the in Houston, this latest California-based transaction will further enhance the competitiveness of LYB in the U.S. recycled products market.

About LyondellBasell

We are LyondellBasell (NYSE: LYB) ― a leader in the global chemical industry creating solutions for everyday sustainable living. Through advanced technology and focused investments, we are enabling a circular and low carbon economy. Across all we do, we aim to unlock value for our customers, investors and society. As one of the world's largest producers of polymers and a leader in polyolefin technologies, we develop, manufacture and market high-quality and innovative products for applications ranging from sustainable transportation and food safety to clean water and quality healthcare. For more information,

Cautionary Note Regarding Forward-looking Statements
The statements in this release relating to matters that are not historical facts are forward-looking statements. These forward-looking statements are based upon assumptions of management which are believed to be reasonable at the time made and are subject to significant risks and uncertainties. Actual results could differ materially from the projections, anticipated results, or other expectations expressed in this release, including, but not limited to, receipt of required regulatory approvals; the successful construction and operation of the proposed facilities described in this release; and our ability to meet our sustainability goals, including the ability to increase production of recycled and renewable-based polymers to meet our targets and forecasts. While these statements and projections are made in good faith, LyondellBasell and its management cannot guarantee that anticipated future results will be achieved. Additional factors that could cause results to differ materially from those described in the forward-looking statements can be found in the "Risk Factors" section of our Form 10-K for the year ended December 31, 2022, which can be found at on the Investor Relations page and on the Securities and Exchange Commission's

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Working in the fast lane: Mechanical engineering student secures work term with Formula One

John MacIsaac always had a special interest in cars and engines. "Any maintenance large or small my dad would walk me through, and I would be encouraged to understand how the mechanism works and to research a solution," he says. This hobby paved the way for his interest in high-performance vehicles.

The third-year mechanical engineering student had the opportunity of a lifetime this past fall, completing his first work term at the Aston Martin Aramco Formula One® Team factory in England.

Through a contact made at the Canadian Grand Prix, John was able to connect with Aston Martin Aramco Formula One® Team's head of talent and recruitment. After applying for a position and completing the interview process, John was hired as a placement student in the Research and Development department.

When John arrived, the organization had just moved into a state-of-the-art factory. Initially, he was anxious to be working in such an advanced environment as a new engineer. His nerves soon diminished as his team welcomed him and gave him the chance to join projects and contribute.

During his time at the organization, John worked with his supervisor, who was responsible for most of the R&D and testing of the F1 cars' cooling systems. He was able to develop his skills by working with different types of software and running tests in the labs with the help of technicians. John noted that it was easy to develop relationships and receive input whenever it was required.

"My supervisor was comfortable allowing me to run tests on my own, which was invaluable for my personal development," he says, "My supervisor would also walk through every intricate detail of why a test is required; this allowed me to further analyze and explain our findings in our weekly team meetings. I found this to be the perfect work environment to grow professionally."

The projects John worked on took a lot of patience and attention to detail, and he was grateful to contribute and make an impact on the organization. "Knowing that my projects and tests will have a potential impact on the cars' performance makes them all incredibly special," he says.

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