Audi’s V8 engine could become a casualty of the automaker’s impending shift towards downsized engines and electrification. A source close to the Volkswagen-owned firm has revealed that its new V8 is most likely its last.

Mr. VIKRANT CHAUHAN

 “It would be very difficult to justify the huge investment in another new V8 because of the cost of developing electric drivetrains and battery packs. You have to ask what is the best use of investment money,” explained an anonymous inside source in a recent interview with British magazine Autocar.

The source added that Audi hopes battery-electric vehicles will make up anywhere between 25 and 35 percent of the cars it sells by the year 2025. The company’s current lineup doesn’t include an all-electric car, so the technology needs to be developed from scratch. Luckily, Audi can share the cost burden with other Volkswagen-owned firms.

Fear not, big displacement fans, Audi’s V8 engine still has several years ahead of it. The diesel-powered variant of the engine (pictured) was just introduced under the hood of the SQ7 TDI, and it will be found between the fenders of the brand new second-generation Porsche Panamera as early as next year. And while we’re unlikely to see the 4.0-liter TDI mill in the United States for obvious reasons, a gasoline-burning variant of the eight will power upcoming Audi, Porsche, and even Bentley models for years to come.

 

Do the 4th, 5th, 6th or higher derivatives appear often in real world problems (physics, etc.)? If not, why is that?

This is a fascinating question that really illustrates a lot about the structure of nature.

TL;DR: The answer is that higher order differential questions appear ubiquitously in physics, but rarely in an important way.

Ubiquity of Higher Order Derivatives

So first, derivatives of all orders appear in Taylor series. So anytime you’re dealing with approximations, you’re likely going to run into Taylor series or approximation methods that are morally equivalent to a Taylor series. So therefore, you’re going to run into higher order derivatives all over the place. This includes both classical and quantum mechanical perturbative methods.

Almost nothing can be solved exactly in physics — except for the the harmonic oscillator. This means that you’re going to run into higher order derivatives all the time if you go to high enough order in the approximation. These higher order termes can be essential for getting the right numerical answer.

I would call these higher derivatives inessential. Sure, you need to know about higher order derivatives (which aren’t anything special), but they don’t change anything conceptual aspects of the problem.

Important Higher Order Derivatives

Essential higher order derivatives are when you have to solve a higher order differential equation. These are few and far between in physics, but they do occur. The biharmonic equation:

∇2∇2ϕ=0∇2∇2ϕ=0

is one equation that occasionally appears in physics, most notably in continuum mechanics. You may have to solve a fourth order differential equation.

The reason these higher order differential equations are few and far between is because generally there is nothing that forbids the lower order differential operator from appearing in the equation, so generically you’d expect

(a∇2+b∇4)ϕ=0(a∇2+b∇4)ϕ=0

So this is a fourth order differential equation still, but notice that there are units associated with the constants aa and bb , in particular

dim (b/a)=distance2dim (b/a)=distance2

In most systems, this ratio with be some short distance scale having to do with atomic size (or some other short distance phenomena); however, the equations you’re solving are only expectation for the lowest order behavior of most physical systems.valid for much longer distances. So the higher order derivative is going to make contributions of the size

δ∼(b/al2)≪1δ∼(b/al2)≪1

relative to the first term where ll is the size of the phenomena that is being described.

If you insist on taking that higher order term seriously and start solving a fourth order differential equation, you have to explain why the next higher derivative doesn’t matter

(a∇2+b∇4+c∇6+d∇8+⋯)ϕ=0(a∇2+b∇4+c∇6+d∇8+⋯)ϕ=0

where the relative sizes of these different operators is generally

b/a∼c/b∼d/cb/a∼c/b∼d/c

so when the fourth order operator starts becoming important, all the different orders start becoming important at the same time and the equation isn't a good approximation to the phenomena being described.

In some systems you can either have accidentally small or large coefficients — or in some modern condensed matter or optical systems, you can tune parameters to be large or small. In these cases you can choose to end up with higher order differential equations. Some of these are being constructed to study novel physical phenomena where the ordinary harmonic oscillator isn’t the lowest order behavior.

But aside from these unusual situations, the near-guarantee of the ∇2∇2 term dominating the long-distance behavior of physical systems is the reason when higher order derivatives are rarely discussed or used, they can usually only be treated as perturbations to the original equation and not as the core parts of the equation.

There are these rare exceptions, oftentimes due to weird symmetries, where higher order differential equations appear, but these are the exception not the rule.

And ultimately this is why the harmonic oscillator is the most important model in physics: because it forms the basis for all perturbative methods because it is the generic

Trendline

New Laser Created from Jellyfish's Fluorescent Proteins

Fluorescent proteins from jellyfish that were grown in bacteria have been used to create a laser for the first time, according to a new study.

The breakthrough represents a major advance in so-called polariton lasers, the researchers said. These lasers have the potential to be far more efficient and compact than conventional ones and could open up research avenues in quantum physics and optical computing, the researchers said.

Traditional polariton lasers using inorganic semiconductors need to be cooled to incredibly low temperatures. More recent designs based onorganic electronics materials, like those used in organic light-emitting diode (OLED) displays, operate at room temperature but need to be powered by picosecond (one-trillionth of a second) pulses of light. [Science Fact or Fiction? The Plausibility of 10 Sci-Fi Concepts]

By repurposing the fluorescent proteins that have revolutionized biomedical imaging, and by allowing scientists to monitor processes inside cells, the team created a polariton laser that operates at room temperature powered by nanosecond pulses — just billionths of a second.

"Picosecond pulses of a suitable energy are about a thousandfold more difficult to make than nanosecond pulses, so it really simplifies making these polariton lasers quite significantly," said Malte Gather, a professor in the School of Physics and Astronomy at the University of St. Andrews in Scotland and one of the laser's inventors.

A schematic illustration of a fluorescent protein polariton laser in action. Particles made from a mixture of light and electronic energy are created in a film of green fluorescent protein produced by live cells.

Credit: Dietrich/Höfling/Gather

Gather told Live Science that fluorescent proteins have been used as a marker in living cells or living tissue before, but now the researchers have started using them as a material. "This work shows for the first time that their molecular structure is actually favorable for operation at high brightness — as required, for example, for turning them into lasers," he said.

Genetically modified bacteria

Gather and colleagues from the University of Würzburg and Dresden University of Technology, both in Germany, genetically engineered E. coli bacteria to produce enhanced green fluorescent protein (eGFP).

The researchers filled optical microcavities with this protein before subjecting them to "optical pumping," where nanosecond flashes of light are used to bring the system up to the required energy to create laser light.

Importantly, after reaching the threshold for polariton lasing, pumping more energy into the device resulted in conventional lasing. This helps confirm the first emission was due to polariton lasing, Gather said, which is something other approaches using organic materials have been unable to demonstrate so far.

Conventional lasers create their intense beams by taking advantage of the fact that photons can be amplified by excited atoms in the laser's so-called "gain medium." This is typically made from inorganic materials, such as glasses, crystals or gallium-based semiconductors.

Polariton laser light is nearly indistinguishable from conventional laser light, but the physical process that creates it relies on a quantum phenomenon to amplify the light.

Repeated absorption and re-emission of photons by atoms or molecules in the gain medium gives rise to quasiparticles called polaritons. In certain conditions — before the energy level required for conventional lasing is reached — the polaritons synchronize into a joint quantum state called a condensate, which gives off laser light.

Conventional lasers require more than half of the atoms in the gain medium to enter an excited state before laser light is produced. This is not the case in polariton lasers, which means, in theory, they require less energy to be pumped into the system, the researchers said.

Laser innovations

According to Gather, one of the key advantages of the new approach is that the light  emitting part of the protein molecules   is protected within a nanometer-scale cylindrical shell, which prevents them from interfering with each other.

This overcomes a major problem that has plagued previous designs, said Stéphane Kéna-Cohen, an assistant professor in the Department of Engineering Physics at Polytechnique Montréal in Canada, who has worked on organic polariton lasers but was not involved with the new study.

"This allows the laser to operate with much longer pump pulses, which are easier to generate and allows for simpler implementations," Kéna-Cohen told Live Science. "At the moment, many challenges remain for such lasers to be useful because the [excitation] threshold is so high, but they are a fascinating platform for studying physics that normally occur only at ultralow temperatures."

Gather said the fundamental physics suggests design improvements should eventually allow polariton lasers with considerably lower thresholds than conventional ones, which would allow them to be much more efficient and compact.

This makes the new study promising for the field of optical computing, he said, and a tiny laser based on biomaterials could also potentially be implanted in the human body for medical applications. In the meantime, he added that they are a useful model for investigating fundamental questions in quantum physics.

The results of the new study were published online today (Aug. 19) in thejournal Science Advances.