Supersonic jet produced when a marble is dropped in a liquid

For imaginative and inquiring minds, even very familiar daily events may contain some totally unexpected shocks, which give them great pleasures. Every one may think he is quite conversant with what might happen when he throws a stone in a basin of water. But, any way, if you read this interesting piece of work, you'll still feel surprised and may proclaim 'O, I did not anticipate this at all !' This kind of work should always be holy in themselves. They challenge common knowledge and refreshes minds and refuels one's passion and curiosity. Now read a review of it.

When scientists speak of a “jet” they are usually referring to a fast flowing column of material, typically air or water. These jets range from the mundane, like water rushing out of a hose, to the exotic, such as the relativistic plasma jets that beam out from quasars or monster black holes. A turbo-jet, for example, pushes an aircraft forward using the supersonic thrust of air that streams out of the back of the engine.

Writing in Physical Review Letters, Stephan Gekle and colleagues at the University of Twente, The Netherlands, in collaboration with the Universidad de Sevilla, Spain, have found a supersonic jet in a surprising place: the collapsing splash from an object falling into water [1]. Their general setup is easy to reproduce by dropping a marble into a deep bowl of water (a billiard ball into a full bucket works even better). This effort is rewarded with not one, but three jets (see Fig.1): First, one of upward streaming supersonic air, followed by an obvious upward jet of water, along with a less evident downward jet of water toward the marble. Although Gekle et al. perform a more controlled experiment—they pull a disk downward through the liquid surface at a controlled speed—the general features of what they find are the same. Moreover, the disk enables Gekle et al. to have good control of the experimental conditions.

In the kitchen version of the experiment, the marble creates a crown-shaped splash and crater as it falls into the liquid. The crater deepens to the point at which the walls start to contract. This is due to both the weight of the water outside and possibly surface tension, both of which create pressure gradients that force the collapse. Air inside this collapsing neck must escape upward or downward as the neck approaches pinch-off. It is in this escaping air that Gekle et al. found supersonic velocities—the first jet in this simple experiment (see Video 1).

The shape of the neck plays an interesting role. As the air escapes through the neck, right before the neck closes, it is accelerated to supersonic speeds as it is driven by high pressures from the collapsing cavity below to low pressures in the air above the water’s surface. Engineers have designed a similar process and shape into the convergent-divergent nozzle (or, De Laval nozzle) that is used as the exhaust port in many rocket engines. In our situation, however, the nozzle forms naturally and is quickly changing shape.

At the moment of pinch-off, very large pressures accompany the impact of the water surface on itself. In fact, the pinch-off is a type of near singularity where nearly all observables—velocities, surface curvatures, pressure gradients, etc.,—become very large [2]. Consequently, just after the pinch-off, large pressures accelerate the water upward and downward to very high velocities [3, 4]. This drives two spikes of liquid—called rebound jets—up above the water surface and another one downward into the cavity following the marble. These are our second and third jets produced by this experiment. In a low viscosity fluid such as water, the jets often quickly break up into a spray of droplets. Each of these fission events also involves a near singular pinch-off of a fluid neck [2]. In fact, there are cases where the upward spray goes higher than the initial height of the dropped marble [5].

In each case these jets are the consequence of the kinetic energy density locally rapidly rising. The analysis of these processes involves the interplay of inertia and in some cases surface tension. The root cause of these self-focusing events is that the surface is changing its topology. When the crater collapses, the surface cleaves from one sheet to one sheet plus a bubble. These high velocities (and high surface curvatures) all occur right around the time of pinch-off. Other examples where a change in topology is accompanied by divergent observables include the reconnection of quantized vortices in a superfluid [6], the formation of black holes in numerical studies of general relativity [7], crater collapse and jet formation in capillary waves [2], and the coalescence of droplets [8].

In many of these situations the rapid divergence has a small length scale cutoff because there is a crossover to a different balance of forces (e.g., at really small length scales, capillary action and the molecular structure of the fluid matters). In such cases, we speak of a near singularity rather than a singularity. For instance, viscosity, the speed of sound, or the speed of light might cap some near singularities. One is tempted to generalize that near-singular behavior may usually be present in any change in topology. In some of the examples above it is clear that the system, if forced, produces a local region of high curvature (corners) on the interface that is undergoing topology change. It is fascinating that such an ordinary event as dropping a stone into a pond holds such richness.

References

1. S. Gekle, I. R. Peters, J. M. Gordillo, D. van der Meer, and D. Lohse, Phys. Rev. Lett. 104, 024501 (2010).
2. B. W. Zeff, B. Kleber, J. Fineberg, and D. P. Lathrop, Nature 403, 401 (2000).
3. J. Eggers and E. Villermaux, Rep. Prog. Phys. 71, 036601 (2008).
4. S. Gekle, J. M. Gordillo, D. van der Meer, and D. Lohse, Phys. Rev. Lett. 102, 034502 (2009).
5. J. E. Hogrefe, N. L. Peffley, C. L. Goodridge, W. T. She, H. G. E. Hentschel, and D. P. Lathrop, Physica D 123, 183 (1998).
6. G. P. Bewley, M. S. Paoletti, K. R. Sreenivasan, and D. P. Lathrop, Proc. Nat. Acad. Sci. USA 105, 13707 (2008).
7. M. W. Chopuik, Phys. Rev. Lett. 70, 9 (1993).
8. J. Eggers, J. R. Lister, and H. A. Stone, Fluid Mech. 401, 293 (1999)

What interests you most in science ?

Making A Supersonic Jet In Your Home

As always, I'm a sucker for articles like this. While it may not have earth-shattering ramifications, I always love reading curious but common phenomenon like this that produced something that is highly unexpected.

The paper shows that when you drop, say, a marble, into a liquid, what happens next can actually produce a supersonic jet of air! A review of this work can be found here, and you can also get access to the actual paper in the link.

In the kitchen version of the experiment, the marble creates a crown-shaped splash and crater as it falls into the liquid. The crater deepens to the point at which the walls start to contract. This is due to both the weight of the water outside and possibly surface tension, both of which create pressure gradients that force the collapse. Air inside this collapsing neck must escape upward or downward as the neck approaches pinch-off. It is in this escaping air that Gekle et al. found supersonic velocities—the first jet in this simple experiment.

A video of this also accompanies the review article.

I often wonder if the fun and fascinating tidbits of apparently "mundane" things like this is the reason why I got into physics in the first place. I know many people cite trying to understand the universe, or wanting to find the meaning of life, etc... etc. as the reason they study physics. I often find that I don't have such grand ambition. Instead, I find delightful pleasure in figuring out if quantum effects causes a pencil balanced on its tip to fall over, or if warm water freezes faster than cold water! Maybe I have a small mind....

tipping time of quantum rod

Here is physicist who wrote a blog on a very pedagogical question on quantum mechanics, which is calculating the tipping time of a vertical rod.

Tipping Time of a Quantum Pencil

I ran across this article in Eur. J. of Phys. and it reminded me of several other articles that I've read on this very topic. This is, of course, a rather familiar problem to many physics students. It involves the a pencil balanced vertically on its tip. So classically, it is in an unstable equilibrium. The problem is to use quantum mechanics, or the Heisenberg Uncertainty principle in particular, to find the tipping time for the pencil. The application of the HUP invokes the fact that the exact position of the top of the pencil can have a natural fluctuation that will tip it off the vertical axis.

The latest paper that I'm aware of on this topic deals with a very detailed calculation of calculating the tipping time of a quantum rod[1]. In this calculation, the author showed that the classical problem can be recovered when the Planck constant goes to zero, and draws the conclusion that:

.. the tipping of the quantum rod can be understood as having been triggered by the uncertainty in angular momentum engendered by localization of the initial state...

The article is a bit difficult to follow, and I didn't get any direct value of the tipping time.

The more interesting papers that I've found earlier on the same topic are much more illuminating than this one. A paper by Don Easton presents a caution for people who tries to apply QM as the basis of the tipping time[2]. His calculation of the tipping time, using QM, gives a humongous number: 0.6 million years. He examined why some posted solutions actually gave a balancing time of the order of 3 seconds, and why those treatment may be faulty.

Another paper that cautioned the use of the HUP in calculating the tipping time is a paper by Shegelski et al.[3] Here, they caution that one can't just use the HUP alone, and they also compared this to the faulty application of the WKB approximation to this problem.

Fascinating! Certainly something that I read in bed before going to sleep! :)

What is special about CNT ?

It was reported in an experiment [1] that the components of a cooper electron pair tunnel into two different arms that made of carbon nanotubes. But why is CNT picked out for this work ? What is special with CNT ?

Can measurement of one quantum system instantaneously affect the measurement outcome of another, even if the systems are spatially separated? This question has never been clearly answered for solid-state materials. Now, a new experiment by L. G. Herrmann in France, working with colleagues in France, Spain, and Germany, published in Physical Review Letters [1] demonstrates that electrons entangled in a superconducting Cooper pair can be spatially separated into different arms of a carbon nanotube, a material thought favorable for the efficient injection and transport of split, entangled pairs. This work may help pave the way for tests of nonlocal effects in solid-state systems, as well as applications such as quantum teleportation and ultrasecure communication.

The question of nonlocal quantum mechanics plagued physicists for decades, as it seemed to violate the rule of special relativity that information cannot travel faster than the speed of light. In fact, in 1935, Albert Einstein, in collaboration with Boris Podolsky and Nathan Rosen, hoped to disprove nonlocal quantum mechanics by publishing a famous thought experiment describing what is now called “the EPR paradox” [2]. In a simple example of this paradox, two particles, A and B, are entangled in a spin singlet, |ψ_AB〉= 1/ √2[|↑〉_A|↓〉_B-|↓〉_A|↑〉_B], where |↑〉 and |↓〉 refer to spin up and spin down, respectively. If the singlet is separated into two noninteracting particles, any subsequent measurement of the spin of particle A (e.g., found to be up spin) should immediately identify the state of particle B (e.g., required to be down spin). Later, John Bell derived a set of inequalities based on correlations between measurements of particles A and B, and showed that breaking these inequalities would prove quantum nonlocality [3].

The EPR paradox was finally resolved experimentally in the early 1980s, when violations of Bell’s inequalities were verified via polarization-entangled photons [4]; nonlocality has more recently been verified in systems such as ions in optical traps [5] and atom/photon hybrids [6]. However, despite recent advances in the manipulation of entangled electron states [7], Bell’s inequalities have not yet been tested in solid-state systems. Besides the fundamental importance of verifying Bell’s inequalities in materials, spatially separated entangled states could potentially form the basis of advanced technologies such as quantum cryptography, teleportation, or information processing, all of which could be integrated with existing solid-state technology and infrastructure.

In the experiment by Herrmann et al., the entangled electrons are formed naturally in an s-wave superconductor, which consists of spin singlets (Cooper pairs) correlated over the superconducting coherence length. Superconductors have been previously proposed and experimentally verified as an excellent source of EPR pairs [8, 9, 10, 11]. Typical charge transfer between a superconductor and a normal metal occurs via a process called “Andreev reflection,” where two electrons in the normal metal pair up to enter the superconductor, and a hole is reflected at the interface to conserve energy (see Fig.1, panel a). In the case of nonlocal transport, also termed “crossed Andreev reflection” (CAR), the incoming electron enters from one normal metal wire, and the hole is reflected in a different, spatially separated wire; this process is equivalent to electrons of a superconducting singlet splitting into two different wires (Fig.1, panel b).

Evidence of CAR was previously demonstrated in groundbreaking experiments that used superconducting pairs injected into two normal metal [11] or ferromagnetic [10] wires. However, these measurements were complicated by the difficulty of distinguishing between contributions from CAR and contributions from pairs tunneling into a single arm (Fig.1, panel c) or from electrons bypassing Andreev reflection and directly tunneling between arms (elastic co-tunneling, see Fig.1, panel d). In addition, CAR signals can be obscured by nonequilibrium effects due to the injection of quasiparticles into the superconductor [12]. A more ideal case in which to test EPR pairs would be if the pair splitting were preferentially enhanced over these other processes. In particular, strong electron interactions—such as Coulomb charging in a quantum dot [8] or correlated states in a one-dimensional wire (e.g., a Luttinger liquid) [9]—could enhance single-particle tunneling over pair tunneling in superconductor-normal injection, thereby enhancing the CAR signal in a split-wire configuration.

Herrmann et al. measure tunneling from a superconductor into two separated quantum dots formed on a carbon nanotube. Quantum dots are isolated puddles of charges where a capacitive charging energy as well as a “particle-in-a-box” quantization energy are required to add additional charges from the leads. Thus simultaneous tunneling of multiple charges into a quantum dot is strongly suppressed. Using this configuration, Hermann et al. observe a strong CAR contribution to the conductance between the superconductor and each of the quantum dots. The conductance is measured at the point of resonance between the dots (where their energy levels line up, so simultaneous tunneling into each dot is enhanced) and then compared to calculations for the superconductor/double-quantum-dot system to extract CAR contributions of up to 55%. In addition, the asymmetry in tunneling between the superconductor and the left or right dot is shown to be consistent with what is expected for a large CAR contribution.

This work is similar to very recent experiments by Hofstetter et al. [13], which also demonstrated enhanced CAR via tunneling from a superconductor into quantum dots; in this case the dots were formed on semiconducting nanowires. However, the experiment on carbon nanotubes not only substantiates the work on nanowires, but also may have significant material advantages. For example, strong electron interactions in the effectively one-dimensional nanotubes are predicted to further enhance pair-splitting processes [9]. Pair splitting is also enhanced by the large quantized energy level spacings in carbon nanotube quantum dots, an effect of their tiny diameters. In addition, metallic carbon nanotubes are predicted to exhibit ballistic transport and long spin-flip scattering lengths, both relevant to the coherent transport of EPR pairs.

The work by Herrmann et al. is important in that it demonstrates that CAR is likely occurring in carbon nanotube quantum dot systems. It sets the stage for future work, in which ideally an experimental parameter can be tuned to separate CAR signals from those of the other tunneling processes. This could be achieved by modifying the gate voltages [13] or various interface transparencies [14], for example. It would also be valuable to clarify the role of the double-dot resonance, as the work on nanowires, in agreement with some theories [8], demonstrated that the relative value of the nonlocal signal was diminished at resonance, likely because the electron number on each dot was not well defined. Finally, a test of Bell’s inequalities requires not just the creation of EPR pairs, but the transport and measurement of them [15]. These measurements entail (1) determining the spin of the electrons in each arm, via spin filters such as polarized ferromagnets, and (2) performing time-resolved spin correlation measurements on currents between the superconductor and each dot. The latter task is quite difficult, due to the large numbers of charge carriers in solid-state systems. A somewhat simpler intermediate step would be to determine noise correlations for transport between the superconducting interface and each quantum dot; correlated signals in this case would be strong evidence of nonlocality [15, 16].

Tests of nonlocality in a solid-state system would be a major breakthrough, enabling not only a greater understanding of entanglement in materials, but also the possibility of using separated entangled states for applications. The observation of enhanced nonlocal transport in carbon nanotubes, a material uniquely favorable for the injection and transport of split, entangled charges, offers an exciting new possibility for the study and use of nonlocality.

[1] L. G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk, Phys. Rev. Lett. 104, 026801 (2010) – Published January 11, 2010

Pulsar bursts move 'faster than light'

Don't be confused by this claim. It means nothing in violation of causality or relativity, according to which none physical signal travels faster than vacuum light speed. A physical signal is a physical object in a particular state. This object can be detected physically and carries energy that can be exchanged with matter. Many unphysical things (such as a shadow) can be faster, but none physical signals in this definition.

Every physicist is taught that information cannot be transmitted faster than the speed of light. Yet laboratory experiments done over the last 30 years clearly show that some things appear to break this speed limit without upturning Einstein's special theory of relativity. Now, astrophysicists in the US have seen such superluminal speeds in space – which could help us to gain a better understanding of the composition of the regions between stars.

Superluminal speeds are associated with a phenomenon known as anomalous dispersion, whereby the refractive index of a medium (such as an atomic gas) increases with the wavelength of transmitted light. When a light pulse – which is comprised of a group of light waves at a number of different wavelengths – passes through such a medium, its group velocity can be boosted to beyond the velocity of its constituent waves. However, the energy of the pulse still travels at the speed of light, which means that information is transferred in agreement with Einstein's theory.

Now, astrophysicists claim to have witnessed this phenomenon in radio pulses that have travelled from a distant pulsar.

Modified pulses

The discovery has been made at the University of Texas at Brownsville, where Frederick Jenet and colleagues have been monitoring a pulsar – a rapidly spinning neutron star – more than 10,000 light years away. As pulsars spin, they emit a rotating beam of radiation that flashes past distant observers at regular intervals like a lighthouse. Because the pulses are modified as they travel through the interstellar medium, astrophysicists can use them to probe the nature of the cosmos.

Several factors are known to affect the pulses. Neutral hydrogen can absorb them, free electrons can scatter them and an additional magnetic field can rotate their polarization. Plasma in the interstellar medium also causes dispersion, which means pulses with longer wavelengths are affected by a smaller refractive index.

Timing is off

Jenet's group thinks that anomalous dispersion should be added to this list. Using the Arecibo Observatory in Puerto Rico, they took radio data of the pulsar PSR B1937+21 at 1420.4 MHz with a 1.5 MHz bandwidth for three days. Oddly, those pulses close to the centre value arrived earlier than would be expected given the pulsar's normal timing, and therefore appeared to have travelled faster than the speed of light.

The cause of the anomalous dispersion for these pulses, according to the Brownsville astrophysicists, is the resonance of neutral hydrogen, which lies at 1420.4 MHz. But like anomalous dispersion seen in the lab, the pulsar's superluminal pulses do not violate causality or relativity because, technically, no information is carried in the pulse. Still, Jenet and colleagues believe that the phenomenon could be used to pick out the properties of clouds of neutral hydrogen in our galaxy.

'Solid result'

"It seems to be very interesting indeed...a solid and rather nice result," says Michael Kramer, an astrophysicist at the University of Manchester who was not involved with the study.

Andrew Lyne, a pulsar astrophysicist who is also based at Manchester, thinks it is an "interesting, if not unexpected result". However, he has doubts that it could help in the understanding of neutral-hydrogen clouds because there are often several clouds in the same line of sight. "It is not clear from the paper quite what extra information will be obtained," he adds.

The research will be published in the Astrophysical Journal. A preprint is available at arXiv:0909.2445v2.

Simulation of Dirac equation

This is an experimental work [1] on mimicking the motion of a particle that is subject to Dirac-type model. It managed to detect a quivering motion, the so-called Zitterbewegung, which is understood to arise from the interference between positive energy components and negative energy components. Such quivering occurs at very high frequency (ten powered to 21 Hz) and with very tiny amplitude (of the order of Compton wavelength) for electrons in vacuum, and very difficult to observe. In this work, the authors considered the Dirac equation in 1+1 dimensions, which was realized with a single trapped ion. For such a 'relativistic' ion, the oscillation period is couple of microseconds.

Experimental recipes:
(1)trap a single 40Ca1 ion in a linear Paul trap22 with axial trapping frequency vax52p31.36MHz and radial trapping frequency vrad52p33 MHz;
(2)prepare the ion in the axial motional ground
state and in the internal state jS1/2,mJ51/2æ (mJ, magnetic quantum
number).
(3)identify spinor states.

How to measure the average position of the trapped ion without a full reconstruction of the state:
To measure the position for a motional state rm, we have to
(1) prepare the ion’s internal state in an eigenstate of sy,
(2) apply a unitary transformation, U(t), that maps information about rm onto the internal states;
(3) record the changing excitation as a function of the probe time t, by measuring
fluorescence22.

Results are displayed on the figures.


[1]Vol 463|7 January 2010| doi:10.1038/nature08688

LHC, a grand oddyssy

With its successful test run at the end of 2009, the Large Hadron Collider near Geneva seized the world record for the highest-energy particle collisions created by mankind. We can now reflect on the next questions: What will it discover, and why should we care?

Despite all we have learned in physics -- from properties of faraway galaxies to the deep internal structure of the protons and neutrons that make up an atomic nucleus -- we still face vexing mysteries. The collider is poised to begin to unravel them. By colliding protons at ultra-high energies and allowing scientists to observe the outcome in its mammoth detectors, the LHC could open new frontiers in understanding space and time, the microstructure of matter and the laws of nature.

We know, for example, that all the types of matter we see, that constitute our ordinary existence, are a mere fraction -- 20% -- of the matter in the universe. The remaining 80% apparently is mysterious "dark matter"; though it is all around us, its existence is inferred only via its gravitational pull on visible matter. LHC collisions might produce dark-matter particles so we can study their properties directly and thereby unveil a totally new face of the universe.

The collider might also shed light on the more predominant "dark energy," which is causing the universe's expansion to accelerate. If the acceleration continues, the ultimate fate of the universe may be very, very cold, with all particles flying away from one another to infinite distances.

More widely anticipated is the discovery of the Higgs particle -- sometimes inaptly called the God particle -- whose existence is postulated to explain why some matter has mass. Were it not for the Higgs, or something like it, the electrons in our bodies would behave like light beams, shooting into space, and we would not exist.

If the Higgs is not discovered, its replacement may involve something as profound as another layer of substructure to matter. It might be that the most elementary known particles, like the quarks that make up a proton, are made from tinier things. This would be revolutionary -- like discovering the substructure of the atom, but at a deeper level.

More profound still, the LHC may reveal extra dimensions of space, beyond the three that we see. The existence of a completely new type of dimension -- what is called "supersymmetry" -- means that all known particles have partner particles with related properties.Supersymmetry could be discovered by the LHC producing these "superpartners," which would make characteristic splashes in its detectors.Superpartners may also make up dark matter -- and two great discoveries would be made at once.

Or, the LHC may find evidence for extra dimensions of a more ordinary type, like those that we see -- still a major revolution. If these extra dimensions exist, they must be wound up into a small size, which would explain in part why we can't see or feel them directly. The LHC detectors might find evidence of particles related to the ones we know but shooting off into these dimensions.

Even more intriguing, if these extra dimensions are configured in certain ways, the LHC could produce microscopic black holes. As first realized by Stephen Hawking, basic principles of quantum physics tell us that such black holes evaporate in about a billionth of a billionth of a billionth of a second -- in a spectacular spray of particles that would be visible to LHC detectors.

This would let us directly probe the deep mystery of reconciling two conflicting pillars of 20th century physics: Einstein's theory of general relativity and quantum mechanics. This conflict produces a paradox -- related to the riddle of what happens to stuff that falls into a black hole -- whose resolution may involve ideas more mind-bending than those of quantum mechanics or relativity.

Other possible discoveries include new forces of nature, similar to electric or magnetic forces. Any of these discoveries would represent a revolution in physics, though one that had been already considered. We may also discover something utterly new and unexpected -- perhaps the most exciting possibility of all. Even not discovering anything is important -- it would tell us where phenomena we know must exist are not to be found.

Such talk of new phenomena has worried some -- might ultra-high-energy particle collisions be dangerous? The simple answer is no. Though it will be very novel to produce these conditions in a laboratory, where they can be carefully studied, nature is performing similar experiments all the time, above our heads. Cosmic ray protons with energies over a million times those at the LHC regularly strike the protons in our atmosphere, and in other cosmic bodies, without calamity. Also, there are significant indications that nature performed such experiments early in the universe, near the Big Bang, without untoward consequences. Physicists have carefully investigated these concerns on multiple occasions.

All this may seem like impractical and esoteric knowledge. But modern society would be unrecognizable without discoveries in fundamental physics. Radio and TV, X-rays, CT scans, MRIs, PCs, iPhones, the GPS system, the Web and beyond -- much that we take for granted would not exist without this type of physics research and was not predicted when the first discoveries were made. Likewise, we cannot predict what future discoveries will lead to, whether new energy sources, means of space travel or communication, or amazing things entirely unimagined.

The cost of this research may appear high -- about $10 billion for the LHC -- but it amounts to less than a ten-thousandth of the gross domestic product of the U.S. or Europe over the approximately 10 years it has taken to build the collider. This is a tiny investment when one accounts for the continuing value of such research to society.

But beyond practical considerations, we should ponder what the value of the LHC could be to the human race. If it performs as anticipated, it will be the cutting edge for years to come in a quest that dates to the ancient Greeks and beyond -- to understand what our world is made of, how it came to be and what will become of it. This grand odyssey gives us a chance to rise above the mundane aspects of our lives, and our differences, conflicts and crises, and try to understand where we, as a species, fit in a wondrous universe that seems beyond comprehension, yet is remarkably comprehensible.

Steve Giddings is a physics professor at UC Santa Barbara and an expert in high-energy and gravitational physics. He coauthored the first papers predicting that black hole production could be an important effect at the LHC and describing certain extradimensional scenarios that the LHC might explore.