Separation device

A newly proposed separation devices has come out (http://physics.aps.org/articles/v5/6).

Rubí and Peter Hänggi of the University of Augsburg, Germany, led a team that has developed a new approach to these ratchet sorters. They start with a mathematical framework in which the entropy of the system is treated like potential energy, with entropy “barriers” that repel particles. These are regions where particles are restricted to a small space, which reduces the number of states (locations and velocities) that a particle can occupy. Fewer states means lower entropy. Like balls rolling down a hill, particles tend to move away from these low entropy spots.

The team applies this formalism to a tube with walls that periodically ramp from a narrow diameter to a wide diameter and back, with an asymmetric or “sawtooth” profile. This shape forms distinct but still connected chambers, or segments, each of which is a few microns long. Entropic barriers inhibit travel between segments; however, the barriers are steeper going to the left, so the net motion of the particles is to the right.

In order to clearly see the entropic effect in their computer simulation and analytical calculations, the researchers apply an oscillating force that essentially shakes the particles back and forth inside the tube. In a real experiment, this force could be an oscillating electric field.

Vitrification vs. Crystalization

The most basic difference between the glass forming (vitrification) process and the crystallization may be seen in the figure on the left. Vitrification is actually not really a transition , because it does not involve any genuinely singular behaviors, in contrast with crystallization. A very likely implication is that, vitrification should not be due to a critical mode that features long-range correlations. Its dynamics should be essentially local, like what happens to a traffic congestion.

thermodynamic zeroth law

I like this brief synopsis: (some simple concepts: intensive and extensive variables)

A system in equilibrium is characterized by a few intensive parameters such as temperature and chemical potential. The zeroth law of thermodynamics implies that when two systems can exchange a conserved, extensive property (e.g., molecules), their intensive parameters (e.g., the chemical potentials) must eventually equalize.

Do such parameters exist for far-from-equilibrium systems? We know that intensive thermodynamic parameters can be defined for nonequilibrium stationary states in systems with short-range spatial correlations. To test whether this is possible in the presence of long-range correlations, often found in such stationary states, Punyabrata Pradhan and colleagues at the University of Stuttgart, Germany, writing in Physical Review E, analyze the driven lattice gas (DLG), a favorite “toy model” of nonequilibrium statistical mechanics, in which particles with short-range interactions hop around on a lattice.

Suppose a DLG, characterized by its size, interparticle interactions, and bias, is placed in contact with an equilibrium lattice gas. Eventually the particle densities of the two gases attain two different stationary values. Consider a second DLG, with different properties, that “equilibrates” via contact with a copy of the equilibrium lattice gas used in the first experiment. If stationary contact between the two systems can indeed be characterized by an intensive variable, we should expect no change in the respective particle densities of the two DLGs while in contact. Using Monte Carlo simulations, the authors verify that the densities, upon contact, indeed remain nearly unchanged, but that there are deviations from the zeroth law, which can be largely understood in terms of an excess chemical potential associated with the contact region. – Ron Dickman

Smectic Coexisting with nematic in cuprate

In the pseudogap phase of cuprate superconductors, incredibly rich and exotic things have been observed, among which are the checkerboard pattern that breaks the C4v symmetry within an unit cell and the stripes that break an additional translational symmetry. These are called electronic nematic and smectic phases, respectively. According to this study, there should be an interesting interplay between the two on cuprates, due to topological defects. The authors formalize the coupling in a gauge invariant way.

Coupling to the smectic fields can then occur either through phase or amplitude fluctuations of the smectic. Here, we focus on the former, which means that couples to local shifts of the wave vectors and . Replacing the gradient in the x direction by a covariant-derivative-like coupling gives(4)and similarly for the gradient in the y direction, to yield a GL term coupling the nematic to smectic states. The vector represents by how much the wave vector, , is shifted for a given fluctuation. Hence, we propose a GL functional (for modulations along ) based on symmetry principles and and being small:(5)where … refers to terms we can neglect for the present purpose (SOM d). If we were to replace by where is the electromagnetic vector potential, Eq. 5 becomes the GL free energy of a superconductor; its minimization in the long-distance limit yields and thus quantization of its associated magnetic flux (22, 23). Analogously, minimization of Eq. 5 implies surrounding each topological defect (SOM e). Here, the vector is proportional to and lies along the line where = 0. The resulting key prediction is that will vanish along the line in the direction of that passes through the core of the topological defect, with becoming greater on one side and less on the other (Fig. 4B). Additional coupling to the smectic amplitude can shift the location of the topological defect away from the line of = 0 (SOM e).

Heat Flow In Small Things

Heat flow is definitely a very interesting problem in physics and also other disciplines. Here is a review on the present status of understanding over this subject concerned with small dimensions.

Advances in the fabrication and characterization of nanoscale systems now allow for a better understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium recent advances are surveyed and an understanding of physical mechanisms of energy transport in nanostructures is presented, focusing mainly on molecular junctions and atomic wires. Basic issues are examined such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density
and temperature gradient—known as Fourier’s law. Both theoretical and experimental progress are critically reported in each of these issues and future research opportunities in the field are discussed. [REVIEW OF MODERN PHYSICS, VOLUME 83, JANUARY–MARCH 2011]

Metastable states are important in reality

Metastable states are common in nature: supercooled or superheated liquid are daily examples. These states are not the lowest-energy state, and, by thermodynamic principles, one should not expect them to be long-lived in nature. Indeed, they exist only under very stringent conditions, and very little disturbance can push the system off to a stable state around. Thermodynamically stable states dwell on one of the global minima of the free energy, around which, however, local minima might exist that are separated from the global minima by energy barriers. When a system has not reached the stable states, it will be constantly kicked by its surroundings and eventually transits from where it is in to a stable state after some period (the life of the metastable state). The interesting point is that, the life time can sometimes be very long and real transitions can hardly be seen, a situation similar to ergodicity breaking. For example, diamond has a higher energy than graphite, but it can exist for ever. The reason is because the time to make the transition is cosmologically long, due to the hugely high barrier. Another material is graphene, which should not be stable according to Wagner-Mermin-Honberg theorem. Yet, it was produced in 2004. Glasses are the third examples, in which case, transition has been frustrated by its structure. In the case of supercooled water, the transition is suppressed by distilling process.

Remarks on phase transitions

It is usually said that, phase transitions are associated with singular, non-analytic and discontinuous behaviors of physical functions such as the thermodynamic potential or other non-equilibrium ones. But this is so only for infinite systems, in which any small difference in energy density can be infinitely magnified due the infinity of volumn. In infinite systems, phase transitions are sharp and abrupt, and ergodicity is completely lost when certain state is selected under symmetry breaking. This means infinite life time of the selected state, and thus very sharp transition. For finite systems, which represent the reality, phase transitions are never as sharp as that in infinite systems, since in this case the life time, though long, but finite. Also, no genuine singularities exist. Only strong crossovers can be observed, provided sufficient resolution. A crucial feature of finite systems might be that, configurations with small energy density differences could have very strong mixing and fluctuations and may not be distinguishable for certain resolutions.

More on the pseudogap in cuprate

This article [http://www.nature.com/nphys/journal/v7/n4/full/nphys1921.html?WT.ec_id=NPHYS-201104#/affil-auth] definitely refreshes one's mind in thinking about the nature of the pseudogap of cuprates. The review is here [http://www.nature.com/nphys/journal/v7/n4/full/nphys1973.html?WT.ec_id=NPHYS-201104]. The authors measured the specific heat of UD YBCO under magnetic field. Oscillations were found above H* ~27T. But not only that, there is a background scaling as the square root of H.
What does this imply ?

Why does it grow in the observed way ?

Crystal growth has been all the time an intriguing but complicated problem. The macroscopic shape depends in a subtle way on several factors, such as the properties of the surroundings. Indebted to the increasing power of computers, physicists are enabled to simulate a real growth. On the other hand, experiments also provide important insights. "Despite the many parameters involved, theorists have predicted that icicles, as well as other natural features like stalactites, should all converge to the same shape as they grow. In a paper appearing in Physical Review E, Antony Chen and Stephen Morris at the University of Toronto, Canada, describe an experimental setup that allows them to image icicles as they grow under controlled conditions, and test these predictions. They mounted a camera through a slot in the side of a refrigerator, within which icicles formed as water dripped from a nozzle and onto a rotating wooden support. Rotating the support helps even out the effects of drafts and temperature gradients." [http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.026307]

Is this energy change possible ?

Mpemba Effect

Water is just mundane and seems well-understood in many respects. However, there are still quite a lot of things that motivate people to find more. For example, how water molecules arrange themselves when they adsorbed on an adsorbate. Another instance is, I think more associated with the thermodynamics of water: it has been claimed that, hot water cools faster than cold water when they are placed in the same chamber. This was named after its discoverer, a middle school student Mpemba. There came a latest study on this [http://arxiv.org/ftp/arxiv/papers/1101/1101.2684.pdf]:

In this paper we have presented data confirming that water initially at higher temperature cools at a faster rate than water initially at a lower temperature and that this trend continues past the point at which the two samples reach the same temperature: the crossover temperature. Furthermore, our data indicates that the starting temperature affects the crossover temperature in a reproducible manner. We have confirmed that warmer water indeed cools faster than colder water and that, surprisingly, this trend continues past the point where the temperatures of the two samples are the same. Our results show that when using optimal initial temperature conditions, the crossover temperature is found to be 2.7 oC whereas our other set of initial conditions gave a crossover temperature of -0.07 oC. These data taken together provide a definite quantitative evidence of the Mpemba effect.

Negative specific heat

It is usually thought that, specific heat of a thermodynamic system is positive, that is, energy must be invested to heat the system. How, these authors demonstrated that[1], such a common sense shall be violated if the system does not obey Boltzman statistics or goes out of equilibrium in the presence of long range interactions. They have considered a particular example to illustrate the statement.

[1]PRL 105, 010601 (2010)

Critical Casirmir effect

Sticky situations

Illustration: A. Gambassi et al., Phys. Rev. E (2009)

Critical Casimir effect in classical binary liquid mixtures

A. Gambassi, A. Maciołek, C. Hertlein, U. Nellen, L. Helden, C. Bechinger, and S. Dietrich

Phys. Rev. E 80, 061143 (Published December 31, 2009)

ShareThis Statistical Mechanics Soft Matter

When two conducting plates are brought in close proximity to one another, vacuum fluctuations in the electromagnetic field between them create a pressure. This effective force, known as the Casimir effect, has a thermodynamic analog: the “critical Casimir effect.” In this case, thermal fluctuations of a local order parameter (such as density) near a continuous phase transition can attract or repel nearby objects when they are in confinement.

In 2008, a team of scientists in Germany presented direct experimental evidence for the critical Casimir effect by measuring the femtonewton forces that develop between a colloidal sphere and a flat silica surface when both are immersed in a liquid near a critical point [1]. Now, writing in Physical Review E, Andrea Gambassi, now at SISSA in Trieste, Italy, and collaborators at the Max Planck Institute for Metals Research, the University of Stuttgart, and the Polish Academy of Sciences, follow up on this seminal experiment and present a comprehensive examination of their experimental results and theory for the critical Casimir effect.

Success in fabricating MEMS and NEMS (micro- and nanoelectromechanical systems) made it possible to explore facets of the quantum Casimir effect that had for many years only been theoretical curiosities. With the availability of tools to track and measure the minute forces between particles in suspension, scientists are able to do the same with the critical Casimir effect. In fact, it may be possible to tune this thermodynamically driven force in small-scale devices so it offsets the attractive (and potentially damaging) force associated with the quantum Casimir effect. Given its detail, Gambassi et al.’s paper may well become standard reading in this emerging field. – Jessica Thomas

[1] C. Hertlein et al., Nature 451, 172 (2008).