Our latest paper on optically-controlled active media

My colleagues and I just published a paper in Nature Photonics entitled "Superdiffusion in Optically Controlled Active Media." You may access the paper via this link to Nature Photonics or read about it in UCF Today.

I should point out that the claims made in the article in UCF Today is a bit over-reaching. What we have done is demonstrated that the coupling between light and particles in suspension models nonequilibrium processes that share some characteristics with similar processes inside cells. This is because the colloidal particles exchange energy randomly with their thermal bath (the water) and with the laser's radiation.

Importantly, the nature of the light-matter coupling is random due to multiple scattering by the particles, which establishes a three dimensional speckle inside the suspension.  This speckle exerts random forces on the particles which adds an additional component to their motion, besides that of Brownian motion. The resulting effect is that the particles move superdiffusively for times that are shorter than the decorrelation time of the speckle (which was about 1 millisecond).

Besides serving as a model system, I think it may be interesting to explore its ability to control some types of reaction kinetics. If reactants in solutions are driven apart from one another before they have a chance to react, then this would present a mechanical way of slowing the reaction of the bulk solution.

If you can access the article, then I hope you enjoy it!

Important equations and numbers to memorize

Many students in science and engineering today claim that the need to memorize certain numbers or equations is outdated with the advent of the internet and the ease with which we may find information. As an undergraduate, I often heard my engineering colleagues complain when they were not offered an equation sheet for a test because real-world engineers don't have to look up "well-known" equations when solving problems.

However, I contend that there are advantages to memorizing a few important equations and numbers. These reasons include the following:

1. You may work faster since you will not need to constantly reference those equations.
2. You may mentally check your work to ensure that the numbers are correct.
3. You may mentally approximate the solutions to certain calculations if you don't have access to reference material. I remember reading once how Feynman would challenge mathematicians by approximating powers of numbers in his head by knowing the natural logarithms of 2 and 10.
4. You may impress the ladies with your abilities (not guaranteed).

So what are some equations and constants I've found useful throughout the years? Here is my list:

1. The binomial expansion
2. The Taylor expansion
3. The power series representation of e 
4. The speed of light in vacuum and the impedance of free space (about 377 Ohms)
5. The refractive index of common glass (~1.5) and water (~1.33)
6. Boltzmann's constant and the thermal energy at 300 K (4.14 Joules) and thermal voltage at 300 K 0.026 eV)

Other important things to memorize, depending on your field, include:

1. Stirling's approximation
2. The Krebs cycle (a biologist once told me that many ideas in molecular biology come back to this)

Consider these as tools in your toolbox. They can make your job a lot easier.

Addendum: Not memorizing the basics is a mistake to avoid in physics according to this Back Page of APS News.

Working around distractions

I've been trying a method for enhancing my productivity during the day. Why am I doing this? Well, I want to maintain a healthy work-life balance; if I get more done at work, I have more time to spend with my fiancee, workout, cook, read, etc. This is incredibly difficult in academia, where there is no limit to the work that can be done. However, I value my personal life as well as my professional one, so a balance must be found.

My approach is simple and is inspired by the No Meat Athlete and Zen Habits blogs. I first make a list of things that need to be done. It can be large or small; it doesn't matter. I then work on one thing on the list and only open programs and browser tabs that directly relate to this task. That's the most important part. Multitasking, I've decided, is the bane of productivity.

If I see an interesting paper, I use Instapaper to save it for later. If I have too many e-mails or unread items, I go through and delete the ones that were once relevant but no longer are. The goal is to reduce the noise and possibilities to be distracted while working. This also includes choosing not to listen to music if I am writing anything or doing something that requires more than passive attention.

Of course, I also account for when I can not avoid being distracted. I allow time to be interrupted (and I will be numerous times) during the day by my colleagues and adviser. I also set time limits that are proportional to the magnitude of the task. If I have lab work, I give myself an hour minimum and two hour maximum; conversely, computer work is usually delegated 15 minutes to an hour. By setting upper time limits, I allow myself to be satisfied with unfinished work, knowing that when I pick it up again I will have a fresher mind. And by setting lower time limits, I ensure that I have enough time to accomplish something meaningful. Once an item on the list is done, I remove it. If it's not done, it stays.

This may be a bit too much micromanaging for some, but with the amount of things that are required of one in academia, I think it's necessary.

I believe that Henri Poincaré had habits similar to these. His goal, in part, was to maximize his creativity. I think this was so because he believed that a creative mind must be allowed to wander around different tasks. In this way, he recruited his subconscious to work on problems while he consciously worked on others.

CREOL Seminar - Becoming a Faculty Member

Today Dr. Mercedeh Khajavikhan gave a brief seminar to the CREOL students about her experiences with finding a job in academia. Though I'd already heard a lot of the information she presented, some points stuck out.

The following are a few notes I made during the talk. Keep in mind that they are her ideas that I've paraphrased (so if I misinterpreted them, then I'm sorry :)

• Considering that a post-doc position is a time to build your CV and publish, a post-doc offering research problems that can easily turn into publications within a year or two would be highly desirable.
• Apply to schools where there is not much overlap between your research and that of the existing faculty. This will minimize competition for valuable resources and money within your own department.
• Related to the point above, consider emphasizing how your strengths can help other faculty while applying. This will make you appear more valuable to the committee considering you for a job.
• Letters of reference are invaluable in the job search. (I need to work on building relationships with more faculty members!)

Astronomical crowdsourcing

I just read a short piece in this month's issue of Nature Physics about a number of astronomical discoveries made this past month. One exciting discovery was of a Neptune-sized exoplanet found in a complicated orbit around four stars about 5000 light years away. I find this absolutely amazing, and even more so considering that it was found by a crowdsourcing website called PlanetHunters.org that recruits public users in identifying transits from a large database of astronomical data.

This is one example of data-centric science, but it is slightly different from the way I've presented it in past posts. In particular, this is an observation that was not driven by some unanswered question. Rather, people were simply looking at data to find planets.

I think that this is really cool, but I do wonder why somebody hasn't written some code to do the data analysis.

The Effective Temperature as a Description for Non-equilibrium Systems

Cugliandolo wrote a survey last year of recent work involving the effective temperature. This is a macroscopic quantity that characterizes a system driven out of equilibrium. The review states that the effective temperature was initially used as an intuitive description of glassy and slowly relaxing systems, but only recently have theoreticians placed it on firmer ground by linking it to the fluctuation-dissipation theorem (FDT).

In practice, the effective temperature is the negative inverse slope of a system's dc susceptibility (a.k.a. its time-integrated impulse response) vs. the time-correlation function of some observable (a.k.a. the description of its thermal fluctuations). Importantly, a departure from the straight line joining the points (1,0) and (0, 1/temperature) on a properly normalized plot may signify a system that is not at equilibrium with its bath. In the paper, Cugliandolo assumes a canonical ensemble, or a system coupled to an equilibriated thermal bath. Also, because it is based on the FDT, this treatment is only valid for extremely small perturbations to the system such that an impulse response is an appropriate description.

Most recent work has been focused on determining whether the effective temperature meets our intuitive requirements for a temperature, like being measurable by a thermometer, and whether it is an appropriate thermodynamic description, i.e. it is a single number that summarizes the state of a large ensemble of random system parts. It seems that very slow relaxations, either forced or natural, must be present for this quantity to be useful.

What is nonequilibrium thermodynamics?

An important topic in thermodynamics and statistical mechanics is the description of systems that are not in equilibrium. It is important because most systems are not in thermodynamic equilibrium and routinely exchange energy and matter with their surroundings. Somewhat surprisingly, the equilibrium thermodynamics of pioneers such as Boltzmann, Gibbs, and Carnot has sufficed for many years, in part, I think, because of its success at guiding the design of heat engines and describing chemical reactions. A theoretical description of nonequilibrium systems, though, still remains a challenge and active area of research.

So what is a nonequilibrium thermodynamic system? I am seeking an intuitive answer, not the unenlightened, yet all-too-common statement "a system that is not in equilibrium."

Unfortunately I cannot find the answer in any one place. I've read several research articles, particularly on active matter, which provide about zero insight to the question. This is probably because journal articles typically assume some familiarity with a topic. Wikipedia's page on nonequilibrium thermodynamics, which I linked to above, seems to provide a good answer in the form of a long description. However, I usually run into problems when trying to identify what about a particular system drives it out of equilibrium or why classical thermodynamics fails to describe the system. For example, on the Wikipedia page noted above under basic concepts, a system between two thermostats at different temperatures is described as a nonequilibrium system, even though basic heat engines from (equilibrium) thermodynamics texts are modeled in this way.

I suspect that a general definition of a nonequilibrium system is elusive because we usually must appeal to specialized statements about the system at hand, such as what spatial and temporal scales we are interested in, and whether the system is in a steady state.

My intuitive understandings about nonequilibrium steady states are given below:

1. Thermal, pressure, or particle density gradients are present, resulting in fluxes.
2. The behavior of the system changes with spatial and temporal scales.
3. There are many ways to drive a system out of equilibrium, so general descriptions must include the nature of the driving processes.
4. Macroscopic properties are not easily defined. Microscopic properties, however, appear easier to describe.

Addendum
The link about nonequilibrium steady states contains one important quality about these systems: work must continuously be performed on a system to maintain its state.

Finding similar ideas in other fields - ecology and thermodynamics of complex systems

I very much like to find connections between ideas in different fields. The Wikipedia page on Ecology contains the following quote:

System behaviors must first be arrayed into levels of organization. Behaviors corresponding to higher levels occur at slow rates. Conversely, lower organizational levels exhibit rapid rates. For example, individual tree leaves respond rapidly to momentary changes in light intensity, CO₂ concentration, and the like. The growth of the tree responds more slowly and integrates these short-term changes.
O'Neill, et al., A Hierarchical Concept of Ecosystems, Princeton University Press, p. 253 (1986).

This is not much unlike the microscopic and macroscopic descriptions of a material system. Small-scale fluctuations in the microscopic arrangement of a material often don't significantly impact the macroscopic qualities of this system [1]. Rather, many small-scale changes must occur in concert to cause a large-scale change. For example, the momenta and positions of various gas molecules in a container at equilibrium with its surroundings may change about some average, but the pressure of the gas on the container's walls will not. If the average molecular speed changes, though, pressure will likely change as well.

In addition, if the interaction between the microscopic constituents is nonlinear, it becomes much more likely that small changes in the microscopic description will result in macroscopic changes as well.

Notes
[1] In fact, most fluctuations are dissipated by the system. If the system is in equilibrium with its environment, then energy conservation, among other things, implies that a fluctuation away from equilibrium of a local volume inside a system will eventually be "smoothed out" by the system. This is an important property of complex systems known as the fluctuation-dissipation theorem.