Physics Research

J. Lowensohn, B. Oyarzun, G. Narvaez Paliza, B. M. Mognetti, W. B. Rogers
arXiv, (2019) https://arxiv.org/abs/1902.08883
The possibility of prescribing local interactions between nano- and microscopic components that direct them to assemble in a predictable fashion is a central goal of nanotechnology research. In this article we advance a new paradigm in which self-assembly of DNA-functionalized colloidal particles is programmed using linker oligonucleotides dispersed in solution. We find a phase diagram that is surprisingly rich compared to phase diagrams typical of other DNA-functionalized colloidal particles that interact by direct hybridization, including a re-entrant melting transition upon increasing linker concentration, and show that multiple linker species can be combined together to prescribe many interactions simultaneously. A new theory predicts the observed phase behavior quantitatively without any fitting parameters. Taken together, these experiments and model lay the groundwork for future research in programmable self-assembly, enabling the possibility of programming the hundreds of specific interactions needed to assemble fully-addressable, mesoscopic structures, while also expanding our fundamental understanding of the unique phase behavior possible in colloidal suspensions.

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Poster presentation for Summer Science Research Program at Brandeis University
The use of DNA linkers in combination with colloidal suspensions brings along multiple advantages that direct-hybridization based micromaterials lack, and new characteristics such as a fluid phase re-entry when increasing the concentration of linkers past a threshold concentration. Linker-mediated systems provide a useful tool for the research of biological and synthetic self-assembly processes, as well as having important potential engineering applications.

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Written for the "Advanced Physics Laboratory" course at Brandeis University.
In the microscopic world, physical systems are significantly more sensitive to individual interactions than macroscopic ones. Microparticles tend to follow a diffusive motion rather than a ballistic motion, making it harder to predict the dynamics of a system. Here we explore the validity of using computer simulations to substitute real physical systems and predict their dynamical properties using mathematical and probabilistic tools. We explore flexible polymers in solution and particles undergoing Brownian motion in a one-dimensional medium and show that the systems can be safely approximated by numerical methods involving the generation of random numbers. We show that the anisotropy of flexible polymers’ shapes is mostly due to the random walk nature of the system and not due to intramolecular interactions or self-avoiding effects. We show that the Langevine equation can be used to predict the trajectory of a Brownian particle while ignoring the inertial term, and that a Monte Carlo algorithm can be used to describe more precisely and at a cheaper cost the properties of an equilibrated system.

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Written for the "Advanced Physics Laboratory" course at Brandeis University.
Magnetic materials can be found everywhere in our daily lives. However, we often think of magnetic materials to be any material that has some magnetization, i.e. a magnet. What we often do not consider is that magnetic materials can exist in two different phases, the ferromagnetic phase and the paramagnetic phase. The ferromagnetic phase is a consequence of the alignment of magnetic spins that generate a net magnetization, while the paramagnetic phase is a result of spins being randomly oriented, resulting in a zero magnetization due to the random nature of the spin configuration. Here we prove through computer simulations that the Ising model can be used to show the existence of the two magnetic phases. We show that in the one-dimensional Ising model there is no phase transition, while in the two-dimensional case there exists a transition around the critical temperature of 2.4 J/k_B.

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Written for the "Advanced Physics Laboratory" course at Brandeis University.
For many deterministic systems we can exploit the laws of Physics to make an accurate estimation of the system state. For example, we can determine the speed of a falling ball at a given moment if we know the initial conditions and the time at which it was released. However, some systems that are completely constrained to the laws of Physics, seem to be unpredictable. We call this systems chaotic. Chaotic systems appear random because the intrinsic uncertainty of the measurement of the initial conditions grows quickly, specifically as an exponential function. As time increases, the uncertainty becomes large and predictions innacurate. Here, we explore the non-linear, damped, driven pendulum, and explore the conditions under which the pendulum undergoes periodic, semiperiodic, and chaotic motion. We prove resonance and hysteresis in the driven pendulum and give several characterizations of motion that help us determine if a system is periodic or chaotic. Finally, we produce a bifurcation plot, which allows us to observe the phase transition of a system that goes back and forth, from periodic to chaotic.

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