Development of Two-dimensional Stark Spectroscopy for the Investigation of Photosynthetic Charge Separation

Charge transfer reactions are critical for the efficient function of photosynthetic enzymes. With growing energy demand, understanding the design principles of natural photosynthetic systems is important to aid efforts in developing sustainable energy sources that do not add to the carbon-dioxide burden of the atmosphere. Photosystem II is particularly interesting because it is an ideal model for artificial photovoltaic devices for energy applications: it is efficient, stabilizes the energized state for useful times, and is resilient to photo-damage. Despite decades of study, the mechanism of primary charge separation in this system is still under debate, primarily because the charge-transfer intermediates involved in these reactions do not have strong spectral signatures and are extremely short-lived. I have developed a novel spectroscopy method called two-dimensional electronic Stark spectroscopy (2DESS) for the study of fast processes involving the movement of charge in photosynthetic proteins. It combines the high sensitivity of Stark spectroscopy to charge-transfer reactions and the high temporal and spectral resolution of two-dimensional electronic spectroscopy. In collaboration with Darius Abramavicius at Vilnius University in Lithuania, I simulated a charge-transfer dimer system similar to the ``special-pair" chlorophylls found in PSII RC thought to be involved in the primary charge-separation process in this system. Based on these simulations, I demonstrated that the 2DESS and Stark spectra for CT states in the PSII do not follow typical Liptay models. There is also evidence to suspect that the parameters used to model the PSII is incorrect. I then demonstrated the experimental technique on an organic polymer often used for photovoltaic applications, observing first-derivative lineshapes consistent with predictions. Following this demonstration, I observed spectral signatures consistent with charge-separation of the PSII RC. Work is underway to extend the simulations to a more complete model system, as well as utilize the experimentally-obtained data to verify proposed models of charge-separation in the PSII RC. In combination with other spectroscopy techniques, 2DESS will allow us to obtain a complete description of the initial charge-separation kinetics in photosystem II and may suggest ways to mimic its extraordinary efficiency. We expect this technique to be applicable to other systems such as organic photovoltaics, in which the role of CT states is unclear or is hard to trace.PHDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138760/1/aloukian_1.pd

Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood estimation procedure of the parameters of the environment. Unlike most of the classical maximum likelihood approach, the limit of the criterion function is in general a nondegenerate random variable and convergence does not hold in probability. Not only the leading term but also the second order asymptotics is needed to fully identify the unknown parameter. We present different frameworks to illustrate these facts. We also explore the numerical performance of our estimation procedure

Uniform deterministic equivalent of additive functionals and non-parametric drift estimation for one-dimensional recurrent diffusions

Usually the problem of drift estimation for a diffusion process is considered under the hypothesis of ergodicity. It is less often considered under the hypothesis of null-recurrence, simply because there are fewer limit theorems and existing ones do not apply to the whole null-recurrent class. The aim of this paper is to provide some limit theorems for additive functionals and martingales of a general (ergodic or null) recurrent diffusion which would allow us to have a somewhat unified approach to the problem of non-parametric kernel drift estimation in the one-dimensional recurrent case. As a particular example we obtain the rate of convergence of the Nadaraya--Watson estimator in the case of a locally H\"{o}lder-continuous drift.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP141 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Spectral gaps and exponential integrability of hitting times for linear diffusions

Let X be a regular continuous positively recurrent Markov process with state space R, scale function S and speed measure m. For a ∈ R denote B+a = sup x≥a m(]x,+∞[)(S(x) − S(a)) B−a = sup x≤a m(]−∞;x[)(S(a) − S(x)) It is well known that the finiteness of B±a is equivalent to the existence of spectral gaps of generators associated with X. We show how these quantities appear independently in the study of the exponential moments of hitting times of X. Then we establish a very direct relation between exponential moments and spectral gaps, all by improving their classical bounds

A Sampled-data Regulator using Sliding Modes and Exponential Holder for Linear Systems

In a general command tracking and disturbance rejection problem, it is known that a sampled-data controller using zero-order hold may only guarantee asymptotic tracking at the sampling instances, but in general cannot guarantee the absence of ripples between the sampling instants. In this paper, a discrete robust regulator and a sampled-data robust regulator using slide modes techniques and exponential holder are presented. In particular, it is shown that the controller proposed for the sampled-data system ensures asymptotic tracking when applied to the continuous-time system