We consider the escape of particles located in the middle well of a symmetric triple well potential driven sinusoidally by two forces such that the potential wells roll as in stochastic resonance and the height of the potential barrier oscillates symmetrically about a mean as in resonant activation. It has been shown that depending on their phase difference the application of these two synchronized signals may lead to a splitting of time averaged Kramers escape rate and a preferential product distribution in a parallel chemical reaction in the steady state.
A correlation between two noise processes driving the thermally activated particles in a symmetric triple well potential, may cause a symmetry breaking and a difference in relative stability of the two side wells with respect to the middle one. This
leads to an asymmetric localization of population and splitting of Kramers rate of escape from the middle well, ensuring a preferential distribution of the products in the course of a parallel reaction.
This paper proposes SplitSGD, a new dynamic learning rate schedule for stochastic optimization. This method decreases the learning rate for better adaptation to the local geometry of the objective function whenever a stationary phase is detected, tha
t is, the iterates are likely to bounce at around a vicinity of a local minimum. The detection is performed by splitting the single thread into two and using the inner product of the gradients from the two threads as a measure of stationarity. Owing to this simple yet provably valid stationarity detection, SplitSGD is easy-to-implement and essentially does not incur additional computational cost than standard SGD. Through a series of extensive experiments, we show that this method is appropriate for both convex problems and training (non-convex) neural networks, with performance compared favorably to other stochastic optimization methods. Importantly, this method is observed to be very robust with a set of default parameters for a wide range of problems and, moreover, yields better generalization performance than other adaptive gradient methods such as Adam.
Cross sections for the 90,92,94Zr(p,n) reactions were measured at energies of 79.2 and 119.4 MeV. A phenomenological model was developed to describe the variation with bombarding energy of the position of the L=1 peak observed in these and other (p,n
) reactions. The model yields the splitting between the giant dipole and giant spin dipole resonances. Values of these splittings are obtained for isotopes of Zr and Sn and for 208Pb.
We introduce an asymmetric classical Ginzburg-Landau model in a bounded interval, and study its dynamical behavior when perturbed by weak spatiotemporal noise. The Kramers escape rate from a locally stable state is computed as a function of the inter
val length. An asymptotically sharp second-order phase transition in activation behavior, with corresponding critical behavior of the rate prefactor, occurs at a critical length l_c, similar to what is observed in symmetric models. The weak-noise exit time asymptotics, to both leading and subdominant orders, are analyzed at all interval lengthscales. The divergence of the prefactor as the critical length is approached is discussed in terms of a crossover from non-Arrhenius to Arrhenius behavior as noise intensity decreases. More general models without symmetry are observed to display similar behavior, suggesting that the presence of a ``phase transition in escape behavior is a robust and widespread phenomenon.
The current state of the art in direct water splitting in photo-electrochemical cells (PECs) is presented together with: (i) a case study of water splitting using a simple solar cell with the most efficient water splitting electrodes and (ii) a detai
led mechanism analysis. Detailed analysis of the energy balance and efficiency of solar hydrogen production are presented. The role of hydrogen peroxide formation as an intermediate in oxygen evolution reaction is newly revealed and explains why an oxygen evolution is not taking place at the thermodynamically expected 1.23 V potential. Solar hydrogen production with electrical-to-hydrogen conversion efficiency of 52% is demonstrated using a simple ~0.7%-efficient n-Si/Ni Schottky solar cell connected to a water electrolysis cell. This case study shows that separation of the processes of solar harvesting and electrolysis avoids photo-electrode corrosion and utilizes optimal electrodes for hydrogen and oxygen evolution reactions and achieves ~10% efficiency in light-to-hydrogen conversion with a standard 18% efficient household roof Si-solar cells.
Pulak Kumar Ghosh
,Bidhan Chandra Bag
,Deb Shankar Ray
.
(2012)
.
"Interference of stochastic resonances: Splitting of Kramers rate"
.
Pulak Kumar Ghosh Dr.
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