Mechanisms of kinetic trapping in self-assembly and phase transformation

In self-assembly processes, kinetic trapping effects often hinder the formation of thermodynamically stable ordered states. In a model of viral capsid assembly and in the phase transformation of a lattice gas, we show how simulations in a self-assembling steady state can be used to identify two distinct mechanisms of kinetic trapping. We argue that one of these mechanisms can be adequately captured by kinetic rate equations, while the other involves a breakdown of theories that rely on cluster size as a reaction coordinate. We discuss how these observations might be useful in designing and optimising self-assembly reactions

Hybrid Method for Digits Recognition using Fixed-Frame Scores and Derived Pitch

This paper presents a procedure of frame normalization based on the traditional dynamic time warping (DTW) using the LPC coefficients. The redefined method is called as the DTW frame-fixing method (DTW-FF), it works by normalizing the word frames of the input against the reference frames. The enthusiasm to this study is due to neural network limitation that entails a fix number of input nodes for when processing multiple inputs in parallel. Due to this problem, this research is initiated to reduce the amount of computation and complexity in a neural network by reducing the number of inputs into the network. In this study, dynamic warping process is used, in which local distance scores of the warping path are fixed and collected so that their scores are of equal number of frames. Also studied in this paper is the consideration of pitch as a contributing feature to the speech recognition. Results showed a good performance and improvement when using pitch along with DTW-FF feature. The convergence rate between using the steepest gradient descent is also compared to another method namely conjugate gradient method. Convergence rate is also improved when conjugate gradient method is introduced in the back-propagation algorithm

Reduction and reconstruction of stochastic differential equations via symmetries

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance

When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant \u until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $\rho$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(\rho)$ causes phase separation in dimensions $d=2,3$, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of \u-dependent motilities

Spatially Resolved Mapping of Local Polarization Dynamics in an Ergodic Phase of Ferroelectric Relaxor

Spatial variability of polarization relaxation kinetics in relaxor ferroelectric 0.9Pb(Mg1/3Nb2/3)O3-0.1PbTiO3 is studied using time-resolved Piezoresponse Force Microscopy. Local relaxation attributed to the reorientation of polar nanoregions is shown to follow stretched exponential dependence, exp(-(t/tau)^beta), with beta~~0.4, much larger than the macroscopic value determined from dielectric spectra (beta~~0.09). The spatial inhomogeneity of relaxation time distributions with the presence of 100-200 nm "fast" and "slow" regions is observed. The results are analyzed to map the Vogel-Fulcher temperatures on the nanoscale.Comment: 23 pages, 4 figures, supplementary materials attached; to be submitted to Phys. Rev. Let

Peak Forecasting for Battery-based Energy Optimizations in Campus Microgrids

Battery-based energy storage has emerged as an enabling technology for a variety of grid energy optimizations, such as peak shaving and cost arbitrage. A key component of battery-driven peak shaving optimizations is peak forecasting, which predicts the hours of the day that see the greatest demand. While there has been significant prior work on load forecasting, we argue that the problem of predicting periods where the demand peaks for individual consumers or micro-grids is more challenging than forecasting load at a grid scale. We propose a new model for peak forecasting, based on deep learning, that predicts the k hours of each day with the highest and lowest demand. We evaluate our approach using a two year trace from a real micro-grid of 156 buildings and show that it outperforms the state of the art load forecasting techniques adapted for peak predictions by 11-32%. When used for battery-based peak shaving, our model yields annual savings of $496,320 for a 4 MWhr battery for this micro-grid.Comment: 5 pages. 4 figures, This paper will appear in the Proceedings of ACM International Conference on Future Energy Systems (e-Energy'20), June 202

Interaction of Vortices in Complex Vector Field and Stability of a ``Vortex Molecule''

We consider interaction of vortices in the vector complex Ginzburg--Landau equation (CVGLE). In the limit of small field coupling, it is found analytically that the interaction between well-separated defects in two different fields is long-range, in contrast to interaction between defects in the same field which falls off exponentially. In a certain region of parameters of CVGLE, we find stable rotating bound states of two defects -- a ``vortex molecule".Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let