Locating topological phase transitions using nonequilibrium signatures in local bulk observables

Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work however, we show that signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest themselves as non-analyticities in their expectation values taken over a family of non-equilibrium states generated using a quantum quench protocol. The signature can be used for precisely locating the critical points in parameter space. A large class of initial states can be chosen for the quench (including finite temperature states), the sufficient condition being existence of a finite occupation-gradient with respect to energy for the single-particle critical mode. We demonstrate these results in tractable models of non-interacting fermions exhibiting topological phase transitions in one and two spatial dimensions. We also show that the non-analyticities can be absent if the gap-closing is non-topological, i.e., when it corresponds to no phase transition.Comment: 4.5 pages, 5 figures + supplementary material, version published in Phys. Rev. B as a Rapid Communicatio

Mathematical models and analysis for demand side management in residential electricity distribution networks.

Development of smart grids along with communication technologies have led to the increased attention and adoption of demand side management (DSM) in the residential sector. Among various DSM schemes, demand response (DR) is a market- based mechanism to shave peak electricity consumption at the system level. In the past decade, the academia has seen a growing literature studying load management methodologies for residential consumers. A typical demand response program has three important facets: the energy cost, comfort of the consumers and overall system efficiency. In this dissertation, we investigate and develop models for effective load control to minimize energy cost and for understanding electricity consumer behavior so as to best design DR schemes. Participation in a real-world field demonstration not only stimulated our motivation for these studies, but also provided us with real- world data to validate the developed models and analyses. This in fact makes the dissertation distinct from current academic literature. We first develop a control algorithm for Heating Ventilation Air-Conditioning (HVAC) systems in households during a peak period. The dynamic programming based model can determine the optimal temperature set-points of a thermostat given the lower and upper limits of temperature that household feels comfortable and the desired duration of the control. The temperature limits act as a quantitative metric for the comfort level of consumers. The objective is to minimize the energy consumption. The model is particularly suitable for DR programs with critical peak pricing, in which a higher electricity rate occurs during the peak period. When deployed separately during the peak and adjoining two periods, the model can keep the inside temperature within the given limits while consuming minimal energy during the peak period. This ensures that the HVAC system would have minimal usage during the peak period as the temperature is kept within the limits. In addition, we show that alternative start and end times of the control algorithm can be tested for each home. Analyses of the alternative options provide us with information about the insulation of the building. We perform computational experiments with real-world data to show the efficacy of the proposed methodology. Second, we propose a mixed-integer linear fractional programming (MILFP) model to optimally deploy the dynamic programming based HVAC controllers among a pool of homes in a staggered fashion. Doing so, the model aims to flatten the demand curve over time thus maximizing the load factor for the entire distribution network. In addition, we develop a reformulation of the MILFP model into an MILP model which significantly reduces computational time for medium-scale instances. Furthermore, for large-scale instances, excessive computational times by general purpose solvers motivate us to develop a customized bi-section search algorithm. Our extensive computational experiments conclude that the customized algorithm is able to solve real-world as well as randomly generated instances in reasonable CPU times. In another effort, we study the behavior of consumers when subject to dynamic pricing under a DR program. We model the price-responsive behavior with utility functions and develop a bi-level programming model to estimate the coefficients of such a function utilizing consumption data from advanced metering infrastructure (AMI) from the field demonstration project mentioned previously. The upper level objective is to minimize the estimation error between the measured data and the optimum consumption while the lower level is for each household/consumer to maximize their total utility of energy consumption. We propose a trust-region algorithm to solve the non-linear bi-level utility estimation (BLUE) model after employing linear and quadratic approximation for the upper and lower level objective function, respectively. A mathematical property of the optimal solution is exploited to develop a cut that has significantly improved the computational time. Numerical experiments with real world data are conducted to validate the proposed models. In addition, we show the strong positive correlation between the utility coefficients and the widely used price elasticity property. Finally, this dissertation also presents several empirical models to assess the effect of smart technologies on electricity consumption under a demand charge dynamic pricing rate. The models developed here were being utilized in the aforementioned demand response pilot study. We present a statistical test based model to estimate the change of coincident load of residential consumers with the installation of efficient appliances including heat pump water heaters, smart thermostats, and battery storage units. The method utilizes a day matching algorithm to pair days with similar weather conditions. The consumption data from the two paired up days are used to conduct a paired t-test to evaluate the statistical significance of the changes. The results reveal that insulation plays an important role in energy savings along with battery systems

Oscillating Shells and Oscillating Balls in AdS

It has recently been reported that certain thin timelike shells undergo oscillatory motion in AdS. In this paper, we compute two-point function of a probe field in the geodesic approximation in such an oscillating shell background. We confirm that the two-point function exhibits an oscillatory behaviour following the motion of the shell. We show that similar oscillatory dynamics is possible when the perfect fluid on the shell has a polytropic equation of state. Moreover, we show that certain ball like configurations in AdS also exhibit oscillatory motion and comment on how such a solution can be smoothly matched to an appropriate exterior solution. We also demonstrate that the weak energy condition is satisfied for these oscillatory configurations.Comment: 23 pages, 5 figures; v2: refs added; v3: JHEP versio

Multifractality without fine-tuning in a Floquet quasiperiodic chain

Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of $critical$ wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.Comment: 22 pages, 13 figures, SciPost submissio

Velocity Field around a Rigid Flapping Wing with a Winglet in Quiescent Water

This study investigated the effect of a winglet on the velocity field around a rigid flapping wing. Two-dimensional particle image velocimetry was used to capture the velocity field of asymmetric one-degree-of-freedom flapping motion. A comparison was conducted between wings with and without a winglet at two flapping frequencies, namely 1.5 and 2.0 Hz. The effect of the winglet on the velocity field was determined by systematically comparing the velocity fields for several wing phase angles during the downstroke and upstroke. The presence of a winglet considerably affected the flow field around the wingtip, residual flow, and added mass interaction. The added mass was lower and residual flow was weaker for the wings with a winglet than for the wings without a winglet. The added mass and velocity magnitudes of the flow field increased proportionally with the flapping frequency

An Algebraic System for Constructing Cryptographic Permutations over Finite Fields

In this paper we identify polynomial dynamical systems over finite fields as the central component of almost all iterative block cipher design strategies over finite fields. We propose a generalized triangular polynomial dynamical system (GTDS), and give a generic algebraic definition of iterative (keyed) permutation using GTDS. Our GTDS-based generic definition is able to describe widely used and well-known design strategies such as substitution permutation network (SPN), Feistel network and their variants among others. We show that the Lai-Massey design strategy for (keyed) permutations is also described by the GTDS. Our generic algebraic definition of iterative permutation is particularly useful for instantiating and systematically studying block ciphers and hash functions over $\mathbb{F}_p$ aimed for multiparty computation and zero-knowledge based cryptographic protocols. Finally, we provide the discrepancy analysis a technique used to measure the (pseudo-)randomness of a sequence, for analyzing the randomness of the sequence generated by the generic permutation or block cipher described by GTDS