Quenched topological boundary modes can persist in a trivial system

Topological boundary modes can occur at the spatial interface between a topological and gapped trivial phase and exhibit a wavefunction that exponentially decays in the gap. Here we argue that this intuition fails for a temporal boundary between a prequench topological phase that possess topological boundary eigenstates and a postquench gapped trivial phase that does not possess any eigenstates in its gap. In particular, we find that characteristics of states (e.g., probability density) prepared in a topologically non-trivial system can persist long after it is quenched into a gapped trivial phase with spatial profiles that appear frozen over long times postquench. After this near-stationary window, topological boundary mode profiles decay albeit, slowly in a power-law fashion. This behavior highlights the unusual features of nonequilibrium protocols enabling quenches to extend and control localized states of both topological and non-topological origins.

Two dimensional nearly de Sitter gravity

We study some aspects of the de Sitter version of Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, we have a boundary mode when we compute observables with a fixed dilaton and metric at the boundary. We compute the no-boundary wavefunctions and probability measures to all orders in perturbation theory. We also discuss contributions from different topologies, borrowing recent results by Saad, Shenker and Stanford. We discuss how the boundary mode leads to gravitational corrections to cosmological observables when we add matter. Finally, starting from a four dimensional gravity theory with a positive cosmological constant, we consider a nearly extremal black hole and argue that some observables are dominated by the two dimensional nearly de Sitter gravity dynamics.

Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation

Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.

Boundary mode lubrication of articular cartilage with a biomimetic diblock copolymer

We report the design of a diblock copolymer with architecture and function inspired by the lubricating glycoprotein lubricin. This diblock copolymer, synthesized by sequential reversible addition–fragmentation chain-transfer polymerization, consists of a cationic cartilage-binding domain and a brush-lubricating domain. It reduces the coefficient of friction of articular cartilage under boundary mode conditions (0.088 ± 0.039) to a level equivalent to that provided by lubricin (0.093 ± 0.011). Additionally, both the EC50 (0.404 mg/mL) and cartilage-binding time constant (7.19 min) of the polymer are comparable to purified human and recombinant lubricin. Like lubricin, the tribological properties of this polymer are dependent on molecular architecture. When the same monomer composition was evaluated either as an AB diblock copolymer or as a random copolymer, the diblock effectively lubricated cartilage under boundary mode conditions whereas the random copolymer did not. Additionally, the individual polymer blocks did not lubricate independently, and lubrication could be competitively inhibited with an excess of binding domain. This diblock copolymer is an example of a synthetic polymer with lubrication properties equal to lubricin under boundary mode conditions, suggesting its potential utility as a therapy for joint pathologies like osteoarthritis.

Basic and Quasi Structures of Step-Up Switched Based dc/dc Converter: Steady-State Analysis and Design in Different Operating Modes

In this paper, basic step-up switched dc/dc converters and its quasi structures are proposed. In dc/dc converters, the operation of the converters can be changed by changing the values of the elements and other parameters such as duty cycle, so the complete analysis of the basic step-up switched dc/dc converter (SSC) in different operating modes is presented. It is shown that, SSC has three different operating modes, which include synchronous operation of diodes (SOD), asynchronous operation of diodes (AOD), and boundary mode (BM). These operating modes are related to the diodes ON and OFF time. Critical inductors are calculated in BM and their values are investigated under various conditions. Inductors current ripple and the output voltage ripple are also calculated. The precise power losses analysis and small signal (SS) analysis for SSC are presented. The high voltage gain quasi structures are introduced and all of the proposed structures are compared with conventional structures. Finally, in order to verify the accuracy of the claims, the experimental results are presented.