Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

New achievements in the realm of nanoscience and innovative techniques of nanomedicine have moved micro/nanoparticles (MNPs) to the point of becoming actually useful for practical applications in the near future. Various differences between the extracellular and intracellular environments of cancerous and normal cells and the particular characteristics of tumors such as physicochemical properties, neovasculature, elasticity, surface electrical charge, and pH have motivated the design and fabrication of inventive “smart” MNPs for stimulus-responsive controlled drug release. These novel MNPs can be tailored to be responsive to pH variations, redox potential, enzymatic activation, thermal gradients, magnetic fields, light, and ultrasound (US), or can even be responsive to dual or multi-combinations of different stimuli. This unparalleled capability has increased their importance as site-specific controlled drug delivery systems (DDSs) and has encouraged their rapid development in recent years. An in-depth understanding of the underlying mechanisms of these DDS approaches is expected to further contribute to this groundbreaking field of nanomedicine. Smart nanocarriers in the form of MNPs that can be triggered by internal or external stimulus are summarized and discussed in the present review, including pH-sensitive peptides and polymers, redox-responsive micelles and nanogels, thermo- or magnetic-responsive nanoparticles (NPs), mechanical- or electrical-responsive MNPs, light or ultrasound-sensitive particles, and multi-responsive MNPs including dual stimuli-sensitive nanosheets of graphene. This review highlights the recent advances of smart MNPs categorized according to their activation stimulus (physical, chemical, or biological) and looks forward to future pharmaceutical applications.

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Smart micro/nanoparticles in stimulus-responsive drug/gene delivery systems

Within a time span of 15 years, acoustic metamaterials have emerged from academic curiosity to become an active field driven by scientific discoveries and diverse application potentials. This review traces the development of acoustic metamaterials from the initial findings of mass density and bulk modulus frequency dispersions in locally resonant structures to the diverse functionalities afforded by the perspective of negative constitutive parameter values, and their implications for acoustic wave behaviors. We survey the more recent developments, which include compact phase manipulation structures, superabsorption, and actively controllable metamaterials as well as the new directions on acoustic wave transport in moving fluid, elastic, and mechanical metamaterials, graphene-inspired metamaterials, and structures whose characteristics are best delineated by non-Hermitian Hamiltonians. Many of the novel acoustic metamaterial structures have transcended the original definition of metamaterials as arising from the collective manifestations of constituent resonating units, but they continue to extend wave manipulation functionalities beyond those found in nature.

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Acoustic metamaterials: From local resonances to broad horizons.

http://ieeexplore.ieee.org/iel5/5/31047/01444179.pdf

Fundamentals of acoustics

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.

Exceptional topology of non-Hermitian systems

In this study, we show that robust and tunable acoustic asymmetric transmission can be achieved through gradient-index metasurfaces by harnessing judiciously tailored losses. We theoretically prove that the asymmetric wave behavior stems from loss-induced suppression of high order diffraction. We further experimentally demonstrate this novel phenomenon. Our findings could provide new routes to broaden applications for lossy acoustic metamaterials and metasurfaces.

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Tunable Asymmetric Transmission via Lossy Acoustic Metasurfaces.

In this letter, a class of honeycomb acoustic metamaterial possessing lightweight and yet sound-proof properties is designed, theoretically proven, and then experimentally verified. It is here reported that the proposed metamaterial having a remarkably small mass per unit area at 1.3 kg/m2 can achieve low frequency (<500 Hz) sound transmission loss (STL) consistently greater than 45 dB. Furthermore, the sandwich panel which incorporates the honeycomb metamaterial as the core material yields a STL that is consistently greater than 50 dB at low frequencies. The proposed metamaterial is promising for constructing structures that are simultaneously strong, lightweight, and sound-proof.

A lightweight yet sound-proof honeycomb acoustic metamaterial

This Letter reports on the experimental observation of a topologically protected edge state and exceptional point in an open and non-Hermitian (lossy) acoustic system. Although the theoretical underpinning is generic to wave physics, the simulations and experiments are performed for an acoustic system. It has nontrivial topological properties that can be characterized by the Chern number provided that a synthetic dimension is introduced. Unidirectional reflectionless propagation, a hallmark of exceptional points, is unambiguously observed in both simulations and experiments.

Simultaneous Observation of a Topological Edge State and Exceptional Point in an Open and Non-Hermitian Acoustic System

Medical techniques such as transcranial ultrasound beam focusing suffer from energy losses and distorted acoustic fields. Researchers show how metamaterials can be used to enhance acoustic transmission.

https://link.aps.org/pdf/10.1103/PhysRevX.4.041033

Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers

We present a design of acoustic metasurfaces yielding asymmetric transmission within a certain frequency band. The design consists of a layer of gradient-index metasurface and a layer of low refractive index metasurface. Incident waves are controlled in a wave vector dependent manner to create strong asymmetric transmission. Numerical simulations show that the approach provides high transmission contrast between the two incident directions within the designed frequency band. This is further verified by experiments. Compared to previous designs, the proposed approach yields a compact and planar device. Our design may find applications in various scenarios such as noise control and therapeutic ultrasound.

Yun Jing

Papers

Tunable Asymmetric Transmission via Lossy Acoustic Metasurfaces.

A lightweight yet sound-proof honeycomb acoustic metamaterial

Simultaneous Observation of a Topological Edge State and Exceptional Point in an Open and Non-Hermitian Acoustic System

Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers

Asymmetric acoustic transmission through near-zero-index and gradient-index metasurfaces