In recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, nonperturbative quantum theory for Lorentzian gravitational field on four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete at fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory.In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of kinematical Ashtekar-IshamLewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background independent quantum gauge theories. There is no divergence within this background independent and diffeomorphism invariant quantization programme of matter coupled to gravity.
In this paper, the effects of long-term storage in compressed cold
hibernated elastic memory (CHEM) polyurethane foam, a kind of shape memory
polymer, are investigated experimentally. The foams were pre-strained at a
high temperature, which was above the glass transition temperature, to 80%
and 93.4%, respectively, and then cooled back to room temperature. After
various periods of cold hibernation (up to two months), they were heated up at
fixed length or against different constant loads. It is found that: (1) the
maximum stress that the foam could exert at fixed length depends heavily on
the amount of pre-strain; (2) expansion rates of 380 and 1273% from the
hibernated size against a 1 N load (pre-strained by 80 and 93.4%,
respectively) are achievable. However, upon further increases in load, the
expansion is reduced dramatically. It appears that the tested CHEM
polyurethane foam retains its shape memory properties even after being stored
in a compacted state for a long period. Complete strain recovery is attainable
for a hibernation period of up to two months.
Abstract. Shape memory materials are featured by their ability to recover their original shapes when a particular stimulus, such as heat, light, magnetic field, even moisture/water, etc. is applied. However, it is not an easy task for non-professionals to synthesize a shape memory material which can meet all the requirements of a particular application. Even for professionals, like materials researchers, it could involve tedious trial and error procedures. In this paper, the concept of water-responsive shape memory hybrid is proposed and the advantages are demonstrated by two examples. The hybrid concept is versatile and can be easily accessed by those even without much polymer/chemistry background. Moreover, the performance of such hybrids can be well-predicted. This concept can be further extended into solvent-responsive shape memory hybrids, which can be routinely designed and realized in a Do-It-Yourself manner by almost anyone.
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