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Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems./
作者:	Sarkar, Siddhartha.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	298 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Applied physics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28649149
ISBN:	9798460486540

Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems.
Sarkar, Siddhartha.

Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 298 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--Princeton University, 2021.

This item must not be sold to any third party vendors.

In recent years, we have seen exciting new developments in research on mechanical metamaterials, topological phononics, and mechanics of atomically thin 2D materials. In this thesis, I present how methods from physics can help us in understanding the mechanical properties of these systems as well as gaining further intuition. First, we develop a multipole expansion method to describe the deformation of infinite as well as finite solid structures with cylindrical holes and inclusions by borrowing concepts from electrostatics, such as induction and method of image charges. Our method shows excellent agreement with finite element simulations and experiments. Next, using representation theory, I show how symmetries of phononic crystals affect the degeneracies in their phononic band structures. Deformation of phononic crystals under external load that causes breaking of some symmetries can lead to the lifting of degeneracies for bands and creating gaps such that waves of certain frequencies become disallowed. Finally, using methods from statistical physics, I present how the mechanical properties of atomically thin 2D sheets and shells get modified due to thermal fluctuations. Freely suspended sheets subject to such fluctuations are much harder to bend, but easier to stretch, compress and shear, beyond a characteristic thermal length scale, which is on the order of nanometers for graphene at room temperatures. Just like in critical phenomena, these renormalized elastic constants become scale dependent with universal power-law exponents. In nanotubes, competition between stretching and bending costs associated with radial fluctuations introduces another characteristic elastic length scale, which is proportional to the geometric mean of the radius and effective thickness. Beyond this elastic length scale, bending rigidities and in-plane elastic constants of nanotubes become anisotropic.

ISBN: 9798460486540Subjects--Topical Terms:

3343996
Applied physics.
Subjects--Index Terms:

Elasticity

Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems.
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245 1 0 $a Multipoles, Symmetry Representations and Thermal Fluctuations in Elastic Systems.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 298 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Kosmrlj, Andrej.
502 $a Thesis (Ph.D.)--Princeton University, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a In recent years, we have seen exciting new developments in research on mechanical metamaterials, topological phononics, and mechanics of atomically thin 2D materials. In this thesis, I present how methods from physics can help us in understanding the mechanical properties of these systems as well as gaining further intuition. First, we develop a multipole expansion method to describe the deformation of infinite as well as finite solid structures with cylindrical holes and inclusions by borrowing concepts from electrostatics, such as induction and method of image charges. Our method shows excellent agreement with finite element simulations and experiments. Next, using representation theory, I show how symmetries of phononic crystals affect the degeneracies in their phononic band structures. Deformation of phononic crystals under external load that causes breaking of some symmetries can lead to the lifting of degeneracies for bands and creating gaps such that waves of certain frequencies become disallowed. Finally, using methods from statistical physics, I present how the mechanical properties of atomically thin 2D sheets and shells get modified due to thermal fluctuations. Freely suspended sheets subject to such fluctuations are much harder to bend, but easier to stretch, compress and shear, beyond a characteristic thermal length scale, which is on the order of nanometers for graphene at room temperatures. Just like in critical phenomena, these renormalized elastic constants become scale dependent with universal power-law exponents. In nanotubes, competition between stretching and bending costs associated with radial fluctuations introduces another characteristic elastic length scale, which is proportional to the geometric mean of the radius and effective thickness. Beyond this elastic length scale, bending rigidities and in-plane elastic constants of nanotubes become anisotropic.
590 $a School code: 0181.
650 4 $a Applied physics. $3 3343996
650 4 $a Statistical physics. $3 536281
650 4 $a Mechanical engineering. $3 649730
653 $a Elasticity
653 $a Soft condensed matter
653 $a Statistical mechanics
653 $a Topological mechanics
690 $a 0215
690 $a 0217
690 $a 0548
710 2 $a Princeton University. $b Electrical Engineering. $3 2095953
773 0 $t Dissertations Abstracts International $g 83-05B.
790 $a 0181
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28649149