Non-Euclidean surface growth

Last updated

In the field of surface growth, there are growth processes that result in the surface of an object changing shape over time. As the object grows, its surface may change from flat to curved, or change curvature. Two points on the surface may also change in distance as a result of deformations of the object or accretion of new matter onto the object. The shape of the surface and its changes can be described in terms of non-Euclidean geometry and in particular, Riemannian geometry with a space- and time-dependent curvature. [1] [2]

Examples of non-Euclidean surface growth are found in the mechanics of growing gravitational bodies, [3] [4] [5] [6] [7] [8] propagating fronts of phase transitions, [9] epitaxial growth of nanostructures and additive 3D printing, [10] growth of plants, [11] , and cell motility [12]

Related Research Articles

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state.

Solid mechanics is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist both shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

Quantum 1/f noise is an intrinsic and fundamental part of quantum mechanics. Fighter pilots, photographers, and scientists all appreciate the higher quality of images and signals resulting from the consideration of quantum 1/f noise. Engineers have battled unwanted 1/f noise since 1925, giving it poetic names due to its mysterious nature. The Quantum 1/f noise theory was developed about 50 years later, describing the nature of 1/f noise, allowing it to be explained and calculated via straightforward engineering formulas. It allows for the low-noise optimization of materials, devices and systems of most high-technology applications of modern industry and science. The theory includes the conventional and coherent quantum 1/f effects (Q1/fE). Both effects are combined in a general engineering formula, and present in Q1/f noise, which is itself most of fundamental 1/f noise. The latter is defined as the result of the simultaneous presence of nonlinearity and a certain type of homogeneity in a system, and can be quantum or classical.

<span class="mw-page-title-main">Attosecond physics</span> Study of physics on quintillionth-second timescales

Attosecond physics, also known as attophysics, or more generally attosecond science, is a branch of physics that deals with light-matter interaction phenomena wherein attosecond photon pulses are used to unravel dynamical processes in matter with unprecedented time resolution.

Hysteresivity derives from “hysteresis”, meaning “lag”. It is the tendency to react slowly to an outside force, or to not return completely to its original state. Whereas the area within a hysteresis loop represents energy dissipated to heat and is an extensive quantity with units of energy, the hysteresivity represents the fraction of the elastic energy that is lost to heat, and is an intensive property that is dimensionless.

Jozef T. Devreese was a Belgian scientist, with a long career in condensed matter physics. He was professor emeritus of theoretical physics at the University of Antwerp. He died on November 1, 2023.

<span class="mw-page-title-main">Shear band</span>

A shear band is a narrow zone of intense shearing strain, usually of plastic nature, developing during severe deformation of ductile materials. As an example, a soil specimen is shown in Fig. 1, after an axialsymmetric compression test. Initially the sample was cylindrical in shape and, since symmetry was tried to be preserved during the test, the cylindrical shape was maintained for a while during the test and the deformation was homogeneous, but at extreme loading two X-shaped shear bands had formed and the subsequent deformation was strongly localized.

<span class="mw-page-title-main">Marvin L. Cohen</span> American physicist

Marvin Lou Cohen is an American–Canadian theoretical physicist. He is a physics professor at the University of California, Berkeley. Cohen is a leading expert in the field of condensed matter physics. He is widely known for his seminal work on the electronic structure of solids.

Pseudoelasticity, sometimes called superelasticity, is an elastic (reversible) response to an applied stress, caused by a phase transformation between the austenitic and martensitic phases of a crystal. It is exhibited in shape-memory alloys.

Emmanuel I. Rashba is a Soviet-American theoretical physicist of Jewish origin who worked in Ukraine, Russia and in the United States. Rashba is known for his contributions to different areas of condensed matter physics and spintronics, especially the Rashba effect in spin physics, and also for the prediction of electric dipole spin resonance (EDSR), that was widely investigated and became a regular tool for operating electron spins in nanostructures, phase transitions in spin-orbit coupled systems driven by change of the Fermi surface topology, Giant oscillator strength of impurity excitons, and coexistence of free and self-trapped excitons. The principal subject of spintronics is all-electric operation of electron spins, and EDSR was the first phenomenon predicted and experimentally observed in this field.

<span class="mw-page-title-main">Oreste Piro</span> Argentine biophysicist

Oreste Piro is a dynamical systems theorist and biophysicist. He is at the Universitat de les Illes Balears (UIB) in Palma de Mallorca.

Giulio Casati is Emeritus Professor of Theoretical Physics at University of Insubria. Casati is known for his work on chaos, both classical and quantum, being considered one of the pioneers of the latter. Casati is in fact principally known for the discovery of quantum dynamical localization phenomenon, that highlighted the relevance of chaos in quantum mechanics. His landmark paper, with Boris Chirikov, Joseph Ford and Felix Izrailev, is among the most quoted in the field. With Boris Chirikov, Italo Guarneri and Dima Shepelyansky Casati also discovered that quantum localization deeply affects the excitation of hydrogen atom in strong monochromatic fields. Further major contributions considered the connections between quantization of non integrable systems and the statistical theory of spectra. With the advent of quantum computing Casati and his coworkers studied the efficient quantum computing of complex dynamics. On the classical side, Casati's interests regarded mostly energy conduction in non-linear lattices: from the earliest numerical proof of the validity of Fourier law in one-dimensional many body systems, obtained in collaboration with Bill Wisscher, Franco Vivaldi, and Joseph Ford, to the description of a thermal rectifier and of a thermal transistor. The same techniques lead to the theoretical demonstration of a one-way mirror for light

<span class="mw-page-title-main">John F. Brady (chemical engineer)</span> American chemical engineer and professor

John Francis Brady is an American chemical engineer and the Chevron Professor of Chemical Engineering and Mechanical Engineering at the California Institute of Technology. He is a fluid mechanician and creator of the Stokesian dynamics method for simulating suspensions of spheres and ellipsoids in low Reynolds number flows. He is an elected fellow of the American Physical Society, a fellow of the Society of Rheology, as well as a member of the National Academy of Sciences, the National Academy of Engineering, and the American Academy of Arts and Sciences.

Surajit Sen is a physicist who works on theoretical and computational problems in non-equilibrium statistical physics and in nonlinear dynamics of many body systems. He holds a Ph.D in physics from The University of Georgia (1990) where he studied with M. Howard Lee. He is also interested in applying physics to study problems of relevance in a societal context. He is a professor of physics at the State University of New York, Buffalo. Much of Sen's recent work can be found in his RUSA lecture at Bharatidasan University.

<span class="mw-page-title-main">Vladimir Dubrovskii</span>

Vladimir G. Dubrovskii is the head of Laboratory of physics of nanostructures at St. Petersburg Academic University, a leading research scientist at Ioffe Institute, and a professor at St. Petersburg State University and ITMO University.

<span class="mw-page-title-main">Fiber network mechanics</span>

Fiber network mechanics is a subject within physics and mechanics that deals with the deformation of networks made by the connection of slender fibers,. Fiber networks are used to model the mechanics of fibrous materials such as biopolymer networks and paper products. Depending on the mechanical behavior of individual filaments, the networks may be composed of mechanical elements such as Hookean springs, Euler-Bernoulli beams, and worm-like chains. The field of fiber network mechanics is closely related to the mechanical analysis of frame structures, granular materials, critical phenomena, and lattice dynamics.

<span class="mw-page-title-main">Alain Goriely</span> Belgian mathematician

Alain Goriely is a Belgian mathematician, currently holding the statutory professorship (chair) of mathematical modelling at the University of Oxford, Mathematical Institute. He is director of the Oxford Centre for Industrial Mathematics (OCIAM), of the International Brain and Mechanics Lab (IBMTL) and Professorial Fellow at St Catherine's College, Oxford. At the Mathematical Institute, he was the director of external relations and public engagement, from 2013 until 2022, initiating the Oxford Mathematics series of public lectures. In 2022, he was elected to the Royal Society., and Gresham Professor of Geometry at the Gresham College (London) in 2024.

<span class="mw-page-title-main">Slip bands in metals</span> Deformation mechanism in crystallines

Slip bands or stretcher-strain marks are localized bands of plastic deformation in metals experiencing stresses. Formation of slip bands indicates a concentrated unidirectional slip on certain planes causing a stress concentration. Typically, slip bands induce surface steps and a stress concentration which can be a crack nucleation site. Slip bands extend until impinged by a boundary, and the generated stress from dislocations pile-up against that boundary will either stop or transmit the operating slip depending on its (mis)orientation.

Valery I Levitas is a Ukrainian mechanics and material scientist, academic and author. He is an Anson Marston Distinguished Professor and Murray Harpole Chair in Engineering at Iowa State University and was a faculty scientist at the Ames National Laboratory.

References

  1. Truskinovsky, Lev; Zurlo, Giuseppe (2019-05-03). "Nonlinear elasticity of incompatible surface growth". Physical Review E. 99 (5). American Physical Society (APS): 053001. arXiv: 1901.06182 . doi:10.1103/physreve.99.053001. ISSN   2470-0045.
  2. Zurlo, Giuseppe; Truskinovsky, Lev (2017-07-26). "Printing Non-Euclidean Solids". Phys. Rev. Lett. 119 (4). American Physical Society (APS): 048001. arXiv: 1703.03082 . doi:10.1103/PhysRevLett.119.048001. ISSN   2470-0045.
  3. E. I. Rashba, Construction sequence dependent stresses in massive bodies due to their weight, Proc. Inst. Struct. Mech. Acad. Sci. Ukrainian SSR 18, 23 (1953).
  4. Brown, C. B.; Goodman, L. E. (1963-12-17). "Gravitational stresses in accreted bodies". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 276 (1367). The Royal Society: 571–576. doi:10.1098/rspa.1963.0227. ISSN   2053-9169.
  5. V. E. Naumov, Mechanics of growing deformable solids: A review, J. Eng. Mech. 120, 207 (1994).
  6. J. G. Bentler and J. F. Labuz, Performance of a Cantilever retaining wall, J. Geotech. Geoenviron. Eng. 132, 1062 (2006).
  7. Bacigalupo, Andrea; Gambarotta, Luigi (2012). "Effects of Layered Accretion on the Mechanics of Masonry Structures". Mechanics Based Design of Structures and Machines. 40 (2). Informa UK Limited: 163–184. doi:10.1080/15397734.2011.628622. ISSN   1539-7734.
  8. S. A. Lychev, Geometric aspects of the theory of incompatible deformations in growing solids, in Mechanics for Materials and Technologies, ed. by H. Altenbach, R. Goldstein, and E.Murashkin, Advanced Structured Materials, 46 (Springer, New York, 2017).
  9. Wildeman, Sander; Sterl, Sebastian; Sun, Chao; Lohse, Detlef (2017-02-23). "Fast Dynamics of Water Droplets Freezing from the Outside In". Physical Review Letters. 118 (8). American Physical Society (APS): 084101. arXiv: 1701.06818 . doi:10.1103/physrevlett.118.084101. ISSN   0031-9007.
  10. Ge, Qi; Sakhaei, Amir Hosein; Lee, Howon; Dunn, Conner K.; Fang, Nicholas X.; Dunn, Martin L. (2016-08-08). "Multimaterial 4D Printing with Tailorable Shape Memory Polymers". Scientific Reports. 6 (1). Springer Science and Business Media LLC: 31110. doi: 10.1038/srep31110 . ISSN   2045-2322. PMC   4976324 .
  11. R. R. Archer, Growth Stresses and Strains in Trees, Springer Series in Wood Science (Springer-Verlag, Berlin, 1987)
  12. Dafalias, Yannis F.; Pitouras, Zacharias (2007-12-06). "Stress field in actin gel growing on spherical substrate". Biomechanics and Modeling in Mechanobiology. 8 (1). Springer Science and Business Media LLC: 9–24. doi:10.1007/s10237-007-0113-y. ISSN   1617-7959.

Further reading