A number of processes of surface growth in areas ranging from mechanics of growing gravitational bodies [1] [2] [3] [4] [5] [6] through propagating fronts of phase transitions, [7] epitaxial growth of nanostructures and 3D printing, [8] growth of plants, [9] and cell mobility [10] require non-Euclidean description because of incompatibility of boundary conditions and different mechanisms of developing stresses at interfaces. Indeed, these mechanisms result in the curving of initially flat elements of the body and changing separation between different elements of it (especially in the soft matter). Gradual accumulation of deformations under the influx of accumulating mass results in the memory-conscious grows of the body and makes strains the subject of long-range forces. As a result of all above factors, generic non-Euclidean growth is described in terms of Riemannian geometry with a space- and time-dependent curvature. [11] [12]
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.
Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially, it is called a shear crack, slip band or dislocation.
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.
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 the 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.
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.
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.
Harry L. Swinney is an American physicist noted for his contributions to the field of nonlinear dynamics.
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.
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces and frictional stresses acting tangentially between the surfaces. Normal contact mechanics or frictionless contact mechanics focuses on normal stresses caused by applied normal forces and by the adhesion present on surfaces in close contact, even if they are clean and dry. Frictional contact mechanics emphasizes the effect of friction forces.
Picosecond ultrasonics is a type of ultrasonics that uses ultra-high frequency ultrasound generated by ultrashort light pulses. It is a non-destructive technique in which picosecond acoustic pulses penetrate into thin films or nanostructures to reveal internal features such as film thickness as well as cracks, delaminations and voids. It can also be used to probe liquids. The technique is also referred to as picosecond laser ultrasonics or laser picosecond acoustics.
In statistical mechanics, the metastate is a probability measure on the space of all thermodynamic states for a system with quenched randomness. The term metastate, in this context, was first used in by Charles M. Newman and Daniel L. Stein in 1996..
Oreste Piro is a dynamical systems theorist and biophysicist. He is at the Universitat de les Illes Balears (UIB) in Palma de Mallorca.
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.
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.
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.
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.
F. Sozio, M.F. Shojaei, S. Sadik, and A. Yavari, Nonlinear mechanics of thermoelastic accretion, \emph{Zeitschrift f\"ur Angewandte Mathematik und Physik (ZAMP)} \textbf{71}(3), 2020, 87.
F. Sozio and A. Yavari, Nonlinear mechanics of accretion, \emph{Journal of Nonlinear Science} \textbf{29}(4), 2019, 1813-1863.
F. Sozio and A. Yavari, Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies, \emph{Journal of the Mechanics and Physics of Solids} \textbf{98}, 2017, pp. 12-48.