Explore the vast range of titles available.

The concept of mass is one of the most fundamental notions in physics, comparable in importance only to those of space and time. But in contrast to the latter, which are the subject of innumerable physical and philosophical studies, the concept of mass has been but rarely investigated. Here Max Jammer, a leading philosopher and historian of physics, provides a concise but comprehensive, coherent, and self-contained study of the concept of mass as it is defined, interpreted, and applied in contemporary physics and as it is critically examined in the modern philosophy of science. With its focus on theories proposed after the mid-1950s, the book is the first of its kind, covering the most recent experimental and theoretical investigations into the nature of mass and its role in modern physics, from the realm of elementary particles to the cosmology of galaxies. The book begins with an analysis of the persistent difficulties of defining inertial mass in a noncircular manner and discusses the related question of whether mass is an observational or a theoretical concept. It then studies the notion of mass in special relativity and the delicate problem of whether the relativistic rest mass is the only legitimate notion of mass and whether it is identical with the classical (Newtonian) mass. This is followed by a critical analysis of the different derivations of the famous mass-energy relationship E = mc2 and its conflicting interpretations. Jammer then devotes a chapter to the distinction between inertial and gravitational mass and to the various versions of the so-called equivalence principle with which Newton initiated his Principia but which also became the starting point of Einstein's general relativity, which supersedes Newtonian physics. The book concludes with a presentation of recently proposed global and local dynamical theories of the origin and nature of mass. Destined to become a much-consulted reference for philosophers and physicists, this book is also written for the nonprofessional general reader interested in the foundations of physics.

Earthquake and Volcano Deformationis the first textbook to present the mechanical models of earthquake and volcanic processes, emphasizing earth-surface deformations that can be compared with observations from Global Positioning System (GPS) receivers, Interferometric Radar (InSAR), and borehole strain- and tiltmeters. Paul Segall provides the physical and mathematical fundamentals for the models used to interpret deformation measurements near active faults and volcanic centers. Segall highlights analytical methods of continuum mechanics applied to problems of active crustal deformation. Topics include elastic dislocation theory in homogeneous and layered half-spaces, crack models of faults and planar intrusions, elastic fields due to pressurized spherical and ellipsoidal magma chambers, time-dependent deformation resulting from faulting in an elastic layer overlying a viscoelastic half-space and related earthquake cycle models, poroelastic effects due to faulting and magma chamber inflation in a fluid-saturated crust, and the effects of gravity on deformation. He also explains changes in the gravitational field due to faulting and magmatic intrusion, effects of irregular surface topography and earth curvature, and modern concepts in rate- and state-dependent fault friction. This textbook presents sample calculations and compares model predictions against field data from seismic and volcanic settings from around the world. Earthquake and Volcano Deformationrequires working knowledge of stress and strain, and advanced calculus. It is appropriate for advanced undergraduates and graduate students in geophysics, geology, and engineering. Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide.

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non-conservative microscopic interactions. These active moduli enter the antisymmetric (or odd) part of the static elastic modulus tensor and quantify the amount of work extracted along quasistatic strain cycles. In two-dimensional isotropic media, two chiral odd-elastic moduli emerge in addition to the bulk and shear moduli. We discuss microscopic realizations that include networks of Hookean springs augmented with active transverse forces and non-reciprocal active hinges. Using coarse-grained microscopic models, numerical simulations and continuum equations, we uncover phenomena ranging from auxetic behaviour induced by odd moduli to elastic wave propagation in overdamped media enabled by self-sustained active strain cycles. Our work sheds light on the non-Hermitian mechanics of two- and three-dimensional active solids that conserve linear momentum but exhibit a non-reciprocal linear response. Active, non-conservative interactions can give rise to elastic moduli that are forbidden in equilibrium and enter the antisymmetric part of the stiffness tensor. The resulting solids function as distributed elastic engines that can perform work on their surroundings through quasistatic strain cycles.

Human brain wrinkling has been implicated in neurodevelopmental disorders and yet its origins remain unknown. Polymer gel models suggest that wrinkling emerges spontaneously due to compression forces arising during differential swelling, but these ideas have not been tested in a living system. Here, we report the appearance of surface wrinkles during the in vitro development and self-organization of human brain organoids in a microfabricated compartment that supports in situ imaging over a timescale of weeks. We observe the emergence of convolutions at a critical cell density and maximal nuclear strain, which are indicative of a mechanical instability. We identify two opposing forces contributing to differential growth: cytoskeletal contraction at the organoid core and cell-cycle-dependent nuclear expansion at the organoid perimeter. The wrinkling wavelength exhibits linear scaling with tissue thickness, consistent with balanced bending and stretching energies. Lissencephalic (smooth brain) organoids display reduced convolutions, modified scaling and a reduced elastic modulus. Although the mechanism here does not include the neuronal migration seen in vivo, it models the physics of the folding brain remarkably well. Our on-chip approach offers a means for studying the emergent properties of organoid development, with implications for the embryonic human brain.

Sr2RuO4 has stood as the leading candidate for a spin-triplet superconductor for 26 years1. However, recent NMR experiments have cast doubt on this candidacy2,3 and it is difficult to find a theory of superconductivity that is consistent with all experiments. The order parameter symmetry for this material therefore remains an open question. Symmetry-based experiments are needed that can rule out broad classes of possible superconducting order parameters. Here, we use resonant ultrasound spectroscopy to measure the entire symmetry-resolved elastic tensor of Sr2RuO4 through the superconducting transition. We observe a thermodynamic discontinuity in the shear elastic modulus c66, which implies that the superconducting order parameter has two components. A two-component p-wave order parameter, such as px + ipy, naturally satisfies this requirement. As this order parameter appears to have been precluded by recent NMR experiments, we suggest that two other two-component order parameters, namely {dxz,dyz} and {dx2−y2,gxy(x2−y2)}, are now the prime candidates for the order parameter of Sr2RuO4.Ultrasound measurements show that the superconducting order parameter in strontium ruthenate must have two components.

A bstract We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on the Mandelstam representation of the amplitude and iterations of unitarity. The input for the iterative procedure is given by the multi-particle double spectral density, the S-wave inelasticity, and the value of the amplitude at the crossing-symmetric point. The output, obtained at the fixed point of the iteration of unitarity, is a nonperturbative scattering amplitude. The amplitudes we obtain exhibit interesting features, such as non-zero particle production, intricate high-energy and near the two-particle threshold behavior. Scattering amplitudes obtained by initializing the iteration process with zero (or small) multi-particle input end up close to saturating the S-matrix bounds derived by other methods. There is a version of the iterative algorithm that is directly related to Feynman diagrams: it effectively re-sums infinitely many two-particle reducible planar Feynman graphs in the ϕ 4 theory, which remarkably produces a unitary nonperturbative scattering amplitude function. Finally, we discuss how the algorithm can be further refined by including multi-particle unitarity.

Palpation utilizes the fact that solid breast tumours are stiffer than the surrounding tissue. However, cancer cells tend to soften, which may enhance their ability to squeeze through dense tissue. This apparent paradox proposes two contradicting hypotheses: either softness emerges from adaptation to the tumour’s microenvironment or soft cancer cells are already present inside a rigid primary tumour mass giving rise to cancer cell motility. We investigate primary tumour explants from patients with breast and cervix carcinomas on multiple length scales. We find that primary tumours are highly heterogeneous in their mechanical properties on all scales from the tissue level down to individual cells. This results in a broad rigidity distribution—from very stiff cells to cells softer than those found in healthy tissue—that is shifted towards a higher fraction of softer cells. Atomic-force-microscopy-based tissue rheology reveals that islands of rigid cells are surrounded by soft cells. The tracking of vital cells confirms the coexistence of jammed and unjammed areas in tumour explants. Despite the absence of a percolated backbone of stiff cells and a large fraction of unjammed, motile cells, cancer cell clusters show a heterogeneous solid behaviour with a finite elastic modulus providing mechanical stability. Cervix and breast carcinomas are highly heterogeneous in their mechanical properties across scales. This heterogeneity provides the tumour with stability and room for cell motility.

Defects are often introduced to increase the stiffness of three-dimensional materials. Evidence now suggests that the elastic modulus of two-dimensional graphene sheets can also be increased by controlled defect creation. The extraordinary strength, stiffness 1 and lightness of graphene have generated great expectations of its application in flexible electronics and as a mechanical reinforcement agent. However, the presence of lattice defects, unavoidable in sheets obtained by scalable routes, might degrade its mechanical properties 2 , 3 . Here we report a systematic study on the elastic modulus and strength of graphene with a controlled density of defects. Counter-intuitively, the in-plane Young’s modulus increases with increasing defect density up to almost twice the initial value for a vacancy content of ∼0.2%. For a higher density of vacancies, the elastic modulus decreases with defect inclusions. The initial increase in Young’s modulus is explained in terms of a dependence of the elastic coefficients on the momentum of flexural modes predicted for two-dimensional membranes 4 , 5 . In contrast, the fracture strength decreases with defect density according to standard fracture continuum models. These quantitative structure–property relationships, measured in atmospheric conditions, are of fundamental and technological relevance and provide guidance for applications in which graphene mechanics represents a disruptive improvement.

Soft particulate gels are composed of a small amount of particulate matter dispersed in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction. However, the diverse range of different functional dependencies reported experimentally has challenged efforts to identify general scaling laws. Here we reveal a hidden hierarchical organization of fractal elements that controls the viscoelastic spectrum, and which is associated with the spatial heterogeneity of the solid matrix topology. The fractal elements form the foundations of a viscoelastic master curve, constructed using large-scale three-dimensional (3D) microscopic simulations of model gels, which can be described by a recursive rheological ladder model over a range of particle volume fractions and gelation rates. The hierarchy of the fractal elements provides the missing general framework required to predict the gel elasticity and the linear viscoelastic response of these complex materials.Colloidal gels consist of particles embedded in a fluid. It is now found that a gel’s viscoelastic spectrum, relating mechanical properties and deformation frequencies, can be understood by modelling these gels as networks of fractal viscoelastic units, connected hierarchically.