Enumerating low-frequency nonphononic vibrations in computer glasses.

In addition to Goldstone phonons that generically emerge in the low-frequency vibrational spectrum of any solid, crystalline or glassy, structural glasses also feature other low-frequency vibrational modes. The nature and statistical properties of these modes-often termed "excess modes"-have been the subject of decades-long investigation. Studying them, even using well-controlled computer glasses, has proven challenging due to strong spatial hybridization effects between phononic and nonphononic excitations, which hinder quantitative analyses of the nonphononic contribution DG(ω) to the total spectrum D(ω), per frequency ω. Here, using recent advances indicating that DG(ω)=D(ω)-DD(ω), where DD(ω) is Debye's spectrum of phonons, we present a simple and straightforward scheme to enumerate nonphononic modes in computer glasses. Our analysis establishes that nonphononic modes in computer glasses indeed make an additive contribution to the total spectrum, including in the presence of strong hybridizations. Moreover, it cleanly reveals the universal DG(ω)∼ω4 tail of the nonphononic spectrum, and opens the way for related analyses of experimental spectra of glasses.

Cellular orientational fluctuations, rotational diffusion and nematic order under periodic driving.

The ability of living cells to sense the physical properties of their microenvironment and to respond to dynamic forces acting on them plays a central role in regulating their structure, function and fate. Of particular importance is the cellular sensitivity and response to periodic driving forces in noisy environments, encountered in vital physiological conditions such as heart beating, blood vessel pulsation and breathing. Here, we first test and validate two predictions of a mean-field theory of cellular reorientation under periodic driving, which combines the minimization of cellular anisotropic elastic energy with active remodeling forces. We then extend the mean-field theory to include uncorrelated, additive nonequilibrium fluctuations, and show that the theory quantitatively agrees with the experimentally observed stationary probability distributions of the cell body orientation, under a range of biaxial periodic driving forces. The fluctuations theory allows the extraction of the dimensionless active noise amplitude of various cell types, and consequently their rotational diffusion coefficient. We then focus on intra-cellular nematic order, i.e. on orientational fluctuations of actin stress fibers around the cell body orientation, and show experimentally that intra-cellular nematic order increases with both the magnitude of the driving forces and the biaxiality strain ratio. These results are semi-quantitatively explained by applying the same cell body fluctuations theory to orientationally correlated actin stress fiber domains. Finally, an estimate of the energy scale of cellular orientational fluctuations for one cell type is shown to be about six order of magnitude larger than the thermal energy at room temperature. The implications of our findings, which make the quantitative analysis of cell mechanosensitivity more accessible, are discussed.

Internally Stressed and Positionally Disordered Minimal Complexes Yield Glasslike Nonphononic Excitations.

Glasses, unlike their crystalline counterparts, exhibit low-frequency nonphononic excitations whose frequencies ω follow a universal D(ω)∼ω^{4} density of states. The process of glass formation generates positional disorder intertwined with mechanical frustration, posing fundamental challenges in understanding the origins of glassy nonphononic excitations. Here we suggest that minimal complexes-mechanically frustrated and positionally disordered local structures-embody the minimal physical ingredients needed to generate glasslike excitations. We investigate the individual effects of mechanical frustration and positional disorder on the vibrational spectrum of isolated minimal complexes, and demonstrate that ensembles of marginally stable minimal complexes yield D(ω)∼ω^{4}. Furthermore, glasslike excitations emerge by embedding a single minimal complex within a perfect lattice. Consequently, minimal complexes offer a conceptual framework to understand glasslike excitations from first principles, as well as a practical computational method for introducing them into solids.

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling.

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k†, where phonons are no longer quantized into bands. For k < k†, finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k†, we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼k¯d+1 (¯d is the spatial dimension) and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼k¯d+1 log(k0/k) emerges (k0 > k† is a characteristic wavenumber). Our results suggest that macroscopic glasses-and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations-exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.

Tissue-Level Mechanosensitivity: Predicting and Controlling the Orientation of 3D Vascular Networks.

Understanding the mechanosensitivity of tissues is a fundamentally important problem having far-reaching implications for tissue engineering. Here we study vascular networks formed by a coculture of fibroblasts and endothelial cells embedded in three-dimensional biomaterials experiencing external, physiologically relevant forces. We show that cyclic stretching of the biomaterial orients the newly formed network perpendicular to the stretching direction, independent of the geometric aspect ratio of the biomaterial's sample. A two-dimensional theory explains this observation in terms of the network's stored elastic energy if the cell-embedded biomaterial features a vanishing effective Poisson's ratio, which we directly verify. We further show that under a static stretch, vascular networks orient parallel to the stretching direction due to force-induced anisotropy of the biomaterial polymer network. Finally, static stretching followed by cyclic stretching reveals a competition between the two mechanosensitive mechanisms. These results demonstrate tissue-level mechanosensitivity and constitute an important step toward developing enhanced tissue repair capabilities using well-oriented vascular networks.

An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules.

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.

Self-driven configurational dynamics in frustrated spring-mass systems.

Various physical systems relax mechanical frustration through configurational rearrangements. We examine such rearrangements via Hamiltonian dynamics of simple internally stressed harmonic four-mass systems. We demonstrate theoretically and numerically how mechanical frustration controls the underlying potential energy landscape. Then, we examine the harmonic four-mass systems' Hamiltonian dynamics and relate the onset of chaotic motion to self-driven rearrangements. We show such configurational dynamics may occur without strong precursors, rendering such dynamics seemingly spontaneous.

Characteristic energy scales of active fluctuations in adherent cells.

Cell-matrix and cell-cell adhesion play important roles in a wide variety of physiological processes, from the single-cell level to the large scale, multicellular organization of tissues. Cells actively apply forces to their environment, either extracellular matrix or neighboring cells, as well as sense its biophysical properties. The fluctuations associated with these active processes occur on an energy scale much larger than that of ordinary thermal equilibrium fluctuations, yet their statistical properties and characteristic scales are not fully understood. Here, we compare measurements of the energy scale of active cellular fluctuations-an effective cellular temperature-in four different biophysical settings, involving both single-cell and cell-aggregate experiments under various control conditions, different cell types, and various biophysical observables. The results indicate that a similar energy scale of active fluctuations might characterize the same cell type in different settings, though it may vary among different cell types, being approximately six to eight orders of magnitude larger than the ordinary thermal energy at room temperature. These findings call for extracting the energy scale of active fluctuations over a broader range of cell types, experimental settings, and biophysical observables and for understanding the biophysical origin and significance of such cellular energy scales.

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals, and boundary effects.

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e., they feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that, in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce the fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both two and three dimensions. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.