We present a systematic study of temperature-driven nonaffine rearrangements in a model amorphous solid across the full thermodynamic range, from a high-temperature liquid through supercooled and subglass regimes into deeply glassy states. By subtracting the best local affine map from the particle displacements, we obtain componentwise nonaffine residuals whose exponential tails yield the characteristic length scales ${\xi }_{\mathrm{NA},x}$ and ${\xi }_{\mathrm{NA},y}$. For comparison, we compute the Van Hove self-distributions $G_x\left(u_x\right)$ and $G_y\left(u_y\right)$ of the total particle displacement and extract the corresponding Van Hove length scale ${\xi }_{\mathrm{VH}}$. A central result is that ${\xi }_{\mathrm{VH}}>{\xi }_{\mathrm{NA}}$ for all temperatures, densities, and temporal-sampling protocols studied here, and our companion analytical derivation verifies this ordering at the model level. Notably, the particle-level nonaffine field itself reveals distinct dynamical regimes: appreciable nonaffine activity persists below the thermodynamic glass-transition temperature, indicating a mechanically active viscoelastic regime, whereas deep in the glass the field becomes strongly suppressed, signaling a mechanically locked state. The near equality of ${\xi }_{\mathrm{NA},x}$ and ${\xi }_{\mathrm{NA},y}$ further shows that the thermally driven nonaffine rearrangements are isotropic. Overall, the present work provides a particle-level framework for quantifying thermal nonaffinity and for distinguishing mechanically active and mechanically locked regimes in amorphous materials.

“Every object that biology studies is a system of systems.” (François Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, we show that modular compositions generically decouple the spectral and Fiedler dimensions so that networks with identical thermodynamic exponents can exhibit parametrically different equilibration dynamics.

We establish a general quantum fluctuation-response inequality that bounds the difference in expectation values of an observable between two quantum states via the quantum relative entropy. For observables with bounded spectra, we further strengthen this result by exploiting the sub-Gaussian property and explicitly relate our bound to the sub-Gaussian norm of the observable. This allows us to derive a novel nonasymptotic bound on the sum of statistical errors in quantum hypothesis testing, which complements and can be more informative than existing bounds. We also demonstrate the versatility of our results through problems such as thermodynamic hypothesis testing and quantum speed-limits in physics and generalizability of algorithms in machine learning.

We construct families of periodic tessellations of the plane with arbitrarily high critical temperature, $T_{\mathrm{c}}$, for the classical uniform and nearest-neighbor ferromagnetic Ising model. Our approach is motivated by recently found exact bounds, which imply that large values of $T_{\mathrm{c}}$ require large values of the maximal coordination number of the lattice, $q_{\max }$. We create such lattices through iterative triangulation and derive explicit expressions for their $T_{\mathrm{c}}$. Furthermore, we show that $T_{\mathrm{c}}$ for these families scales asymptotically as $T_{\mathrm{c}}/J\sim Aln{q}_{\max }-2lnln{q}_{\max }$ with a universal prefactor $A=2/ln2$. We introduce a function $T_{\mathrm{c}}^{*}\left(q_{\max }\right)$ that we conjecture to be an upper bound on the critical temperature of any periodic tessellation of the plane. We show that the family of so-called Apollonian lattices, which are derived from the triangular lattice through iterative triangulation, saturates this bound. The lattices discussed in this work are relevant for theoretical questions of optimality in network systems and may be realized experimentally in Coherent Ising Machine or topoelectric circuits in the future.

We study critical dynamics and phase-ordering kinetics in active model B (AMB) and its minimal extension, active model $\mathrm{B}+$ ($\mathrm{AMB}+$), using deterministic simulations in two dimensions. At criticality $r_c=0$, both models display identical mean-field scaling despite nonequilibrium currents, with order-parameter decay with time as $m\left(t\right)\sim t^{-\alpha }$, with $\alpha =\frac{1}{4}$, and the dynamical exponent being $z=4$. A generalized equal-area construction yields the binodal densities and phase diagram of $\mathrm{AMB}+$. For supercritical quenches, domain size grows as $L\left(t\right)\sim t^{1/3}(1+c/lnt)$, revealing logarithmic corrections to the classic $t^{1/3}$ growth law; moreover, it is consistent with the functional renormalization group predictions for marginal activity in $d=2$. The logarithmic corrections are clearly evident in both AMB and $\mathrm{AMB}+$ in the macrophase-separated regime. However, in $\mathrm{AMB}+$, domain growth is arrested in the parameter regime where the active current opposes the formation of macroscopic clusters, leading to long-lived microphase-separated states.

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These nonstationary yet recurrent systems are described, in the long-time limit, by a non-normalizable infinite invariant density. Extreme events in such systems emerge in a joint limit where the observation time $t$ is long and the number of variables $N$ is large. We show that the resulting extreme-value statistics is controlled by the return exponent $\alpha$ and the infinite invariant measure, and therefore departs from the classical Fréchet, Gumbel, and Weibull universality classes. We illustrate the theory for weakly chaotic intermittent maps, overdamped diffusion in an asymptotically flat potential, and a stochastic model of subrecoil laser cooling, and show how measurements of extremes can be used to infer the infinite-density structure.

We study the long-time dynamics of small even perturbations of the soliton in a one-dimensional quadratic nonlinear Klein-Gordon equation. The soliton possesses both an internal mode and an unstable mode. On a codimension-one manifold of fine-tuned initial data, the instability is suppressed and the internal mode decays slowly by transferring energy into the continuum. We show that this decay and the associated nonlinear frequency shift are accurately captured by a cubic resonant approximation, with the damping rate determined by a Fermi golden rule-type coefficient. This provides a quantitative description of an irreversible energy transfer from the internal mode to dispersive radiation.

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale oscillations. The analysis and prediction of such dynamics are highly challenging, however, due to the combination of high-dimensionality, nonlinearity and delay. Here, we investigate how structural complexity and delayed feedback are associated with oscillatory dynamics in complex systems, and provide an analytical approach combining theoretical dimension reduction and data-driven prediction. We reveal that oscillations emerge from the interplay of structural complexity and delay, with reduced models uncovering their critical thresholds and showing that greater connectivity lowers the delay required for their onset. Our theory is empirically tested in an experiment on a programmable electronic circuit, where oscillations are observed once structural complexity and feedback delay exceeded the critical thresholds predicted by our theory. Finally, we deploy a reservoir computing pipeline to accurately predict the onset of oscillations directly from time-series data. Our findings deepen understanding of oscillatory regulation and provide useful insights into predicting dynamics in complex networks.

Multifractal formalisms characterize complex interactions across scales in natural and behavioral systems. They capture an excess form of power-law scaling beyond the single power-law relationship between fluctuation and scale in monofractality. Because monofractality fits neatly within the general linear model via fractional integration, multifractality can provide evidence of nonlinear correlations across scales. That is, multifractality might reflect variability exceeding the correlations articulable by the best linear model. The classic expectation under nonlinear correlations across scales is that multifractal spectra for the original series, $\mathrm{\Delta }{\alpha }_{\text{orig}}$, will show statistically significantly greater width than multifractal spectrum widths for linear surrogates, $\mathrm{\Delta }{\alpha }_{\text{surr}}$, yielding large positive $t$ statistics, $t_{\text{MF}}$. Thus, $\mathrm{\Delta }{\alpha }_{\text{orig}}\gg \mathrm{\Delta }{\alpha }_{\text{surr}}$ supports the conclusion of nonlinear correlations across scales consistent with multiplicative cascade dynamics. By contrast, the interpretation of sublinear multifractality—$\mathrm{\Delta }{\alpha }_{\text{orig}}\ll \mathrm{\Delta }{\alpha }_{\text{surr}}$, and hence negative $t_{\text{MF}}$—has been less clear, including whether it reflects or rules out nonlinear correlations across scales consistent with multiplicative cascades. We identify five distinct mechanisms by which random multiplicative cascades and related linear processes can in principle produce nonlinear correlations with significantly negative $t_{\text{MF}}$, that is, $\mathrm{\Delta }{\alpha }_{\text{orig}}\ll \mathrm{\Delta }{\alpha }_{\text{surr}}$, and we characterize which mechanisms do so robustly under stringent surrogate-testing protocols. We show how various nonmultiplicative constraints on the nonlinear correlations across scales of a multiplicative cascade might produce sublinear multifractality. These constraints may serve as analogues to the physical limits characteristic of homeostatic regulation and feedback control in complex systems. Altogether, this framework builds expectations for how cascade dynamics collaborate with regulatory processes in physics, biology, and engineered systems.

Using tools from network theory, we analyze the organization of a MYH9-oriented druglike library in chemical space using a multidescriptor framework. The dataset is drawn from ZINC, a publicly available database of commercially accessible compounds curated for virtual screening and drug discovery. Starting from 6004 molecules, preprocessing yields 5000 structurally valid and descriptor-complete compounds. Similarity is defined via Tanimoto distance on Morgan fingerprints and single-descriptor distances for xLogP, HBD, HBA, molecular weight, and rotatable bonds. For each representation we construct $k$-nearest-neighbor networks and identify communities using the Louvain–Leiden algorithm. All networks exhibit highly significant modularity ($Q=0.91-0.99$) relative to degree-preserving null models, demonstrating pronounced nonrandom chemical organization across descriptors. Cross-descriptor robustness is quantified through a coclustering matrix over $1.25\times {10}^7$ molecular pairs, measuring how consistently compound pairs co-occur within the same community across descriptor-specific networks. Although most pairs show limited agreement, a sparse high-consensus core emerges, highlighting the complementarity of the descriptors. Minimum spanning trees derived from structural and consensus similarities reveal distinct backbone topologies: a scaffold-driven, sparse structure versus a compact, hub-rich consensus network. Betweenness centrality on these backbones identifies compounds that are both structurally central and descriptor-balanced. These results provide a statistically validated network representation of chemical space and a principled strategy to extract consensus-stable compounds for downstream screening.

Ultrafast oscillations (UFOs) are brief bursts of high-frequency (2–8 kHz) activity recorded using depth electrodes in epileptic brain tissue. While reliably detected at small scales using microelectrodes, UFOs have thus far likely not been observed at larger scales using macroelectrodes. Here we show that faint echoes of these bursting patterns can be detected in macroelectrode signals using a model of cross-scale propagation. To model this cross-scale effect, we extend the classical damped wave equation to include an explicit scale coordinate governed by the dilation operator. We then use Green's functions to obtain an expression for the spectral echo expected at the macroelectrode scale. This echo takes the form of a carrier envelope modulated by the temporal structure of the original microscale bursting event. We test the predicted signature echo pattern in human intracranial recordings from eleven epilepsy patients implanted with both micro- and macroelectrodes. Statistically significant echoes are confirmed in two out of eleven patients, appearing in 2% of all tested micro-macro pairs.

The theory of using transducer arrays for the contactless and stable manipulation of Rayleigh objects ($ka\ll 1$, where $k$ is the wave number and $a$ is the averaged radius of object) is well established, whereas retrieving the transducer parameters required for the stable and dynamic manipulation of Mie objects ($1<ka<10$) remains a significant challenge. Here, we develop an analytical model for the stable trapping and transportation of Mie (axisymmetric) objects by directly presetting the desired radiation force and torque, with appropriate stability constraints incorporated to ensure dynamical stability. Specifically, acoustic contributions from multiple transducers are superimposed using the translation addition theorem. The geometric features of the object are mapped onto a sphere through a conformal transformation, allowing the acoustic radiation force and torque to be expressed in terms of partial-wave expansions. The radiation force is further reformulated as a position-dependent function with the help of the addition theorem, enabling an analytical derivation of its partial derivatives. These derivatives are then used to express the Lyapunov stability conditions in closed form. Finally, a system of nonlinear inequality governing equations, incorporating the radiation force, torque, and stability constraints, is constructed to retrieve a set of transducer parameters capable of stably trapping a Mie object at specified spatial positions. At these positions, the partial derivatives of the radiation forces (i.e., the stability) are negative, implying the presence of a restoring mechanism that stabilizes the object at the target positions. The analytical predictions for both the radiation force and its partial derivatives show well agreement with the finite-element simulations. In practice, by switching among the retrieved sets of transducer parameters corresponding to different trapping positions, we demonstrate that a Mie object with a radius of $10\mathrm{mm}$ (with $ka\approx 7.39$) can be stably transported over a distance equivalent to one transducer radius, i.e., $5\mathrm{mm}$ with $kd/2\approx 3.69$.

Plasma spectroscopy is a fundamental tool for diagnosing laboratory and astrophysical plasmas. Accurate interpretation of spectra depends upon precise modeling and comprehension of Stark broadening and other mechanisms affecting spectral lines. In this context, computer simulations have emerged as valuable tools, offering idealized experiments with well-defined conditions. Molecular dynamics simulations, in particular, excel at replicating the particle interactions within the plasma and their impact on the state of a radiating atom or ion. However, these simulations present challenges in tracking electron capture processes, since setting an unambiguous criterion to distinguish between bound and free electrons is not trivial. In this paper we introduce an algorithm that, within a classical framework, precisely identifies the scenario in which an electron is captured by an ion and then follows a stable orbit around it. The algorithm's applicability extends to emitters with charges $Z\ge 1$. The procedure enables the correct identification of valid time histories of the electric microfield perturbing the emitting ion, which will be used for subsequent line shape calculations. The ionization balance results obtained from the application of this algorithm are compared with an additional method based on the potential energy of the particles in the simulations and with atomic kinetic simulations. For both methods, we find good agreement, therefore validating the use of this approach.

We present calculations of diffusion coefficients in grain boundaries (GBs) in Yukawa crystals for astrophysics. Our methods follow from our recent work calculating diffusion coefficients in perfect body-centered cubic crystals. These diffusion coefficients show only a weak dependence on the crystal orientations at the GB and are consistent with those expected for a supercooled liquid scaled down by 1–2 orders of magnitude. We argue that the local disorder at the GB produces a landscape of potential barriers similar to that of an amorphous liquid thin film, significantly reducing activation barriers to diffusive hops relative to the bulk solid. This also introduces a screening dependence, such that boundary diffusion does not exhibit the same universality as the bulk crystal. These diffusion coefficients suggest that GBs may be a dominant source of plastic dissipation in neutron star crusts.

Membrane tethers are long, slender membrane tubes that transport biological cargo (proteins and viruses) and engineered materials (particles and drugs) in organelles, vesicles, and cells. Nanoparticles with enhanced bioavailability and reduced toxicity are attracting great attention in nanomedicine for their ability to target membrane tethers, particularly tunneling nanotubes, which share similar structures and functions with membrane tethers. Nevertheless, the molecular mechanisms that control the cooperative wrapping of nanoparticles within and on membrane tethers are not well understood. Our study aims to map the wrapping behavior and the associated membrane deformation for spherical nanoparticles entering and exiting membrane tethers (modeling both out-to-in and in-to-out wrapping). By integrating continuum membrane models and finite-element analysis, we systematically quantify how the equilibrium shapes, obtained via energy minimization, are governed by membrane spontaneous curvature, nanoparticle size, and interparticle distance. For out-to-in wrapping, the discontinuous binding-envelopment transitions between the nonwrapped and the complete-wrapped states are facilitated by long interparticle distances and small particle sizes, for which both the adhesion strengths and the energy barriers are low. For negative spontaneous curvature, however, the adhesion strengths are low while the energy barriers are high. The deformations of the contact lines that separate the membrane into the bound and unbound segments are larger for the shortest or the longest interparticle distances. For in-to-out wrapping, the stable partial-wrapped states are identified. In particular, the short interparticle distances lead to the discontinuous transitions between the shallow-wrapped and the deep-wrapped states. Negative spontaneous curvature, short interparticle distances, and large particle sizes favor the stable partial-wrapped states. Instead of aggregating into compact linear chains along the membrane tethers, the nanoparticles remain separated at well-defined lowest-energy positions. The deformations of the contact lines are slightly larger than those for out-to-in wrapping. The competition between the local curvature and the spontaneous curvature of the membrane gives rise to rich wrapping diagrams, and our numerically determined adhesion strengths are in agreement with the theoretical predictions. Our findings provide important insights into tether-nanoparticle interactions and offer guidelines for the design of functional nanomedicines.

We numerically investigate percolation of independent frictionless glued-sphere rodlike particles under gravity through a disordered static bed of larger spheres. We identify two distinct regimes: a trapping regime, where rods stop after percolating a limited distance in the bed and a passing regime, where rods percolate continuously with constant mean velocity. The transition between these regimes is governed by the length of the rod and the geometrical trapping threshold for spherical particles based on the rod diameter and the minimum pore throat diameter defined by three touching large spheres. The percolation velocity for all rod geometries, including the single sphere limit, collapses onto a single curve when scaled with the gravitational acceleration and the bed sphere diameter. The results also demonstrate that short rods percolate nearly twice as fast as long rods due to the geometric constraints associated with the disordered pore structure of the static bed. Consequently, long rods are more susceptible to trapping via specific contact configurations with the bed spheres, which differ from those for short rods. These results reveal how shape anisotropy introduces dynamical constraints and thresholds in granular percolation, with implications for predicting segregation in mixtures of nonspherical particles.

We present an effective potential that allows quantum thermal expectation values of a position-dependent observable to be estimated as a classical ensemble average of the corresponding function. We follow the approach of Feynman and Hibbs but perform the mean-field treatment of quantum fluctuations about the path starting point rather than the path centroid. Furthermore, rather than performing a full variational optimization of the potential, we explore approximate functional forms that yield numerical robustness. The resulting closed-form potential is exact in the classical and harmonic limits; benchmarks against exact position distributions for one-dimensional quartic, Morse, and double-well potentials show good agreement for potentials with harmonic support.